From 75c953a1d50cd707e2afe4dd46888056a71eb501 Mon Sep 17 00:00:00 2001
From: Abigail <abigail@abigail.be>
Date: Mon, 19 Apr 2021 13:49:21 +0200
Subject: README.md for week 109

---
 challenge-109/abigail/README.md | 105 +++++++++++++++++++---------------------
 1 file changed, 51 insertions(+), 54 deletions(-)

diff --git a/challenge-109/abigail/README.md b/challenge-109/abigail/README.md
index 32dc7d1d9d..860949d790 100644
--- a/challenge-109/abigail/README.md
+++ b/challenge-109/abigail/README.md
@@ -1,70 +1,67 @@
 # Solutions by Asbigail
-## [Locate Memory](https://perlweeklychallenge.org/blog/perl-weekly-challenge-108/#TASK1)
+## [Chowla Numbers](https://perlweeklychallenge.org/blog/perl-weekly-challenge-109/#TASK1)
 
-Write a script to declare a variable or constant and print it's
-location in the memory.
+Write a script to generate first 20 Chowla Numbers, named after,
+Sarvadaman D. S. Chowla, a London born Indian American mathematician.
+It is defined as:
+
+    C(n) = (sum of divisors of n) - 1 - n
+
+### Output
+
+    0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
 
 ### Solutions
-* [C](c/ch-1.c)
-* [Fortran](fortran/ch-1.f90)
-* [Go](go/ch-1.go)
-* [Pascal](pascal/ch-1.p)
-* [Perl](perl/ch-1.pl)
-* [Python](python/ch-1.py)
-* [R](r/ch-1.r)
-* [Ruby](ruby/ch-1.rb)
 
 ### Blog
-[Locate Memory](https://abigail.github.io/HTML/Perl-Weekly-Challenge/week-108-1.html)
 
 
-## [Bell Numbers](https://perlweeklychallenge.org/blog/perl-weekly-challenge-108/#TASK2)
+## [Four Squares Puzzle](https://perlweeklychallenge.org/blog/perl-weekly-challenge-109/#TASK2)
+
+You are given four squares as below with numbers named `a`, `b`,
+`c`, `d`, `e`, `f`, `g`.
+
+              (1)                    (3)
+        ╔══════════════╗      ╔══════════════╗
+        ║              ║      ║              ║
+        ║      a       ║      ║      e       ║
+        ║              ║ (2)  ║              ║  (4)
+        ║          ┌───╫──────╫───┐      ┌───╫─────────┐
+        ║          │   ║      ║   │      │   ║         │
+        ║          │ b ║      ║ d │      │ f ║         │
+        ║          │   ║      ║   │      │   ║         │
+        ║          │   ║      ║   │      │   ║         │
+        ╚══════════╪═══╝      ╚═══╪══════╪═══╝         │
+                   │       c      │      │      g      │
+                   │              │      │             │
+                   │              │      │             │
+                   └──────────────┘      └─────────────┘
 
-Write a script to display top 10 Bell Numbers. Please refer to
-[wikipedia page](https://en.wikipedia.org/wiki/Bell_number) for
-more informations.
+Write a script to place the given unique numbers in the square box
+so that sum of numbers in each box is the same.
 
 ### Example
-* `B_0 = 1`, as you can only have one partition of zero element set
-* `B_1 = 1`, as you can only have one partition of one element set {a}.
-* `B_2 = 2`, `{a}{b}`, `{a,b}`.
-* `B_3 = 5`, `{a}{b}{c}`, `{a,b}{c}`, `{a}{b,c}`, `{a,c}{b}`, `{a,b,c}`.
-* `B_4 = 15`, `{a}{b}{c}{d}`, `{a,b,c,d}`, `{a,b}{c,d}`, `{a,c}{b,d}`,
-              `{a,d}{b,c}`, `{a,b}{c}{d}`, `{a,c}{b}{d}`, `{a,d}{b}{c}`,
-              `{b,c}{a}{d}`, `{b,d}{a}{c}`, `{c,d}{a}{b}`, `{a}{b,c,d}`,
-              `{b}{a,c,d}`, `{c}{a,b,d}`, `{d}{a,b,c}`
+
+~~~~
+Input: 1,2,3,4,5,6,7
+
+Output:
+
+    a = 6
+    b = 4
+    c = 1
+    d = 5
+    e = 2
+    f = 3
+    g = 7
+
+    Box 1: a + b = 6 + 4 = 10
+    Box 2: b + c + d = 4 + 1 + 5 = 10
+    Box 3: d + e + f = 5 + 2 + 3 = 10
+    Box 4: f + g = 3 + 7 = 10
+~~~~
 
 ### Solutions
-* [AWK](awk/ch-2.awk)
-* [Bash](bash/ch-2.sh)
-* [BASIC](basic/ch-2.bas)
-* [bc](bc/ch-2.bc)
-* [Befunge-93][befunge-93/ch-2.bf93]
-* [C](c/ch-2.c)
-* [Cobol](cobol/ch-2.cb)
-* [Csh](csh/ch-2.csh)
-* [Erlang](erlang/ch-2.erl)
-* [Forth](forth/ch-2.fs)
-* [Fortran](fortran/ch-2.f90)
-* [Go](go/ch-2.go)
-* [Java](java/ch-2.java)
-* [Lua](lua/ch-2.lua)
-* [m4](m4/ch-2.m4)
-* [Node.js](node/ch-2.js)
-* [Ocaml](ocaml/ch-2.ml)
-* [Pascal](pascal/ch-2.p)
-* [Perl](perl/ch-2.pl)
-* [PHP](php/ch-2.php)
-* [PostScript](postscript/ch-2.ps)
-* [Python](python/ch-2.py)
-* [R](r/ch-2.r)
-* [Rexx](rexx/ch-2.rexx)
-* [Ruby](ruby/ch-2.rb)
-* [Scheme](scheme/ch-2.scm)
-* [sed](sed/ch-2.sed)
-* [SQL](sql/ch-2.sql)
-* [Tcl](tcl/ch-2.tcl)
 
 ### Blog
-[Bell Numbers](https://abigail.github.io/HTML/Perl-Weekly-Challenge/week-108-2.html)
 
-- 
cgit 


From 610ff9605ec7b308051a8f04f9b21d6f4060a8cd Mon Sep 17 00:00:00 2001
From: Abigail <abigail@abigail.be>
Date: Mon, 19 Apr 2021 20:16:47 +0200
Subject: Solutions in 29 languages for week 109, part 1.

---
 challenge-109/abigail/README.md            | 29 ++++++++++++++++
 challenge-109/abigail/awk/ch-1.awk         | 37 +++++++++++++++++++++
 challenge-109/abigail/bash/ch-1.sh         | 35 ++++++++++++++++++++
 challenge-109/abigail/basic/ch-1.bas       |  9 +++++
 challenge-109/abigail/bc/ch-1.bc           | 10 ++++++
 challenge-109/abigail/befunge-93/ch-1.bf93 |  2 ++
 challenge-109/abigail/c/ch-1.c             | 53 ++++++++++++++++++++++++++++++
 challenge-109/abigail/cobol/ch-1.cb        | 14 ++++++++
 challenge-109/abigail/csh/ch-1.csh         | 11 +++++++
 challenge-109/abigail/erlang/ch-1.erl      | 15 +++++++++
 challenge-109/abigail/forth/ch-1.fs        |  5 +++
 challenge-109/abigail/fortran/ch-1.f90     | 12 +++++++
 challenge-109/abigail/go/ch-1.go           | 15 +++++++++
 challenge-109/abigail/java/ch-1.java       | 13 ++++++++
 challenge-109/abigail/lua/ch-1.lua         | 43 ++++++++++++++++++++++++
 challenge-109/abigail/m4/ch-1.m4           |  1 +
 challenge-109/abigail/node/ch-1.js         | 45 +++++++++++++++++++++++++
 challenge-109/abigail/ocaml/ch-1.ml        |  9 +++++
 challenge-109/abigail/pascal/ch-1.p        | 13 ++++++++
 challenge-109/abigail/perl/ch-1.pl         | 51 ++++++++++++++++++++++++++++
 challenge-109/abigail/php/ch-1.php         | 11 +++++++
 challenge-109/abigail/postscript/ch-1.ps   | 10 ++++++
 challenge-109/abigail/python/ch-1.py       | 39 ++++++++++++++++++++++
 challenge-109/abigail/r/ch-1.r             |  9 +++++
 challenge-109/abigail/rexx/ch-1.rexx       |  9 +++++
 challenge-109/abigail/ruby/ch-1.rb         | 44 +++++++++++++++++++++++++
 challenge-109/abigail/scheme/ch-1.scm      |  9 +++++
 challenge-109/abigail/sed/ch-1.sed         | 12 +++++++
 challenge-109/abigail/sql/ch-1.sql         |  9 +++++
 challenge-109/abigail/t/ctest.ini          | 35 ++++++++++++++++++++
 challenge-109/abigail/t/input-1-1          |  1 +
 challenge-109/abigail/t/input-1-2          |  0
 challenge-109/abigail/t/input-1-3          |  0
 challenge-109/abigail/t/input-1-4          |  0
 challenge-109/abigail/t/output-1-1.exp     |  1 +
 challenge-109/abigail/t/output-1-2.exp     |  1 +
 challenge-109/abigail/t/output-1-3.exp     |  1 +
 challenge-109/abigail/t/output-1-4.exp     |  1 +
 challenge-109/abigail/tcl/ch-1.tcl         |  9 +++++
 39 files changed, 623 insertions(+)
 create mode 100644 challenge-109/abigail/awk/ch-1.awk
 create mode 100644 challenge-109/abigail/bash/ch-1.sh
 create mode 100644 challenge-109/abigail/basic/ch-1.bas
 create mode 100644 challenge-109/abigail/bc/ch-1.bc
 create mode 100644 challenge-109/abigail/befunge-93/ch-1.bf93
 create mode 100644 challenge-109/abigail/c/ch-1.c
 create mode 100644 challenge-109/abigail/cobol/ch-1.cb
 create mode 100644 challenge-109/abigail/csh/ch-1.csh
 create mode 100644 challenge-109/abigail/erlang/ch-1.erl
 create mode 100644 challenge-109/abigail/forth/ch-1.fs
 create mode 100644 challenge-109/abigail/fortran/ch-1.f90
 create mode 100644 challenge-109/abigail/go/ch-1.go
 create mode 100644 challenge-109/abigail/java/ch-1.java
 create mode 100644 challenge-109/abigail/lua/ch-1.lua
 create mode 100644 challenge-109/abigail/m4/ch-1.m4
 create mode 100644 challenge-109/abigail/node/ch-1.js
 create mode 100644 challenge-109/abigail/ocaml/ch-1.ml
 create mode 100644 challenge-109/abigail/pascal/ch-1.p
 create mode 100644 challenge-109/abigail/perl/ch-1.pl
 create mode 100644 challenge-109/abigail/php/ch-1.php
 create mode 100644 challenge-109/abigail/postscript/ch-1.ps
 create mode 100644 challenge-109/abigail/python/ch-1.py
 create mode 100644 challenge-109/abigail/r/ch-1.r
 create mode 100644 challenge-109/abigail/rexx/ch-1.rexx
 create mode 100644 challenge-109/abigail/ruby/ch-1.rb
 create mode 100644 challenge-109/abigail/scheme/ch-1.scm
 create mode 100644 challenge-109/abigail/sed/ch-1.sed
 create mode 100644 challenge-109/abigail/sql/ch-1.sql
 create mode 100644 challenge-109/abigail/t/ctest.ini
 create mode 100644 challenge-109/abigail/t/input-1-1
 create mode 100644 challenge-109/abigail/t/input-1-2
 create mode 100644 challenge-109/abigail/t/input-1-3
 create mode 100644 challenge-109/abigail/t/input-1-4
 create mode 100644 challenge-109/abigail/t/output-1-1.exp
 create mode 100644 challenge-109/abigail/t/output-1-2.exp
 create mode 100644 challenge-109/abigail/t/output-1-3.exp
 create mode 100644 challenge-109/abigail/t/output-1-4.exp
 create mode 100644 challenge-109/abigail/tcl/ch-1.tcl

diff --git a/challenge-109/abigail/README.md b/challenge-109/abigail/README.md
index 860949d790..57a25f7869 100644
--- a/challenge-109/abigail/README.md
+++ b/challenge-109/abigail/README.md
@@ -12,6 +12,35 @@ It is defined as:
     0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
 
 ### Solutions
+* [AWK](awk/ch-1.awk)
+* [Bash](bash/ch-1.sh)
+* [BASIC](basic/ch-1.bas)
+* [bc](bc/ch-1.bc)
+* [Befunge-93][befunge-93/ch-1.bf93]
+* [C](c/ch-1.c)
+* [Cobol](cobol/ch-1.cb)
+* [Csh](csh/ch-1.csh)
+* [Erlang](erlang/ch-1.erl)
+* [Forth](forth/ch-1.fs)
+* [Fortran](fortran/ch-1.f90)
+* [Go](go/ch-1.go)
+* [Java](java/ch-1.java)
+* [Lua](lua/ch-1.lua)
+* [m4](m4/ch-1.m4)
+* [Node.js](node/ch-1.js)
+* [Ocaml](ocaml/ch-1.ml)
+* [Pascal](pascal/ch-1.p)
+* [Perl](perl/ch-1.pl)
+* [PHP](php/ch-1.php)
+* [PostScript](postscript/ch-1.ps)
+* [Python](python/ch-1.py)
+* [R](r/ch-1.r)
+* [Rexx](rexx/ch-1.rexx)
+* [Ruby](ruby/ch-1.rb)
+* [Scheme](scheme/ch-1.scm)
+* [sed](sed/ch-1.sed)
+* [SQL](sql/ch-1.sql)
+* [Tcl](tcl/ch-1.tcl)
 
 ### Blog
 
diff --git a/challenge-109/abigail/awk/ch-1.awk b/challenge-109/abigail/awk/ch-1.awk
new file mode 100644
index 0000000000..6b889ae3a0
--- /dev/null
+++ b/challenge-109/abigail/awk/ch-1.awk
@@ -0,0 +1,37 @@
+#!/usr/bin/awk
+
+#
+# See ../README.md
+#
+
+#
+# Run as: awk -f ch-1.awk [plain | compute]
+#
+
+function divisor_sum (n, i) {
+    sum = 0
+    for (i = 2; i < n; i ++) {
+        if (n % i == 0) {
+            sum += i
+        }
+    }
+    return (sum)
+}
+
+BEGIN {
+    COUNT = 20
+    if (!ARGV [1] || ARGV [1] != "compute") {
+        print "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21"
+    }
+    else {
+        for (i = 1; i <= COUNT; i ++) {
+            if (i > 1) {
+                printf ", ";
+            }
+            printf "%d", divisor_sum(i)
+        }
+        printf "\n";
+    }
+    delete ARGV
+}
+
diff --git a/challenge-109/abigail/bash/ch-1.sh b/challenge-109/abigail/bash/ch-1.sh
new file mode 100644
index 0000000000..d4eec1f2d9
--- /dev/null
+++ b/challenge-109/abigail/bash/ch-1.sh
@@ -0,0 +1,35 @@
+#!/bin/sh
+
+#
+# See ../README.md
+#
+
+#
+# Run as: bash ch-1.sh [plain | compute]
+#
+
+set -f
+
+COUNT=20
+
+function divisor_sum () {
+    sum=0
+    local i
+    for ((i = 2; i < n; i ++))
+    do  if   ((n % i == 0))
+        then ((sum += i))
+        fi
+    done
+}
+
+if   [ "X$1" != "Xcompute" ]
+then echo "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21"
+else for ((n = 1; n <= COUNT; n ++))
+     do  if   ((n > 1))
+         then printf ", "
+         fi
+         divisor_sum $n
+         printf $sum
+     done
+     echo ""
+fi
diff --git a/challenge-109/abigail/basic/ch-1.bas b/challenge-109/abigail/basic/ch-1.bas
new file mode 100644
index 0000000000..2af64900eb
--- /dev/null
+++ b/challenge-109/abigail/basic/ch-1.bas
@@ -0,0 +1,9 @@
+010 REM 
+020 REM See ../README.md
+030 REM 
+
+040 REM 
+050 REM Run as: basic ch-1.bas
+060 REM 
+
+100 PRINT "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21"
diff --git a/challenge-109/abigail/bc/ch-1.bc b/challenge-109/abigail/bc/ch-1.bc
new file mode 100644
index 0000000000..4c739fdd23
--- /dev/null
+++ b/challenge-109/abigail/bc/ch-1.bc
@@ -0,0 +1,10 @@
+#
+# See ../README.md
+#
+
+#
+# Run as: bc ch-1.bc
+#
+"0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
+"
+quit
diff --git a/challenge-109/abigail/befunge-93/ch-1.bf93 b/challenge-109/abigail/befunge-93/ch-1.bf93
new file mode 100644
index 0000000000..e5f947956f
--- /dev/null
+++ b/challenge-109/abigail/befunge-93/ch-1.bf93
@@ -0,0 +1,2 @@
+< v,_@#:<   "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21" +55
+  >     ^
diff --git a/challenge-109/abigail/c/ch-1.c b/challenge-109/abigail/c/ch-1.c
new file mode 100644
index 0000000000..e6716c148a
--- /dev/null
+++ b/challenge-109/abigail/c/ch-1.c
@@ -0,0 +1,53 @@
+# include <stdlib.h>
+# include <stdio.h>
+# include <string.h>
+
+/*
+ * See ../README.md
+ */
+
+/*
+ * Run as: cc -o ch-1.o ch-1.c; ./ch-1.o [plain | compute]
+ */
+
+# define PLAIN    0
+# define COMPUTE  1
+
+# define COUNT   20
+
+typedef int number;  /* Change if we want large numbers */
+# define fmt "%d"
+
+number divisor_sum (number n) {
+    number sum = 0;
+    for (number i = 2; i < n; i ++) {
+        if (!(n % i)) {
+            sum += i;
+        }
+    }
+    return (sum);
+}
+
+int main (int argc, char * argv []) {
+    int type = PLAIN;
+    if (argc > 1) {
+        if (strncmp (argv [1], "compute", 8) == 0) {
+            type = COMPUTE;
+        }
+    }
+
+    if (type == PLAIN) {
+        printf ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, ");
+        printf ("0, 15, 0, 9, 8, 14, 0, 20, 0, 21\n");
+    }
+    if (type == COMPUTE) {
+        for (number i = 1; i <= COUNT; i ++) {
+            if (i != 1) {
+                printf (", ");
+            }
+            printf (fmt, divisor_sum (i));
+        }
+        printf ("\n");
+    }
+    exit (0);
+}
diff --git a/challenge-109/abigail/cobol/ch-1.cb b/challenge-109/abigail/cobol/ch-1.cb
new file mode 100644
index 0000000000..06a7dcece4
--- /dev/null
+++ b/challenge-109/abigail/cobol/ch-1.cb
@@ -0,0 +1,14 @@
+IDENTIFICATION DIVISION.
+PROGRAM-ID. XXX.
+
+*>
+*> See ../README.md
+*>
+
+*>
+*> Run as: cobc -xF -o ch-1.o ch-1.cb; ./ch-1.o
+*>
+
+PROCEDURE DIVISION.
+    DISPLAY "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21".
+    STOP RUN.
diff --git a/challenge-109/abigail/csh/ch-1.csh b/challenge-109/abigail/csh/ch-1.csh
new file mode 100644
index 0000000000..9a612ffab8
--- /dev/null
+++ b/challenge-109/abigail/csh/ch-1.csh
@@ -0,0 +1,11 @@
+#!/bin/csh
+
+#
+# See ../README.md
+#
+
+#
+# Run as: csh ch-1.csh
+#
+
+echo "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21"
diff --git a/challenge-109/abigail/erlang/ch-1.erl b/challenge-109/abigail/erlang/ch-1.erl
new file mode 100644
index 0000000000..c0b458def9
--- /dev/null
+++ b/challenge-109/abigail/erlang/ch-1.erl
@@ -0,0 +1,15 @@
+%
+% See ../README.md
+%
+
+%
+% Run as: ln ch-1.erl ch1.erl
+%         erl -compile ch1
+%         erl -noshell -s ch1 main -s init stop
+%
+
+-module (ch1).
+-export ([main/0]).
+
+main () ->
+    io:fwrite ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21\n").
diff --git a/challenge-109/abigail/forth/ch-1.fs b/challenge-109/abigail/forth/ch-1.fs
new file mode 100644
index 0000000000..8a88bf0b28
--- /dev/null
+++ b/challenge-109/abigail/forth/ch-1.fs
@@ -0,0 +1,5 @@
+\
+\ See ../README.md
+\
+
+.( 0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21)
diff --git a/challenge-109/abigail/fortran/ch-1.f90 b/challenge-109/abigail/fortran/ch-1.f90
new file mode 100644
index 0000000000..be6055f839
--- /dev/null
+++ b/challenge-109/abigail/fortran/ch-1.f90
@@ -0,0 +1,12 @@
+!
+! See ../README.md
+!
+
+!
+! Run as: gfortran -o ch-1.o ch-1.f90; ./ch-1.o
+!
+
+program ch1
+    implicit none
+    write (*, *) "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21"
+end
diff --git a/challenge-109/abigail/go/ch-1.go b/challenge-109/abigail/go/ch-1.go
new file mode 100644
index 0000000000..78d9ca1148
--- /dev/null
+++ b/challenge-109/abigail/go/ch-1.go
@@ -0,0 +1,15 @@
+package main
+
+//
+// See ../README.md
+//
+
+//
+// Run as: go run ch-1.go
+//
+
+import "fmt"
+
+func main () {
+    fmt . Print ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21\n")
+}
diff --git a/challenge-109/abigail/java/ch-1.java b/challenge-109/abigail/java/ch-1.java
new file mode 100644
index 0000000000..b50b73f0d2
--- /dev/null
+++ b/challenge-109/abigail/java/ch-1.java
@@ -0,0 +1,13 @@
+//
+// See ../README.md
+//
+
+//
+// Run as: ln ch-1.java ch1.java; javac ch1; java ch1
+//
+
+public class ch1 {
+    public static void main (String [] args) {
+        System . out . print ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21\n");
+    }
+}
diff --git a/challenge-109/abigail/lua/ch-1.lua b/challenge-109/abigail/lua/ch-1.lua
new file mode 100644
index 0000000000..5eb2d477f9
--- /dev/null
+++ b/challenge-109/abigail/lua/ch-1.lua
@@ -0,0 +1,43 @@
+#!/opt/local/bin/lua
+
+--
+-- See ../README.md
+--
+
+--
+-- Run as: lua ch-1.lua [plain | compute]
+--
+
+local PLAIN   =  0
+local COMPUTE =  1
+
+local COUNT   = 20
+
+function divisor_sum (n)
+    local sum = 0
+    for i = 2, n - 2 do
+        if   n % i == 0 
+        then sum = sum + i
+        end
+    end
+    return (sum)
+end
+
+local type = PLAIN
+if   #arg >= 1 and arg [1] == "compute"
+then type = COMPUTE
+end
+
+if   type == PLAIN
+then print ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21")
+end
+
+if   type == COMPUTE
+then for n = 1, COUNT do
+         if n > 1 
+         then io . write (", ")
+         end
+         io . write (divisor_sum (n))
+     end
+     io . write ("\n")
+end
diff --git a/challenge-109/abigail/m4/ch-1.m4 b/challenge-109/abigail/m4/ch-1.m4
new file mode 100644
index 0000000000..9299e87f97
--- /dev/null
+++ b/challenge-109/abigail/m4/ch-1.m4
@@ -0,0 +1 @@
+0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
diff --git a/challenge-109/abigail/node/ch-1.js b/challenge-109/abigail/node/ch-1.js
new file mode 100644
index 0000000000..d7cff7b0f5
--- /dev/null
+++ b/challenge-109/abigail/node/ch-1.js
@@ -0,0 +1,45 @@
+#!/usr/local/bin/node
+
+//
+// See ../README.md
+//
+
+//
+// Run as: node ch-1.js [plain | compute]
+//
+
+let PLAIN   =  0
+let COMPUTE =  1
+
+let COUNT   = 20
+
+function divisor_sum (n) {
+    let sum = 0
+    for (let i = 2; i < n; i ++) {
+        if (n % i == 0) {
+            sum += i
+        }
+    }
+    return (sum)
+}
+
+let type = PLAIN
+if (process . argv . length > 2 &&
+    process . argv [2] == "compute") {
+    type = COMPUTE
+}
+
+if (type == PLAIN) {
+    console . log ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, " +
+                   "0, 15, 0, 9, 8, 14, 0, 20, 0, 21")
+}
+
+if (type == COMPUTE) {
+    for (let i = 1; i <= COUNT; i ++) {
+        if (i > 1) {
+            process . stdout . write (", ")
+        }
+        process . stdout . write (divisor_sum (i) . toString ())
+    }
+    process . stdout . write ("\n")
+}
diff --git a/challenge-109/abigail/ocaml/ch-1.ml b/challenge-109/abigail/ocaml/ch-1.ml
new file mode 100644
index 0000000000..3311ee44fa
--- /dev/null
+++ b/challenge-109/abigail/ocaml/ch-1.ml
@@ -0,0 +1,9 @@
+(*                  *)
+(* See ../README.md *)
+(*                  *)
+
+(*                       *)
+(* Run as: ocaml ch-1.ml *)
+(*                       *)
+
+print_endline "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21";
diff --git a/challenge-109/abigail/pascal/ch-1.p b/challenge-109/abigail/pascal/ch-1.p
new file mode 100644
index 0000000000..c5d97f86bb
--- /dev/null
+++ b/challenge-109/abigail/pascal/ch-1.p
@@ -0,0 +1,13 @@
+Program XXX;
+
+(*                  *)
+(* See ../README.md *)
+(*                  *)
+
+(*                                           *)
+(* Run as: fpc -och-1.out ch-1.p; ./ch-1.out *)
+(*                                           *)
+
+begin
+    writeln ('0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21')
+end.
diff --git a/challenge-109/abigail/perl/ch-1.pl b/challenge-109/abigail/perl/ch-1.pl
new file mode 100644
index 0000000000..64f21d5d24
--- /dev/null
+++ b/challenge-109/abigail/perl/ch-1.pl
@@ -0,0 +1,51 @@
+#!/opt/perl/bin/perl
+
+use 5.032;
+
+use strict;
+use warnings;
+no  warnings 'syntax';
+
+use experimental 'signatures';
+use experimental 'lexical_subs';
+
+#
+# See ../README.md
+#
+
+#
+# Run as: perl ch-1.pl [plain|fetch|compute]
+#
+
+my $COUNT = 20;
+
+my $TYPE_PLAIN   =  0;
+my $TYPE_FETCH   =  1;
+my $TYPE_COMPUTE =  2;
+
+my $type = $TYPE_PLAIN;   # Default
+   $type = $TYPE_FETCH   if @ARGV && $ARGV [0] eq "fetch";
+   $type = $TYPE_COMPUTE if @ARGV && $ARGV [0] eq "compute";
+
+
+
+if ($type == $TYPE_PLAIN) {
+    say "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21";
+}
+elsif ($type == $TYPE_FETCH) {
+    use OEIS;
+    $, = ", ";
+    say oeis (48050 => $COUNT);  # We want the first numbers from
+                                 # sequence A048050.
+}
+elsif ($type == $TYPE_COMPUTE) {
+    use List::Util qw [sum0];
+    $, = ", ";
+    #
+    # Sum the divisors; a divisor has mod 0. This is very inefficient
+    # even for smallish integers, but since we're asked to only 
+    # calculate the first 20 numbers, we don't have to care about
+    # efficiency.
+    #
+    say map {my $n = $_; sum0 grep {!($n % $_)} 2 .. $_ - 1} 1 .. $COUNT;
+}
diff --git a/challenge-109/abigail/php/ch-1.php b/challenge-109/abigail/php/ch-1.php
new file mode 100644
index 0000000000..0516741cc7
--- /dev/null
+++ b/challenge-109/abigail/php/ch-1.php
@@ -0,0 +1,11 @@
+<?php
+    //
+    // See ../README.md
+    //
+
+    //
+    // Run as: php ch-1.php
+    //
+
+    echo "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21\n"
+?>
diff --git a/challenge-109/abigail/postscript/ch-1.ps b/challenge-109/abigail/postscript/ch-1.ps
new file mode 100644
index 0000000000..2ea67f6701
--- /dev/null
+++ b/challenge-109/abigail/postscript/ch-1.ps
@@ -0,0 +1,10 @@
+%!PS
+%
+% See ../README.md
+%
+
+%
+% Run as: ps2ascii ch-1.ps
+%
+
+(0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21) =
diff --git a/challenge-109/abigail/python/ch-1.py b/challenge-109/abigail/python/ch-1.py
new file mode 100644
index 0000000000..6600bda6d5
--- /dev/null
+++ b/challenge-109/abigail/python/ch-1.py
@@ -0,0 +1,39 @@
+#!/opt/local/bin/python
+
+#
+# See ../README.md
+#
+
+#
+# Run as: python ch-1.py [plain | compute]
+#
+
+import sys
+
+COUNT   = 20
+PLAIN   =  0
+COMPUTE =  1
+
+def divisor_sum (n):
+    sum = 0
+    for i in range (2, n):
+        if n % i == 0:
+            sum = sum + i
+    return (sum)
+
+type = PLAIN
+
+if len (sys . argv) > 1 and sys . argv [1] == "compute":
+    type = COMPUTE
+
+
+if type == PLAIN:
+    print ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21")
+
+
+if type == COMPUTE:
+    for n in range (1, COUNT + 1):
+        if n > 1:
+            print (", ", end = '')
+        print (divisor_sum (n), end = '')
+    print ("")
diff --git a/challenge-109/abigail/r/ch-1.r b/challenge-109/abigail/r/ch-1.r
new file mode 100644
index 0000000000..1c6165807d
--- /dev/null
+++ b/challenge-109/abigail/r/ch-1.r
@@ -0,0 +1,9 @@
+#
+# See ../README.md
+#
+
+#
+# Run as: Rscript ch-1.r
+#
+
+cat ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21\n")
diff --git a/challenge-109/abigail/rexx/ch-1.rexx b/challenge-109/abigail/rexx/ch-1.rexx
new file mode 100644
index 0000000000..3085ab0224
--- /dev/null
+++ b/challenge-109/abigail/rexx/ch-1.rexx
@@ -0,0 +1,9 @@
+/*
+ * See ../README.md
+ */
+
+/*
+ * Run as: rexx ch-1.rexx
+ */
+
+say "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21"
diff --git a/challenge-109/abigail/ruby/ch-1.rb b/challenge-109/abigail/ruby/ch-1.rb
new file mode 100644
index 0000000000..95a38a69cb
--- /dev/null
+++ b/challenge-109/abigail/ruby/ch-1.rb
@@ -0,0 +1,44 @@
+#!/usr/bin/ruby
+
+#
+# See ../README.md
+#
+ 
+#
+# Run as: ruby ch-1.rb [plain | compute]
+#
+
+PLAIN   =  0
+COMPUTE =  1
+
+COUNT   = 20
+
+def divisor_sum (n)
+    sum = 0
+    for i in 2 .. n - 1
+        if   n % i == 0
+        then sum += i
+        end
+    end
+    return sum
+end
+
+type = PLAIN
+
+if   ARGV . length > 0 && ARGV[0] == "compute"
+then type = COMPUTE
+end
+
+if   type == PLAIN
+then puts ("0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21");
+end
+
+if   type == COMPUTE
+then for n in 1 .. COUNT
+         if n > 1
+         then print (", ")
+         end
+         print divisor_sum (n)
+     end
+     puts ("")
+end
diff --git a/challenge-109/abigail/scheme/ch-1.scm b/challenge-109/abigail/scheme/ch-1.scm
new file mode 100644
index 0000000000..bc43f3c502
--- /dev/null
+++ b/challenge-109/abigail/scheme/ch-1.scm
@@ -0,0 +1,9 @@
+;;;
+;;; See ../README.md
+;;;
+
+;;;
+;;; Run as: guile --no-auto-compile ch-1.scm
+;;;
+
+(display "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21\n")
diff --git a/challenge-109/abigail/sed/ch-1.sed b/challenge-109/abigail/sed/ch-1.sed
new file mode 100644
index 0000000000..1c93d3f21c
--- /dev/null
+++ b/challenge-109/abigail/sed/ch-1.sed
@@ -0,0 +1,12 @@
+#
+# See ../README.md
+#
+
+#
+# Run as: sed -f ch-1.sed
+#
+# For each line in the input file, we write the first three
+# self-describing numbers.
+#
+
+s/.*/0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21/
diff --git a/challenge-109/abigail/sql/ch-1.sql b/challenge-109/abigail/sql/ch-1.sql
new file mode 100644
index 0000000000..014860fcd5
--- /dev/null
+++ b/challenge-109/abigail/sql/ch-1.sql
@@ -0,0 +1,9 @@
+--
+-- See ../README.md
+--
+
+-- 
+-- Run as: sqlite3 < ch-1.sql
+--
+
+SELECT "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21";
diff --git a/challenge-109/abigail/t/ctest.ini b/challenge-109/abigail/t/ctest.ini
new file mode 100644
index 0000000000..e2f88e41ce
--- /dev/null
+++ b/challenge-109/abigail/t/ctest.ini
@@ -0,0 +1,35 @@
+# 
+# Configuration file for running tests, using ctest.
+# See https://github.com/Abigail/Misc/blob/master/ctest
+# 
+
+[names]
+1-1 = Fixed output
+1-2 = Fixed output/plain
+1-3 = Fixed output/fetch
+1-4 = Fixed output/compute
+
+
+[1-1]
+no_input = 1
+
+[1-1/sed]
+no_input = 0
+
+[1-1/awk,bash,c,lua,node,perl,python,ruby]
+skip = "Not for this language"
+
+[1-2,1-3,1-4]
+skip = "Not for this language"
+
+[1-2/awk,bash,c,lua,node,perl,python,ruby]
+skip = 0
+args = plain
+
+[1-3/perl]
+skip = 0
+args = fetch
+
+[1-4/awk,bash,c,lua,node,perl,python,ruby]
+skip = 0
+args = compute
diff --git a/challenge-109/abigail/t/input-1-1 b/challenge-109/abigail/t/input-1-1
new file mode 100644
index 0000000000..8b13789179
--- /dev/null
+++ b/challenge-109/abigail/t/input-1-1
@@ -0,0 +1 @@
+
diff --git a/challenge-109/abigail/t/input-1-2 b/challenge-109/abigail/t/input-1-2
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/challenge-109/abigail/t/input-1-3 b/challenge-109/abigail/t/input-1-3
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/challenge-109/abigail/t/input-1-4 b/challenge-109/abigail/t/input-1-4
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/challenge-109/abigail/t/output-1-1.exp b/challenge-109/abigail/t/output-1-1.exp
new file mode 100644
index 0000000000..9299e87f97
--- /dev/null
+++ b/challenge-109/abigail/t/output-1-1.exp
@@ -0,0 +1 @@
+0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
diff --git a/challenge-109/abigail/t/output-1-2.exp b/challenge-109/abigail/t/output-1-2.exp
new file mode 100644
index 0000000000..9299e87f97
--- /dev/null
+++ b/challenge-109/abigail/t/output-1-2.exp
@@ -0,0 +1 @@
+0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
diff --git a/challenge-109/abigail/t/output-1-3.exp b/challenge-109/abigail/t/output-1-3.exp
new file mode 100644
index 0000000000..9299e87f97
--- /dev/null
+++ b/challenge-109/abigail/t/output-1-3.exp
@@ -0,0 +1 @@
+0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
diff --git a/challenge-109/abigail/t/output-1-4.exp b/challenge-109/abigail/t/output-1-4.exp
new file mode 100644
index 0000000000..9299e87f97
--- /dev/null
+++ b/challenge-109/abigail/t/output-1-4.exp
@@ -0,0 +1 @@
+0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
diff --git a/challenge-109/abigail/tcl/ch-1.tcl b/challenge-109/abigail/tcl/ch-1.tcl
new file mode 100644
index 0000000000..7ab10d4661
--- /dev/null
+++ b/challenge-109/abigail/tcl/ch-1.tcl
@@ -0,0 +1,9 @@
+#
+# See ../README.md
+#
+
+#
+# Run as: tclsh ch-1.tcl
+#
+
+puts "0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21"
-- 
cgit 


From 5be6a97a3cf0ff10e023171729a50a386c24622b Mon Sep 17 00:00:00 2001
From: Abigail <abigail@abigail.be>
Date: Tue, 20 Apr 2021 18:24:30 +0200
Subject: Perl solution for week 109, part 2

---
 challenge-109/abigail/README.md        |   1 +
 challenge-109/abigail/perl/ch-2.pl     | 183 +++++++++++++++++++++++++++++++++
 challenge-109/abigail/t/ctest.ini      |   6 ++
 challenge-109/abigail/t/input-2-1      |   1 +
 challenge-109/abigail/t/input-2-2      |   1 +
 challenge-109/abigail/t/output-2-1.exp |   8 ++
 challenge-109/abigail/t/output-2-2.exp |   2 +
 7 files changed, 202 insertions(+)
 create mode 100644 challenge-109/abigail/perl/ch-2.pl
 create mode 100644 challenge-109/abigail/t/input-2-1
 create mode 100644 challenge-109/abigail/t/input-2-2
 create mode 100644 challenge-109/abigail/t/output-2-1.exp
 create mode 100644 challenge-109/abigail/t/output-2-2.exp

diff --git a/challenge-109/abigail/README.md b/challenge-109/abigail/README.md
index 57a25f7869..1f7b55f195 100644
--- a/challenge-109/abigail/README.md
+++ b/challenge-109/abigail/README.md
@@ -91,6 +91,7 @@ Output:
 ~~~~
 
 ### Solutions
+* [Perl](perl/ch-2.pl)
 
 ### Blog
 
diff --git a/challenge-109/abigail/perl/ch-2.pl b/challenge-109/abigail/perl/ch-2.pl
new file mode 100644
index 0000000000..ddbbe4fb38
--- /dev/null
+++ b/challenge-109/abigail/perl/ch-2.pl
@@ -0,0 +1,183 @@
+#!/opt/perl/bin/perl
+
+use 5.032;
+
+use strict;
+use warnings;
+no  warnings 'syntax';
+
+use experimental 'signatures';
+use experimental 'lexical_subs';
+
+#
+# See ../README.md
+#
+
+#
+# Run as: perl ch-2.pl < input-file
+#
+
+#
+# First note that due to symmetry, there cannot be a unique solution [1].
+# If
+#
+#      (a, b, c, d, e, f, g) = (x_1, x_2, x_3, x_4, x_5, x_6, x_7)
+#
+# is a solution, then
+#
+#      (a, b, c, d, e, f, g) = (x_7, x_6, x_5, x_4, x_3, x_2, x_1)
+#
+# must be a solution as well.
+#
+# For instance, the given example has 8 solutions, 4 of which are
+# mirror images.
+#
+# [1] This assumes no duplicate numbers in the input. Clearly, a
+#     solution where a == g, b == f, and c == e doesn't give a
+#     different solution when mirrorred. (For instance, if all 
+#     numbers are 0, there is only one solution).
+
+#
+#
+# It's easy to brute force this. There are a mere 5040 permutations
+# of the seven numbers; it would be hard to find an environment
+# where it takes more than a few milliseconds to try all permutations.
+#
+# We can improve the brute force a little, by determining early we're
+# on a wrong path. For instance, once we have picked an a, b, c, and d,
+# we can check whether a + b == b + c + d. If not, we don't have to
+# continue trying values for e, f, and g.
+#
+# However, that's not the way we go. We will first do some analysis.
+# Let the sum of each box be N. Then we have:
+#
+#   N = a + b        (1)
+#   N = b + c + d    (2)
+#   N = d + e + f    (3)
+#   N = f + g        (4)
+#
+# For (1) and (2), we get:
+#
+#   a + b = b + c + d  =>
+#   a     =     c + d  =>
+#   a - c =         d
+#
+# In the same way, (3) and (4), we get:
+#
+#   g + f = f + e + d  =>
+#   g     =     e + d  =>
+#   g - e =         d
+#
+# This leads to the following algorithm:
+# 
+#   - Calculate the differences between all pairs (7 * 6 == 42 pairs)
+#   - Find all numbers n from the input array for which there are at
+#     least two pairs giving this difference, under the condition n
+#     is not part of such a pair. (Note that if the input contains
+#     two or more of the same number, for this purpose, we treat those
+#     numbers to be different). These numbers will be our candidate for d.
+#   - Of the list of differences equalling d, consider each pair.
+#     Eliminate pairs where the same number appears in each. The first
+#     difference gives candidates for a and c; the second gives candidates
+#     for g and e. (Swapping them leaves to a symmetric solution).
+#   - We now have candidates for a, c, d, e, and g. This leaves two
+#     numbers for b and c.
+#   - Try both, and check whether a + b == b + c + d == d + e + f == f + g.
+#
+# For the given example, this means we only try 32 permutations,
+# giving us 4 different solutions (the other 4 can be found by
+# reversing the numbers).
+#
+# We are not making any assumptions on the sign of the input numbers;
+# our algorithm works fine if the input contains negative numbers.
+#
+# We will also print all solutions (including the symmetric ones)
+#
+
+while (<>) {
+    my @numbers = split;
+
+    #
+    # Find all differences
+    #
+    my %differences;
+    for (my $x = 0; $x < @numbers; $x ++) {
+        for (my $y = $x + 1; $y < @numbers; $y ++) {
+            my $diff = $numbers [$x] - $numbers [$y];
+            push @{$differences { $diff}} => [$x, $y];
+            push @{$differences {-$diff}} => [$y, $x];
+        }
+    }
+
+    #
+    # Now, iterate over the numbers, and see if there 
+    # is a number matching two differences, with all
+    # indices being different.
+    #
+    for (my $d_i = 0; $d_i < @numbers; $d_i ++) {
+        my $d = $numbers [$d_i];
+        #
+        # Find the pairs whose difference is $d. If we don't have
+        # at least two pairs where neither number is $d, this
+        # cannot be a solution.
+        #
+        my @diffs = grep {$$_ [0] != $d_i && $$_ [1] != $d_i}
+                          @{$differences {$d} || []};
+
+        next unless @diffs >= 2;
+
+        #
+        # Now, find two pairs where all indices are different.
+        #
+        for (my $x = 0; $x < @diffs; $x ++) {
+            for (my $y = $x + 1; $y < @diffs; $y ++) {
+                next if $diffs [$x] [0] == $diffs [$y] [0] ||
+                        $diffs [$x] [0] == $diffs [$y] [1] ||
+                        $diffs [$x] [1] == $diffs [$y] [0] ||
+                        $diffs [$x] [1] == $diffs [$y] [1];
+
+                #
+                # W.l.o.g. we can now assume $diffs [$x] are
+                # the indices for $a and $c, and $diffs [$y]
+                # are the indices for $g and $e.
+                #
+                my ($a_i, $c_i) = @{$diffs [$x]};
+                my ($g_i, $e_i) = @{$diffs [$y]};
+
+                #
+                # Find the unused indices
+                #
+                my %indices = map {$_ => 1} keys @numbers;
+                delete $indices {$_} for $a_i, $c_i, $d_i, $e_i, $g_i;
+
+                #
+                # This leaves two indices for $b and $e.
+                # Try them both.
+                #
+                my $left = [keys %indices];
+                foreach my $try ($left, [reverse @$left]) {
+                    my ($b_i, $f_i) = @$try;
+
+                    #
+                    # Do we have a winner?
+                    #
+                    next unless           $numbers [$a_i] + $numbers [$b_i] ==
+                        $numbers [$b_i] + $numbers [$c_i] + $numbers [$d_i] ==
+                        $numbers [$d_i] + $numbers [$e_i] + $numbers [$f_i] ==
+                                          $numbers [$f_i] + $numbers [$g_i];
+
+                    #
+                    # Print result, and the reverse, so we get all
+                    # possible solutions.
+                    #
+                    my @solution =
+                       @numbers [$a_i, $b_i, $c_i, $d_i, $e_i, $f_i, $g_i];
+
+                    local $, = " ";
+                    say         @solution;
+                    say reverse @solution;
+                }
+            }
+        }
+    }
+}
diff --git a/challenge-109/abigail/t/ctest.ini b/challenge-109/abigail/t/ctest.ini
index e2f88e41ce..afa82182bd 100644
--- a/challenge-109/abigail/t/ctest.ini
+++ b/challenge-109/abigail/t/ctest.ini
@@ -8,6 +8,8 @@
 1-2 = Fixed output/plain
 1-3 = Fixed output/fetch
 1-4 = Fixed output/compute
+2-1 = Given example
+2-2 = With a negative number
 
 
 [1-1]
@@ -33,3 +35,7 @@ args = fetch
 [1-4/awk,bash,c,lua,node,perl,python,ruby]
 skip = 0
 args = compute
+
+
+[2-1,2-2]
+sort = 1
diff --git a/challenge-109/abigail/t/input-2-1 b/challenge-109/abigail/t/input-2-1
new file mode 100644
index 0000000000..b4457aae66
--- /dev/null
+++ b/challenge-109/abigail/t/input-2-1
@@ -0,0 +1 @@
+1 2 3 4 5 6 7
diff --git a/challenge-109/abigail/t/input-2-2 b/challenge-109/abigail/t/input-2-2
new file mode 100644
index 0000000000..335e2405f0
--- /dev/null
+++ b/challenge-109/abigail/t/input-2-2
@@ -0,0 +1 @@
+1 -2 3 4 5 6 7
diff --git a/challenge-109/abigail/t/output-2-1.exp b/challenge-109/abigail/t/output-2-1.exp
new file mode 100644
index 0000000000..83687f2b3e
--- /dev/null
+++ b/challenge-109/abigail/t/output-2-1.exp
@@ -0,0 +1,8 @@
+3 7 2 1 5 4 6
+4 5 3 1 6 2 7
+4 7 1 3 2 6 5
+5 6 2 3 1 7 4
+6 4 1 5 2 3 7
+6 4 5 1 2 7 3
+7 2 6 1 3 5 4
+7 3 2 5 1 4 6
diff --git a/challenge-109/abigail/t/output-2-2.exp b/challenge-109/abigail/t/output-2-2.exp
new file mode 100644
index 0000000000..7a67a5be9d
--- /dev/null
+++ b/challenge-109/abigail/t/output-2-2.exp
@@ -0,0 +1,2 @@
+3 7 -2 5 1 4 6
+6 4 1 5 -2 7 3
-- 
cgit 


From 490b2215c7eaeb037b7548564306e2081784b3e4 Mon Sep 17 00:00:00 2001
From: Abigail <abigail@abigail.be>
Date: Tue, 20 Apr 2021 20:43:18 +0200
Subject: Use function argument

---
 challenge-109/abigail/bash/ch-1.sh | 1 +
 1 file changed, 1 insertion(+)

diff --git a/challenge-109/abigail/bash/ch-1.sh b/challenge-109/abigail/bash/ch-1.sh
index d4eec1f2d9..de09aa6414 100644
--- a/challenge-109/abigail/bash/ch-1.sh
+++ b/challenge-109/abigail/bash/ch-1.sh
@@ -13,6 +13,7 @@ set -f
 COUNT=20
 
 function divisor_sum () {
+    local n=$1
     sum=0
     local i
     for ((i = 2; i < n; i ++))
-- 
cgit 


From 7b4fbbe6505b63d2faa62ad34939b6e830ea692b Mon Sep 17 00:00:00 2001
From: Abigail <abigail@abigail.be>
Date: Tue, 20 Apr 2021 20:52:57 +0200
Subject: When looping over possible divisors, stop at n / 2.

---
 challenge-109/abigail/awk/ch-1.awk   | 2 +-
 challenge-109/abigail/bash/ch-1.sh   | 2 +-
 challenge-109/abigail/c/ch-1.c       | 2 +-
 challenge-109/abigail/lua/ch-1.lua   | 2 +-
 challenge-109/abigail/node/ch-1.js   | 2 +-
 challenge-109/abigail/perl/ch-1.pl   | 2 +-
 challenge-109/abigail/python/ch-1.py | 2 +-
 challenge-109/abigail/ruby/ch-1.rb   | 2 +-
 8 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/challenge-109/abigail/awk/ch-1.awk b/challenge-109/abigail/awk/ch-1.awk
index 6b889ae3a0..203c7f1fec 100644
--- a/challenge-109/abigail/awk/ch-1.awk
+++ b/challenge-109/abigail/awk/ch-1.awk
@@ -10,7 +10,7 @@
 
 function divisor_sum (n, i) {
     sum = 0
-    for (i = 2; i < n; i ++) {
+    for (i = 2; i <= n / 2; i ++) {
         if (n % i == 0) {
             sum += i
         }
diff --git a/challenge-109/abigail/bash/ch-1.sh b/challenge-109/abigail/bash/ch-1.sh
index de09aa6414..752a4f9760 100644
--- a/challenge-109/abigail/bash/ch-1.sh
+++ b/challenge-109/abigail/bash/ch-1.sh
@@ -16,7 +16,7 @@ function divisor_sum () {
     local n=$1
     sum=0
     local i
-    for ((i = 2; i < n; i ++))
+    for ((i = 2; i <= n / 2; i ++))
     do  if   ((n % i == 0))
         then ((sum += i))
         fi
diff --git a/challenge-109/abigail/c/ch-1.c b/challenge-109/abigail/c/ch-1.c
index e6716c148a..377caf63f3 100644
--- a/challenge-109/abigail/c/ch-1.c
+++ b/challenge-109/abigail/c/ch-1.c
@@ -20,7 +20,7 @@ typedef int number;  /* Change if we want large numbers */
 
 number divisor_sum (number n) {
     number sum = 0;
-    for (number i = 2; i < n; i ++) {
+    for (number i = 2; i <= n / 2; i ++) {
         if (!(n % i)) {
             sum += i;
         }
diff --git a/challenge-109/abigail/lua/ch-1.lua b/challenge-109/abigail/lua/ch-1.lua
index 5eb2d477f9..74c3b7d914 100644
--- a/challenge-109/abigail/lua/ch-1.lua
+++ b/challenge-109/abigail/lua/ch-1.lua
@@ -15,7 +15,7 @@ local COUNT   = 20
 
 function divisor_sum (n)
     local sum = 0
-    for i = 2, n - 2 do
+    for i = 2, n / 2 do
         if   n % i == 0 
         then sum = sum + i
         end
diff --git a/challenge-109/abigail/node/ch-1.js b/challenge-109/abigail/node/ch-1.js
index d7cff7b0f5..0f75cf4962 100644
--- a/challenge-109/abigail/node/ch-1.js
+++ b/challenge-109/abigail/node/ch-1.js
@@ -15,7 +15,7 @@ let COUNT   = 20
 
 function divisor_sum (n) {
     let sum = 0
-    for (let i = 2; i < n; i ++) {
+    for (let i = 2; i <= Math . floor (n / 2); i ++) {
         if (n % i == 0) {
             sum += i
         }
diff --git a/challenge-109/abigail/perl/ch-1.pl b/challenge-109/abigail/perl/ch-1.pl
index 64f21d5d24..967a0344de 100644
--- a/challenge-109/abigail/perl/ch-1.pl
+++ b/challenge-109/abigail/perl/ch-1.pl
@@ -47,5 +47,5 @@ elsif ($type == $TYPE_COMPUTE) {
     # calculate the first 20 numbers, we don't have to care about
     # efficiency.
     #
-    say map {my $n = $_; sum0 grep {!($n % $_)} 2 .. $_ - 1} 1 .. $COUNT;
+    say map {my $n = $_; sum0 grep {!($n % $_)} 2 .. $_ / 2} 1 .. $COUNT;
 }
diff --git a/challenge-109/abigail/python/ch-1.py b/challenge-109/abigail/python/ch-1.py
index 6600bda6d5..f9e51a0897 100644
--- a/challenge-109/abigail/python/ch-1.py
+++ b/challenge-109/abigail/python/ch-1.py
@@ -16,7 +16,7 @@ COMPUTE =  1
 
 def divisor_sum (n):
     sum = 0
-    for i in range (2, n):
+    for i in range (2, n / 2 + 1):
         if n % i == 0:
             sum = sum + i
     return (sum)
diff --git a/challenge-109/abigail/ruby/ch-1.rb b/challenge-109/abigail/ruby/ch-1.rb
index 95a38a69cb..0c73c368dd 100644
--- a/challenge-109/abigail/ruby/ch-1.rb
+++ b/challenge-109/abigail/ruby/ch-1.rb
@@ -15,7 +15,7 @@ COUNT   = 20
 
 def divisor_sum (n)
     sum = 0
-    for i in 2 .. n - 1
+    for i in 2 .. n / 2
         if   n % i == 0
         then sum += i
         end
-- 
cgit 


From 4a816dae782ebf95a65cb13fe7344e2664d926d3 Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Wed, 21 Apr 2021 17:39:48 +0200
Subject: Task 1 done.

---
 challenge-109/luca-ferrari/raku/ch-1.p6 | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)
 create mode 100644 challenge-109/luca-ferrari/raku/ch-1.p6

diff --git a/challenge-109/luca-ferrari/raku/ch-1.p6 b/challenge-109/luca-ferrari/raku/ch-1.p6
new file mode 100644
index 0000000000..820e7500c2
--- /dev/null
+++ b/challenge-109/luca-ferrari/raku/ch-1.p6
@@ -0,0 +1,20 @@
+#!perl6
+
+#
+# C(n) = sum of divisors of n except 1 and n
+# 
+sub choowla( Int $n ) {
+    # get all divisors
+
+    my @divisors;
+    for 2 .. $n / 2 {
+        @divisors.push: $_ if $n %% $_;
+    }
+
+    return [+] @divisors;
+}
+
+sub MAIN( Int $limit = 20 ) {
+    my @choowla-numbers.push: choowla( $_ ) for 1 .. $limit;
+    @choowla-numbers.join( ',' ).say;
+}
-- 
cgit 


From c6086e3997c25a9398a791fb962f821b7b796dab Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Wed, 21 Apr 2021 17:40:50 +0200
Subject: More compact way of doing divisors.

---
 challenge-109/luca-ferrari/raku/ch-1.p6 | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/challenge-109/luca-ferrari/raku/ch-1.p6 b/challenge-109/luca-ferrari/raku/ch-1.p6
index 820e7500c2..c480b09dfc 100644
--- a/challenge-109/luca-ferrari/raku/ch-1.p6
+++ b/challenge-109/luca-ferrari/raku/ch-1.p6
@@ -6,10 +6,10 @@
 sub choowla( Int $n ) {
     # get all divisors
 
-    my @divisors;
-    for 2 .. $n / 2 {
-        @divisors.push: $_ if $n %% $_;
-    }
+    my @divisors.push: $_ if $n %% $_ for 2 .. $n / 2;
+    # for 2 .. $n / 2 {
+    #     @divisors.push: $_ if $n %% $_;
+    # }
 
     return [+] @divisors;
 }
-- 
cgit 


From 342181744b067fd36499de15529b2f87443db79f Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Wed, 21 Apr 2021 18:16:58 +0200
Subject: Task2 done

---
 challenge-109/luca-ferrari/raku/ch-2.p6 | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)
 create mode 100644 challenge-109/luca-ferrari/raku/ch-2.p6

diff --git a/challenge-109/luca-ferrari/raku/ch-2.p6 b/challenge-109/luca-ferrari/raku/ch-2.p6
new file mode 100644
index 0000000000..1213d407ca
--- /dev/null
+++ b/challenge-109/luca-ferrari/raku/ch-2.p6
@@ -0,0 +1,30 @@
+#!raku
+
+
+sub MAIN() {
+    my @nums    = <1 2 3 4 5 6 7>;
+    my @letters = <a b c d e f g>;
+
+
+    my @solutions;
+
+    for @nums.permutations -> @current {
+        my %squares;
+        %squares{ @letters[ $_ ] } = @current[ $_ ] for 0 ..^ @letters.elems;
+
+
+        my @sums;
+
+        @sums.push: [+] %squares<a b>;
+        @sums.push: [+] %squares<b c d>;
+        @sums.push: [+] %squares<d e f>;
+        @sums.push: [+] %squares<f g>;
+
+        @solutions.push: %squares if @sums[ 0 ] == all @sums;
+    }
+
+
+
+    say $_ for @solutions;
+
+}
-- 
cgit 


From 9b844027cb11bf15f01c897e5d45b44b2387fb8e Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Wed, 21 Apr 2021 18:20:10 +0200
Subject: Command line checks

---
 challenge-109/luca-ferrari/raku/ch-2.p6 | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/challenge-109/luca-ferrari/raku/ch-2.p6 b/challenge-109/luca-ferrari/raku/ch-2.p6
index 1213d407ca..15cc86739b 100644
--- a/challenge-109/luca-ferrari/raku/ch-2.p6
+++ b/challenge-109/luca-ferrari/raku/ch-2.p6
@@ -1,25 +1,25 @@
 #!raku
 
 
-sub MAIN() {
-    my @nums    = <1 2 3 4 5 6 7>;
+sub MAIN(  *@nums where { @nums.grep( * ~~ Int ).elems == @nums.elems && @nums.elems == 7 } ) {
     my @letters = <a b c d e f g>;
-
-
     my @solutions;
 
+    # permutate all numbers to find out the correct sum
     for @nums.permutations -> @current {
+        # build an hash to help visualize the answer
         my %squares;
         %squares{ @letters[ $_ ] } = @current[ $_ ] for 0 ..^ @letters.elems;
 
-
+        # compute the sums
         my @sums;
-
         @sums.push: [+] %squares<a b>;
         @sums.push: [+] %squares<b c d>;
         @sums.push: [+] %squares<d e f>;
         @sums.push: [+] %squares<f g>;
 
+
+        # if the first sum is equal to all the others, push this solution
         @solutions.push: %squares if @sums[ 0 ] == all @sums;
     }
 
-- 
cgit 


From 16814906f220961e56b95cf544b20bf1ac16e890 Mon Sep 17 00:00:00 2001
From: Philip Hood <hood@panix.com>
Date: Wed, 21 Apr 2021 13:42:13 -0400
Subject: challenge 109, in raku

---
 challenge-109/pkmnx/raku/ch-1.raku |  6 ++++++
 challenge-109/pkmnx/raku/ch-2.raku | 27 +++++++++++++++++++++++++++
 2 files changed, 33 insertions(+)
 create mode 100755 challenge-109/pkmnx/raku/ch-1.raku
 create mode 100755 challenge-109/pkmnx/raku/ch-2.raku

diff --git a/challenge-109/pkmnx/raku/ch-1.raku b/challenge-109/pkmnx/raku/ch-1.raku
new file mode 100755
index 0000000000..4d31c01eed
--- /dev/null
+++ b/challenge-109/pkmnx/raku/ch-1.raku
@@ -0,0 +1,6 @@
+#!/usr/bin/env raku
+
+
+my $upr = 20;
+my @chwla = (1 .. $upr).map(-> $n { (2..$n -1).grep({ !($n % $_) }).sum() });
+@chwla.say;
diff --git a/challenge-109/pkmnx/raku/ch-2.raku b/challenge-109/pkmnx/raku/ch-2.raku
new file mode 100755
index 0000000000..f71cf17e84
--- /dev/null
+++ b/challenge-109/pkmnx/raku/ch-2.raku
@@ -0,0 +1,27 @@
+#!/usr/bin/env raku
+
+# See usage:
+# pk@pkx:~/stuff/.../challenge-109/pkmnx/raku$ time ./ch-2.raku 1 2 3 5 4 6 7
+# 3 + 7 == 7 + 2 + 1 == 1 + 5 + 4 == 4 + 6
+# 5 + 6 == 6 + 2 + 3 == 3 + 1 + 7 == 7 + 4
+# 4 + 5 == 5 + 3 + 1 == 1 + 6 + 2 == 2 + 7
+# 4 + 7 == 7 + 1 + 3 == 3 + 2 + 6 == 6 + 5
+# 6 + 4 == 4 + 1 + 5 == 5 + 2 + 3 == 3 + 7
+# 6 + 4 == 4 + 5 + 1 == 1 + 2 + 7 == 7 + 3
+# 7 + 2 == 2 + 6 + 1 == 1 + 3 + 5 == 5 + 4
+# 7 + 3 == 3 + 2 + 5 == 5 + 1 + 4 == 4 + 6
+# 
+# real    0m0.337s
+
+sub MAIN( *@N where @N.elems == 7 && @N.all ~~ Numeric ) {
+
+  @N.permutations.grep({ val(|$_) }).map({ disp(|$_) }).join("\n").say;
+
+}
+     
+sub val ( $a, $b, $c, $d, $e, $f, $g ) { 
+  $a + $b == $b + $c + $d == $d + $e + $f == $f + $g;
+}
+sub disp ( $a, $b, $c, $d, $e, $f, $g ) {
+  "$a + $b == $b + $c + $d == $d + $e + $f == $f + $g";
+} 
-- 
cgit 


From db1fc1a584d92aa682901a624f4b105014dce916 Mon Sep 17 00:00:00 2001
From: PJ Durai <pj.durai@sap.com>
Date: Wed, 21 Apr 2021 11:38:46 -0700
Subject: Week 109  Raku

---
 challenge-109/pjdurai/raku/ch-1.raku | 25 +++++++++++++++++++++++++
 challenge-109/pjdurai/raku/ch-2.raku | 34 ++++++++++++++++++++++++++++++++++
 2 files changed, 59 insertions(+)
 create mode 100755 challenge-109/pjdurai/raku/ch-1.raku
 create mode 100644 challenge-109/pjdurai/raku/ch-2.raku

diff --git a/challenge-109/pjdurai/raku/ch-1.raku b/challenge-109/pjdurai/raku/ch-1.raku
new file mode 100755
index 0000000000..f66ba47b0b
--- /dev/null
+++ b/challenge-109/pjdurai/raku/ch-1.raku
@@ -0,0 +1,25 @@
+#! /usr/bin/env raku
+
+# Returns a list of divisors except 1 and Self.
+
+sub get-divisors ($num){
+    reduce sub (@acc,$i){
+        if $num %% $i && $i != 1 && $i != $num {
+            @acc.push($i) ;
+            my $m = $num / $i;
+            @acc.push($m) if $m != $i;
+        }
+        @acc;
+    }, [], | (1..$num.sqrt.floor);
+}
+
+# Print 20 Chowla Numbers.
+# To input the count do
+
+# 'raku ch-1.raku --N=25'
+
+sub MAIN(
+    Int :$N = 20,
+) {
+    say ([1..$N].map(  {[+] get-divisors($_)}  )).join(",");
+}
diff --git a/challenge-109/pjdurai/raku/ch-2.raku b/challenge-109/pjdurai/raku/ch-2.raku
new file mode 100644
index 0000000000..65b4e2e906
--- /dev/null
+++ b/challenge-109/pjdurai/raku/ch-2.raku
@@ -0,0 +1,34 @@
+#! /usr/bin/env raku
+
+# Call as 'raku ch-2.raku --numbers="1,2,3,4,5,6,7"'
+# Defaults to "1,2,3,4,5,6,7"
+#
+# The problme has multiple solutions. It prints all solutions.
+
+sub MAIN(
+    Str :$numbers = "1,2,3,4,5,6,7"
+){
+    my @labels = ["a".."z"];
+    my @arr = $numbers.split(/\,/);
+
+    my @solutions = @arr.permutations.grep(
+        ->@l
+        {
+            @l[0] + @l[1]  ==  @l[1] + @l[2] + @l[3]  ==  @l[3] + @l[4] + @l[5]  ==  @l[5] + @l[6];
+
+        });
+
+    for @solutions -> @solution {
+        say "Solution: ", @solution;
+        for zip(@labels, @solution) -> @pair {
+            say "@pair[0] = @pair[1]";
+        }
+        say "";
+        say "Box 1: a + b = @solution[0] + @solution[1] = ", @solution[0] + @solution[1];
+        say "Box 2: b + c + d = @solution[1] + @solution[2] + @solution[3] = ", @solution[1] + @solution[2] + @solution[3];
+        say "Box 3: d + e + f = @solution[3] + @solution[4] + @solution[5] = ", @solution[3] + @solution[4] + @solution[5];
+        say "Box 4: a + b = @solution[5] + @solution[6] = ", @solution[5] + @solution[6];
+        say "---------\n";
+
+    }
+}
-- 
cgit 


From fff9e4703ed20a60640c4ef24219499eb532ecb3 Mon Sep 17 00:00:00 2001
From: Lance Wicks <lw@judocoach.com>
Date: Wed, 21 Apr 2021 20:21:20 +0100
Subject: Perl implementation for 108, thanks Mohammad!

---
 challenge-109/lance-wicks/perl/ch-1.pl       | 12 ++++++++++++
 challenge-109/lance-wicks/perl/lib/Chowla.pm | 26 ++++++++++++++++++++++++++
 challenge-109/lance-wicks/perl/t/01-chowla.t | 12 ++++++++++++
 3 files changed, 50 insertions(+)
 create mode 100644 challenge-109/lance-wicks/perl/ch-1.pl
 create mode 100644 challenge-109/lance-wicks/perl/lib/Chowla.pm
 create mode 100644 challenge-109/lance-wicks/perl/t/01-chowla.t

diff --git a/challenge-109/lance-wicks/perl/ch-1.pl b/challenge-109/lance-wicks/perl/ch-1.pl
new file mode 100644
index 0000000000..ddbb11ad8a
--- /dev/null
+++ b/challenge-109/lance-wicks/perl/ch-1.pl
@@ -0,0 +1,12 @@
+use strict;
+use warnings;
+
+use lib './lib';
+use Chowla;
+
+my $c = Chowla->new;
+my $numbers = $c->list(20);
+
+for my $n (@$numbers) {
+    print "$n, ";
+}
diff --git a/challenge-109/lance-wicks/perl/lib/Chowla.pm b/challenge-109/lance-wicks/perl/lib/Chowla.pm
new file mode 100644
index 0000000000..06619c38d2
--- /dev/null
+++ b/challenge-109/lance-wicks/perl/lib/Chowla.pm
@@ -0,0 +1,26 @@
+package Chowla;
+
+use Moo;
+
+sub list {
+    my ($self,$max) = @_;
+    my @chowla_numbers;
+    for my $n (1..$max) {
+        push @chowla_numbers, $self->n($n);
+    }
+    return \@chowla_numbers;
+}
+
+sub n {
+    my ($self,$num) = @_;
+
+    my $total = 0;
+    for my $n (2..$num-1) {
+        if ($num % $n == 0) {
+            $total += $n;
+        }
+    }
+    return $total;
+}
+
+1;
diff --git a/challenge-109/lance-wicks/perl/t/01-chowla.t b/challenge-109/lance-wicks/perl/t/01-chowla.t
new file mode 100644
index 0000000000..15d50ac14e
--- /dev/null
+++ b/challenge-109/lance-wicks/perl/t/01-chowla.t
@@ -0,0 +1,12 @@
+use Test2::V0 -target => 'Chowla';
+
+is $CLASS->list(20),[0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21], 'List the first 20 Chowla numbers';
+
+is $CLASS->n(1),0, 'First Chowla number should be zero';
+is $CLASS->n(2),0, 'Second Chowla number should be zero';
+is $CLASS->n(3),0, 'Third Chowla number should be zero';
+is $CLASS->n(4),2, 'Fourth Chowla number should be two';
+is $CLASS->n(5),0, 'Fifth Chowla number should be 0';
+is $CLASS->n(6),5, 'Sixth Chowla number should be 5';
+
+done_testing;
-- 
cgit 


From fccecc2765b5344e925e4379d3c822fbb674aa97 Mon Sep 17 00:00:00 2001
From: Jörg Sommrey <28217714+jo-37@users.noreply.github.com>
Date: Mon, 19 Apr 2021 17:44:14 +0200
Subject: Solution to task 1

---
 challenge-109/jo-37/perl/ch-1.pl | 49 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100755 challenge-109/jo-37/perl/ch-1.pl

diff --git a/challenge-109/jo-37/perl/ch-1.pl b/challenge-109/jo-37/perl/ch-1.pl
new file mode 100755
index 0000000000..fd3ca1d792
--- /dev/null
+++ b/challenge-109/jo-37/perl/ch-1.pl
@@ -0,0 +1,49 @@
+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0;
+use Math::Prime::Util 'divisor_sum';
+use experimental 'signatures';
+
+our $examples;
+
+run_tests() if $examples;	# does not return
+
+die <<EOS unless @ARGV == 1;
+usage: $0 [-examples] [n]
+
+-examples
+    run the examples from the challenge
+ 
+n
+    print the first n Chowla numbers
+
+EOS
+
+
+### Input and Output
+
+say join ', ', map chowla($_), 1 .. $ARGV[0];
+
+
+### Implementation
+
+# Return the n-th Chowla number as the sum of n's nontrivial divisors.
+# The trivial divisors are 1 and n, which need to be subtracted from the
+# sum of all divisors.  For n = 1 these two numbers coincide and thus
+# only one subtrahend shall be applied.
+sub chowla ($n) {
+    divisor_sum($n) - $n - ($n > 1);
+}
+
+
+### Examples and tests
+
+sub run_tests {
+    my $n;
+    is chowla(++$n), $_, "chowla($n) = $_" for
+        (0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21);
+
+    done_testing;
+    exit;
+}
-- 
cgit 


From 60f434a87bbb5e4156fa7f83f6208a9cb02627e3 Mon Sep 17 00:00:00 2001
From: Jörg Sommrey <28217714+jo-37@users.noreply.github.com>
Date: Mon, 19 Apr 2021 19:06:28 +0200
Subject: Solution to task 2

---
 challenge-109/jo-37/perl/ch-2.pl | 92 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 92 insertions(+)
 create mode 100755 challenge-109/jo-37/perl/ch-2.pl

diff --git a/challenge-109/jo-37/perl/ch-2.pl b/challenge-109/jo-37/perl/ch-2.pl
new file mode 100755
index 0000000000..12a970bf66
--- /dev/null
+++ b/challenge-109/jo-37/perl/ch-2.pl
@@ -0,0 +1,92 @@
+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0;
+use Math::Prime::Util qw(forperm);
+use List::Util qw(sum uniqnum);
+use experimental qw(signatures);
+
+our ($tests, $examples);
+
+run_tests() if $tests || $examples;	# does not return
+
+die <<EOS unless @ARGV == 7;
+usage: $0 [-examples] [-tests] [--] [A B C D E F G]
+
+-examples
+    run the examples from the challenge
+ 
+-tests
+    run some tests
+
+A B C D E F G
+    numbers
+
+EOS
+
+
+### Input and Output
+
+format top =
+     a      b      c      d      e      f      g
+     =      =      =      =      =      =      =
+.
+
+format =
+@>>>>> @>>>>> @>>>>> @>>>>> @>>>>> @>>>>> @>>>>>
+@$_
+.
+
+write for @{puzzle(@ARGV)};
+
+
+### Implementation
+
+# A brute force approach:
+# Iterate over all permutations of the given numbers, assign them to the
+# boxes and select those having equal box sums.
+
+# index-to-box assignments: 
+use constant BOX => ([0, 1], [1, 2, 3], [3, 4, 5], [5, 6]);
+
+sub puzzle (@num) {
+
+    # Iterate over all permutations.
+    my @puzzle;
+    forperm {
+        # Sum over the the numbers contained in each box and count the
+        # unique values thereof.  Collect a solution if the sums consist
+        # of a single value.
+        # Double slice: pick the indices belonging to the current
+        # box from the permutation and then collect the respective
+        # numbers.
+        push @puzzle, [@num[@_]]
+            if uniqnum(map {sum @num[@_[@$_]]} BOX) == 1;
+    } @num;
+
+    \@puzzle;
+}
+
+
+### Examples and tests
+
+sub run_tests {
+    SKIP: {
+        skip "examples" unless $examples;
+        is puzzle(1 .. 7), bag {item [qw(6 4 1 5 2 3 7)]; etc}, 'example';
+    }
+
+    SKIP: {
+        skip "tests" unless $tests;
+
+        # No two pairs have the same sum, thus there cannot be a solution:
+        is puzzle(1, 2, 4, 8, 16, 32, 64), [], 'no solution';
+
+        is puzzle(-1.1, 0, 1.1, 2.2, 3.3, 4.4, 5.5),
+            bag {item [3.3, 2.2, -1.1, 4.4, 1.1, 0, 5.5]; etc},
+            'include negative floating point numbers';
+	}
+
+    done_testing;
+    exit;
+}
-- 
cgit 


From aa5f2d60c7582a0186443d6e9e2d763b0bfb5d68 Mon Sep 17 00:00:00 2001
From: Dave Jacoby <jacoby.david@gmail.com>
Date: Wed, 21 Apr 2021 16:33:51 -0400
Subject: Challenge 109 in Perl and (some) JS, Blogged

---
 challenge-109/dave-jacoby/blog.txt     |  1 +
 challenge-109/dave-jacoby/node/ch-1.js | 17 ++++++++
 challenge-109/dave-jacoby/perl/ch-1.pl | 35 +++++++++++++++
 challenge-109/dave-jacoby/perl/ch-2.pl | 79 ++++++++++++++++++++++++++++++++++
 4 files changed, 132 insertions(+)
 create mode 100644 challenge-109/dave-jacoby/blog.txt
 create mode 100644 challenge-109/dave-jacoby/node/ch-1.js
 create mode 100644 challenge-109/dave-jacoby/perl/ch-1.pl
 create mode 100644 challenge-109/dave-jacoby/perl/ch-2.pl

diff --git a/challenge-109/dave-jacoby/blog.txt b/challenge-109/dave-jacoby/blog.txt
new file mode 100644
index 0000000000..98a826c8ac
--- /dev/null
+++ b/challenge-109/dave-jacoby/blog.txt
@@ -0,0 +1 @@
+https://jacoby.github.io/2021/04/21/iterations-and-permutations-perl-weekly-challenge-109.html
\ No newline at end of file
diff --git a/challenge-109/dave-jacoby/node/ch-1.js b/challenge-109/dave-jacoby/node/ch-1.js
new file mode 100644
index 0000000000..72452fdcb5
--- /dev/null
+++ b/challenge-109/dave-jacoby/node/ch-1.js
@@ -0,0 +1,17 @@
+"use strict";
+
+let list = Array(20)
+  .fill()
+  .map((x, i) => i + 1)
+  .map((x) => chowla(x));
+console.log(list.join(", "));
+
+function chowla(n) {
+  return Array(n)
+    .fill()
+    .map((x, i) => i + 1)
+    .filter((x) => x != 1)
+    .filter((x) => x != n)
+    .filter((x) => n % x == 0)
+    .reduce((a, v) => a + v, 0);
+}
diff --git a/challenge-109/dave-jacoby/perl/ch-1.pl b/challenge-109/dave-jacoby/perl/ch-1.pl
new file mode 100644
index 0000000000..96de494c1a
--- /dev/null
+++ b/challenge-109/dave-jacoby/perl/ch-1.pl
@@ -0,0 +1,35 @@
+#!/usr/bin/env perl
+
+use strict;
+use warnings;
+use feature qw{ postderef say signatures state };
+no warnings qw{ experimental };
+
+use List::Util qw{sum0};
+
+my @test = ( 0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21 );
+
+say join ', ', @test;
+say join ', ', map { chowla($_) } 1 .. 20;
+say join ', ', map { chowla2($_) } 1 .. 20;
+
+# the old-fashioned for-loop way
+sub chowla ( $n ) {
+    my $c = 0;
+    for my $i ( 1 .. $n ) {
+        my $m = $n % $i;
+        next     if $i == 1 || $i == $n;
+        $c += $i if $m == 0;
+    }
+    return $c;
+}
+
+# the new, hot functional approach
+# using sum0 because if given an empty list, 
+# sum0 returns zero instead of undef
+sub chowla2 ( $n ) {
+    return sum0
+        grep { $n % $_ == 0 }
+        grep { $_ != 1 }
+        grep { $_ != $n } 1 .. $n;
+}
diff --git a/challenge-109/dave-jacoby/perl/ch-2.pl b/challenge-109/dave-jacoby/perl/ch-2.pl
new file mode 100644
index 0000000000..d1dba3614c
--- /dev/null
+++ b/challenge-109/dave-jacoby/perl/ch-2.pl
@@ -0,0 +1,79 @@
+#!/usr/bin/env perl
+
+use strict;
+use warnings;
+use feature qw{ postderef say signatures state };
+no warnings qw{ experimental };
+
+use Algorithm::Permute;
+
+my $map = <<'END';
+              (1)                    (3)
+        ╔══════════════╗      ╔══════════════╗
+        ║              ║      ║              ║
+        ║      a       ║      ║      e       ║
+        ║              ║ (2)  ║              ║  (4)
+        ║          ┌───╫──────╫───┐      ┌───╫─────────┐
+        ║          │   ║      ║   │      │   ║         │
+        ║          │ b ║      ║ d │      │ f ║         │
+        ║          │   ║      ║   │      │   ║         │
+        ║          │   ║      ║   │      │   ║         │
+        ╚══════════╪═══╝      ╚═══╪══════╪═══╝         │
+                   │       c      │      │      g      │
+                   │              │      │             │
+                   │              │      │             │
+                   └──────────────┘      └─────────────┘
+END
+
+four_squares( 1 .. 7 );
+
+sub four_squares ( @array ) {
+    my $array = join ', ', @array;
+    my $ap    = Algorithm::Permute->new( \@array );
+    while ( my @perm = $ap->next ) {
+        my $b1   = _box_1(@perm);
+        my $b2   = _box_2(@perm);
+        next if $b1 != $b2;
+        my $b3 = _box_3(@perm);
+        next if $b1 != $b3;
+        my $b4 = _box_4(@perm);
+        next if $b1 != $b4;
+
+        my $a = $perm[0];
+        my $b = $perm[1];
+        my $c = $perm[2];
+        my $d = $perm[3];
+        my $e = $perm[4];
+        my $f = $perm[5];
+        my $g = $perm[6];
+
+        say <<"END";
+        a = $a          e = $e
+        b = $b          f = $f
+        c = $c          g = $g
+        d = $d      
+        Box1 = a + b     = $a + $b     = $b1
+        Box2 = b + c + d = $b + $c + $d = $b2
+        Box3 = d + e + f = $d + $e + $f = $b3
+        Box4 = f + g     = $f + $g     = $b4
+END
+
+    }
+
+}
+
+sub _box_1( @array ) {
+    return $array[0] + $array[1];
+}
+
+sub _box_2( @array ) {
+    return $array[1] + $array[2] + $array[3];
+}
+
+sub _box_3( @array ) {
+    return $array[3] + $array[4] + $array[5];
+}
+
+sub _box_4( @array ) {
+    return $array[5] + $array[6];
+}
-- 
cgit 


From 97ed1c6391ff0077df0c446603be46db1e6bf219 Mon Sep 17 00:00:00 2001
From: Adam Russell <russella3@wit.edu>
Date: Wed, 21 Apr 2021 19:51:47 -0400
Subject: initial commit

---
 challenge-109/adam-russell/blog.txt      | 0
 challenge-109/adam-russell/blog1.txt     | 0
 challenge-109/adam-russell/perl/ch-1.pl  | 0
 challenge-109/adam-russell/perl/ch-2.pl  | 0
 challenge-109/adam-russell/prolog/ch-1.p | 0
 challenge-109/adam-russell/prolog/ch-2.p | 0
 6 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 challenge-109/adam-russell/blog.txt
 create mode 100644 challenge-109/adam-russell/blog1.txt
 create mode 100644 challenge-109/adam-russell/perl/ch-1.pl
 create mode 100644 challenge-109/adam-russell/perl/ch-2.pl
 create mode 100644 challenge-109/adam-russell/prolog/ch-1.p
 create mode 100644 challenge-109/adam-russell/prolog/ch-2.p

diff --git a/challenge-109/adam-russell/blog.txt b/challenge-109/adam-russell/blog.txt
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/challenge-109/adam-russell/blog1.txt b/challenge-109/adam-russell/blog1.txt
new file mode 100644
index 0000000000..e69de29bb2
dif