Merge pull request #3956 from dcw803/master

imported my solutions to this week's challenge..

3 files changed, 200 insertions, 38 deletions

diff --git a/challenge-109/duncan-c-white/README b/challenge-109/duncan-c-white/README
index 5b35941c97..18bce46ea5 100644
--- a/challenge-109/duncan-c-white/README
+++ b/challenge-109/duncan-c-white/README
@@ -1,56 +1,65 @@
-Task 1: "Locate Memory
+Task 1: "Chowla Numbers
 
-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:
 
-My notes: umm, does this just mean "use \ and %p", or something more subtle?
+C(n) = sum of divisors of n except 1 and n
 
+NOTE: Updated the above definition as suggested by Abigail [2021/04/19 18:40].
 
-Task 2: "Bell Numbers
+Output:
 
-Write a script to display top 10 Bell Numbers. Please refer to
+0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
+"
 
-https://en.wikipedia.org/wiki/Bell_number
+My notes: easy and fun.
 
-for more informations.
 
-Example:
+Task 2: "Four Squares Puzzle
 
-B0: 1 as you can only have one partition of zero element set
+You are given four squares as below with numbers named a,b,c,d,e,f,g.
 
-B1: 1 as you can only have one partition of one element set {a}.
+              (1)                    (3)
+        ===============     ===============
+        |             |     |             |
+        |     a       |     |     e       |
+        |             |(2)  |             | (4)
+        |         ---------------     --------------
+        |         |   |     |   |     |   |        |
+        |         | b |     | d |     | f |        |
+        |         |   |     |   |     |   |        |
+        |         |   |     |   |     |   |        |
+        ==========|====     ====|==========        |
+                  |      c      |     |     g      |
+                  |             |     |            |
+                  |             |     |            |
+                  ---------------     --------------
 
-B2: 2
+Write a script to place the given unique numbers in the square box so
+that sum of numbers in each box is the same.
 
-   {a}{b}
-   {a,b}
+Example
 
-B3: 5
+Input: 1,2,3,4,5,6,7
 
-   {a}{b}{c}
-   {a,b}{c}
-   {a}{b,c}
-   {a,c}{b}
-   {a,b,c}
+Output:
 
-B4: 15
+    a = 6
+    b = 4
+    c = 1
+    d = 5
+    e = 2
+    f = 3
+    g = 7
 
-   {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}
+    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
 "
 
-My notes: Bell's triangle has a simple algorithm; let's use that!
+My notes: sounds simple enough.  Find a,b,c,d,e,f st a+b = b+c+d = d+e+f = f+g
+Of course, we'll need to try all permutations of the values given.  There
+are lots of CPAN modules (eg. Algorithm::Permute), but here I decided to
+generate the permutations myself via Rosetta Stone code..
diff --git a/challenge-109/duncan-c-white/perl/ch-1.pl b/challenge-109/duncan-c-white/perl/ch-1.pl
new file mode 100755
index 0000000000..a0823e9de1
--- /dev/null
+++ b/challenge-109/duncan-c-white/perl/ch-1.pl
@@ -0,0 +1,52 @@
+#!/usr/bin/perl
+# 
+# Task 1: "Chowla Numbers
+# 
+# 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 except 1 and n
+# 
+# NOTE: Updated the above definition as suggested by Abigail [2021/04/19 18:40].
+# 
+# Output:
+# 
+# 0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 15, 0, 9, 8, 14, 0, 20, 0, 21
+# "
+# 
+# My notes: easy and fun.
+# 
+
+use strict;
+use warnings;
+use feature 'say';
+use Function::Parameters;
+#use Data::Dumper;
+
+
+#
+# my $x = chowla($n);
+#	Compute and return the $n'th Chowla number:
+#	the sum of the divisors of $n except 1 and $n.
+#
+fun chowla( $n )
+{
+	my $sum = 0;
+	foreach my $div (2..$n-1)
+	{
+		$sum += $div if $n%$div==0;
+	}
+	return $sum;
+}
+
+
+die "Usage: chowla N\n" unless @ARGV==1;
+my $n = shift;
+
+foreach my $i (1..$n)
+{
+	my $x = chowla($i);
+	say "c($i) = $x";
+}
+
diff --git a/challenge-109/duncan-c-white/perl/ch-2.pl b/challenge-109/duncan-c-white/perl/ch-2.pl
new file mode 100755
index 0000000000..1fec2892e6
--- /dev/null
+++ b/challenge-109/duncan-c-white/perl/ch-2.pl
@@ -0,0 +1,101 @@
+#!/usr/bin/perl
+# 
+# Task 2: "Four Squares Puzzle
+# 
+# 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 place the given unique numbers in the square box so
+# that sum of numbers in each box is the same.
+# 
+# Example
+# 
+# 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
+# "
+# 
+# My notes: sounds simple enough.  Find a,b,c,d,e,f st a+b = b+c+d = d+e+f = f+g
+# Of course, we'll need to try all permutations of the values given.  There
+# are lots of CPAN modules (eg. Algorithm::Permute), but here I generate the
+# permutations myself via Rosetta Stone code..
+# 
+
+use strict;
+use warnings;
+use feature 'say';
+use Function::Parameters;
+use Getopt::Long;
+#use Data::Dumper;
+
+my $debug = 0;
+die "Usage: four-squares [--debug] 7 values\n"
+	unless GetOptions("debug"=>\$debug) && @ARGV==7;
+my @v = @ARGV;
+
+
+#
+# allpermutations( \&eachpermcallback, $perm, @v );
+#	compute all permutations of @v with $perm on the front,
+#	calling eachpermcallback for each permutation found.
+#	Adapted from Rosetta Stone..
+#
+fun allpermutations( $cb, $perm, @v )
+{
+	if( @v == 0 )
+	{
+		$cb->( @$perm );
+		return;
+	}
+	foreach my $i (0..$#v)
+	{
+		# remove $v[$i] from the values, append it to the @$perm
+		allpermutations( $cb,
+			[ @$perm, $v[$i] ],
+			@v[0..$i-1], @v[$i+1..$#v] );
+	}
+}
+
+#
+# printifsolution( @perm );
+#	check whether @perm (7 values) is a four-square solution;
+#	print it if so.
+#
+fun printifsolution( @perm )
+{
+	die unless @perm==7;
+	my( $a, $b, $c, $d, $e, $f, $g ) = @perm;
+	my $sum = $a+$b;
+	return unless $sum == $b+$c+$d && $sum == $d+$e+$f && $sum == $f+$g;
+	say "solution: a=$a, b=$b, c=$c, d=$d, e=$e, f=$f, g=$g";
+}
+
+allpermutations( \&printifsolution, [], ,@v );