Merge pull request #3945 from Abigail/abigail/week-109

Abigail/week 109

52 files changed, 1540 insertions, 38 deletions

diff --git a/challenge-109/abigail/README.md b/challenge-109/abigail/README.md
index 32dc7d1d9d..6a72e49070 100644
--- a/challenge-109/abigail/README.md
+++ b/challenge-109/abigail/README.md
@@ -1,70 +1,106 @@
 # 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
+* [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
-[Locate Memory](https://abigail.github.io/HTML/Perl-Weekly-Challenge/week-108-1.html)
 
+[Chowla Numbers](https://abigail.github.io/HTML/Perl-Weekly-Challenge/week-109-1.html)
+
+
+## [Four Squares Puzzle](https://perlweeklychallenge.org/blog/perl-weekly-challenge-109/#TASK2)
 
-## [Bell Numbers](https://perlweeklychallenge.org/blog/perl-weekly-challenge-108/#TASK2)
+You are given four squares as below with numbers named `a`, `b`,
+`c`, `d`, `e`, `f`, `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.
+              (1)                    (3)
+        ╔══════════════╗      ╔══════════════╗
+        ║              ║      ║              ║
+        ║      a       ║      ║      e       ║
+        ║              ║ (2)  ║              ║  (4)
+        ║          ┌───╫──────╫───┐      ┌───╫─────────┐
+        ║          │   ║      ║   │      │   ║         │
+        ║          │ b ║      ║ d │      │ f ║         │
+        ║          │   ║      ║   │      │   ║         │
+        ║          │   ║      ║   │      │   ║         │
+        ╚══════════╪═══╝      ╚═══╪══════╪═══╝         │
+                   │       c      │      │      g      │
+                   │              │      │             │
+                   │              │      │             │
+                   └──────────────┘      └─────────────┘
+
+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)
 
diff --git a/challenge-109/abigail/awk/ch-1.awk b/challenge-109/abigail/awk/ch-1.awk
new file mode 100644
index 0000000000..203c7f1fec
--- /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 / 2; 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/awk/ch-2.awk b/challenge-109/abigail/awk/ch-2.awk
new file mode 100644
index 0000000000..9476ec90e8
--- /dev/null
+++ b/challenge-109/abigail/awk/ch-2.awk
@@ -0,0 +1,126 @@
+#!/usr/bin/awk
+
+#
+# See ../README.md
+#
+
+#
+# Run as: awk -f ch-2.awk < input-file
+#
+
+{
+    SIZE = 7;
+    #
+    # Put the fields into an array.
+    #
+    for (i = 1; i <= SIZE; i ++) {
+        numbers [i] = $i
+    }
+
+    #
+    # Find all the differences between pairs of numbers
+    #
+    delete diffs
+    delete diff_count
+    for (i = 1; i <= SIZE; i ++) {
+        for (j = i + 1; j <= SIZE; j ++) {
+            diff = numbers [i] - numbers [j]
+            diff_count [ diff] ++
+            diff_count [-diff] ++
+            l1 = diff_count [ diff]
+            l2 = diff_count [-diff]
+            diffs [ diff, l1, 1] = i
+            diffs [ diff, l1, 2] = j
+            diffs [-diff, l2, 1] = j
+            diffs [-diff, l2, 2] = i
+        }
+    }
+
+    #
+    # Iterate over the numbers, and see if there is a number
+    # which is equal to at least two differences.
+    #
+    # These numbers will be possibilities for d (at index d_i)
+    #
+    for (d_i = 1; d_i <= SIZE; d_i ++) {
+        d = numbers [d_i]
+        c = diff_count [d]
+        if (diff_count [d] >= 2) {
+            #
+            # Find two pairs whose difference is d, where none
+            # of the five numbers is reused.
+            #
+            for (i = 1; i <= c; i ++) {
+                if (diffs [d, i, 1] != d_i && diffs [d, i, 2] != d_i) {
+                    for (j = i + 1; j <= c; j ++) {
+                        if (diffs [d, j, 1] != d_i &&
+                            diffs [d, j, 2] != d_i &&
+                            diffs [d, i, 1] != diffs [d, j, 1] &&
+                            diffs [d, i, 1] != diffs [d, j, 2] &&
+                            diffs [d, i, 2] != diffs [d, j, 1] &&
+                            diffs [d, i, 2] != diffs [d, j, 2]) {
+                            #
+                            # W.l.o.g we can now assume diffs [d, i]
+                            # contains the indices for a and c,
+                            # and diffs [d, j] the indices for g and e.
+                            #
+                            a_i = diffs [d, i, 1]
+                            c_i = diffs [d, i, 2]
+                            g_i = diffs [d, j, 1]
+                            e_i = diffs [d, j, 2]
+
+                            #
+                            # Find the unused positions for b and f
+                            #
+                            for (b_i = 1; b_i <= SIZE; b_i ++) {
+                                if (b_i != a_i && b_i != c_i && b_i != d_i &&
+                                    b_i != e_i && b_i != g_i) {
+                                    for (f_i = 1; f_i <= SIZE; f_i ++) {
+                                        if (f_i != a_i && f_i != b_i &&
+                                            f_i != c_i && f_i != d_i &&
+                                            f_i != e_i && f_i != g_i) {
+                                            #
+                                            # Do we have a winner?
+                                            #
+                                            target = numbers [a_i] + \
+                                                     numbers [b_i]
+                                            if (target == numbers [b_i] + \
+                                                          numbers [c_i] +  \
+                                                          numbers [d_i] &&
+                                                target == numbers [d_i] + \
+                                                          numbers [e_i] + \
+                                                          numbers [f_i] &&
+                                                target == numbers [f_i] + \
+                                                          numbers [g_i]) {
+                                                #
+                                                # We have a winner. Print
+                                                # it, and the reverse
+                                                #
+                                                printf "%d %d %d %d %d %d %d\n",
+                                                       numbers [a_i],
+                                                       numbers [b_i],
+                                                       numbers [c_i],
+                                                       numbers [d_i],
+                                                       numbers [e_i],
+                                                       numbers [f_i],
+                                                       numbers [g_i]
+                                                printf "%d %d %d %d %d %d %d\n",
+                                                       numbers [g_i],
+                                                       numbers [f_i],
+                                                       numbers [e_i],
+                                                       numbers [d_i],
+                                                       numbers [c_i],
+                                                       numbers [b_i],
+                                                       numbers [a_i]
+                                            }
+                                        }
+                                    }
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
diff --git a/challenge-109/abigail/bash/ch-1.sh b/challenge-109/abigail/bash/ch-1.sh
new file mode 100644
index 0000000000..752a4f9760
--- /dev/null
+++ b/challenge-109/abigail/bash/ch-1.sh
@@ -0,0 +1,36 @@
+#!/bin/sh
+
+#
+# See ../README.md
+#
+
+#
+# Run as: bash ch-1.sh [plain | compute]
+#
+
+set -f
+
+COUNT=20
+
+function divisor_sum () {
+    local n=$1
+    sum=0
+    local i
+    for ((i = 2; i <= n / 2; 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/bash/ch-2.sh b/challenge-109/abigail/bash/ch-2.sh
new file mode 100644
index 0000000000..175ddf807d
--- /dev/null
+++ b/challenge-109/abigail/bash/ch-2.sh
@@ -0,0 +1,83 @@
+#!/bin/sh
+
+#
+# See ../README.md
+#
+
+#
+# Run as: bash ch-2.sh < input-file
+#
+
+SIZE=7
+
+#
+# Just try all possibilities, but continue as soon as we know
+# this cannot lead to a solution.
+#
+# We use 7 variables, a_i .. g_i indicating the indices of of
+# the numbers we try for a .. g. We use nested loops to iterate
+# over all the possibilties. We continue with the next iteration
+# of a loop if:
+#
+#  - We pick an index which is already taken by an outer loop.
+#  - We have a mismatch in the sums in the squares:
+#       + We define a target = numbers [a_i] + numbers [b_i] 
+#       + After picking c_i and d_i, we check whether 
+#         numbers [b_i] + numbers [c_i] + numbers [d_i] equals target.
+#       + After picking e_i and f_i, we check whether
+#         numbers [d_i] + numbers [e_i] + numbers [f_i] equals target.
+#       + After picking g_i, we check whether
+#         numbers [f_i] + numbers [g_i] equals target.
+#       + If we pass all tests, we have a solution.
+#
+
+while read -a numbers
+do   for ((a_i = 0; a_i < SIZE; a_i ++))
+     do  for ((b_i = 0; b_i < SIZE; b_i ++))
+         do  if   ((a_i == b_i))
+             then continue
+             fi
+             ((target = numbers[a_i] + numbers[b_i]))
+             for ((c_i = 0; c_i < SIZE; c_i ++))
+             do  if   ((a_i == c_i || b_i == c_i))
+                 then continue
+                 fi
+                 for ((d_i = 0; d_i < SIZE; d_i ++))
+                 do  if   ((a_i == d_i || b_i == d_i || c_i == d_i ||
+                            target != numbers[b_i] + numbers[c_i] +
+                                      numbers[d_i]))
+                     then continue
+                     fi
+                     for ((e_i = 0; e_i < SIZE; e_i ++))
+                     do  if   ((a_i == e_i || b_i == e_i ||
+                                c_i == e_i || d_i == e_i))
+                         then continue
+                         fi
+                         for ((f_i = 0; f_i < SIZE; f_i ++))
+                         do  if   ((a_i == f_i || b_i == f_i ||
+                                    c_i == f_i || d_i == f_i ||
+                                    e_i == f_i ||
+                                    target != numbers[d_i] + numbers[e_i] +
+                                              numbers[f_i]))
+                             then continue
+                             fi
+                             for ((g_i = 0; g_i < SIZE; g_i ++))
+                             do  if   ((a_i == g_i || b_i == g_i ||
+                                        c_i == g_i || d_i == g_i ||
+                                        e_i == g_i || f_i == g_i ||
+                                        target != numbers[f_i] + numbers[g_i]))
+                                 then continue
+                                 fi
+                                 printf "%d %d %d %d %d %d %d\n" \
+                                         ${numbers[$a_i]} ${numbers[$b_i]} \
+                                         ${numbers[$c_i]} ${numbers[$d_i]} \
+                                         ${numbers[$e_i]} ${numbers[$f_i]} \
+                                         ${numbers[$g_i]}
+                             done
+                         done
+                     done
+                 done
+             done
+         done
+     done
+done
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/blog.txt b/challenge-109/abigail/blog.txt
new file mode 100644
index 0000000000..a9b6fb2f3e
--- /dev/null
+++ b/challenge-109/abigail/blog.txt
@@ -0,0 +1 @@
+https://abigail.github.io/HTML/Perl-Weekly-Challenge/week-109-1.html
diff --git a/challenge-109/abigail/c/ch-1.c b/challenge-109/abigail/c/ch-1.c
new file mode 100644
index 0000000000..377caf63f3
--- /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 / 2; 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/c/ch-2.c b/challenge-109/abigail/c/ch-2.c
new file mode 100644
index 0000000000..19d95ad9f5
--- /dev/null
+++ b/challenge-109/abigail/c/ch-2.c
@@ -0,0 +1,87 @@
+# include <stdlib.h>
+# include <stdio.h>
+# include <string.h>
+
+/*
+ * See ../README.md
+ */
+
+/*
+ * Run as: cc -o ch-2.o ch-2.c; ./ch-2.o < input-file
+ */
+
+# define SIZE 7
+typedef int number;
+
+int main (void) {
+    number * numbers;
+    char *  line    = NULL;
+    size_t  len     = 0;
+
+    if ((numbers = (number *) malloc (SIZE * sizeof (number))) == NULL) {
+        perror ("Malloc numbers failed");
+        exit (1);
+    }
+
+    while (getline (&line, &len, stdin) != -1) {
+        if (sscanf (line, "%d %d %d %d %d %d %d",      &numbers [0],
+                           &numbers [1], &numbers [2], &numbers [3],
+                           &numbers [4], &numbers [5], &numbers [6]) != SIZE) {
+            continue;
+        }
+
+        for (size_t a_i = 0; a_i < SIZE; a_i ++) {
+            for (size_t b_i = 0; b_i < SIZE; b_i ++) {
+                if (a_i == b_i) {
+                    continue;
+                }
+                number target = numbers [a_i] + numbers [b_i];
+                for (size_t c_i = 0; c_i < SIZE; c_i ++) {
+                    if (a_i == c_i || b_i == c_i) {
+                        continue;
+                    }
+                    for (size_t d_i = 0; d_i < SIZE; d_i ++) {
+                        if (a_i == d_i || b_i == d_i || c_i == d_i ||
+                            target != numbers [b_i] + numbers [c_i] +
+                                      numbers [d_i]) {
+