Merge pull request #3659 from wlmb/challenges

Challenges

2 files changed, 40 insertions, 1 deletions

diff --git a/challenge-102/wlmb/perl/ch-1b.pl b/challenge-102/wlmb/perl/ch-1b.pl
index bf4950d7cd..269db9954f 100755
--- a/challenge-102/wlmb/perl/ch-1b.pl
+++ b/challenge-102/wlmb/perl/ch-1b.pl
@@ -23,7 +23,8 @@ for my $N(@ARGV){
 	    next A if $x>$max;
 	    my $y=join '', reverse split '', $x;
 	    next B unless $y==($a**2-$b**2)/2;
-	    say "$x $y $a $b";
+	    my ($s, $d)=($x+$y, $x-$y);
+	    say "N=$N\tx=$x\ty=$y\tx+y=$s=", sqrt($s),"**2\tx-y=$d=",sqrt($d),"**2";
       }
   }
 }
diff --git a/challenge-102/wlmb/perl/ch-1c.pl b/challenge-102/wlmb/perl/ch-1c.pl
new file mode 100755
index 0000000000..9773a7fdee
--- /dev/null
+++ b/challenge-102/wlmb/perl/ch-1c.pl
@@ -0,0 +1,38 @@
+#!/usr/bin/env perl
+# Perl weekly challenge 102
+# Task 1: Rare numbers
+# Faster by breaking the number at the middle.
+use strict;
+use warnings;
+use v5.12;
+use POSIX qw(floor);
+
+foreach my $N(@ARGV){
+    my $min=10**($N-1);
+    my $N2=floor($N/2);
+    my $M=10**$N2;
+    my %seen; # disctint squares mod $M
+    foreach my $a(0..10**$N2){
+	$seen{($a**2)%$M}=1;
+    }
+    my @squares=sort {$a<=>$b} keys %seen;
+    foreach my $a2(@squares){
+	foreach my $b2(@squares){
+	    my $xr=($a2+$b2);
+	    next unless $xr%2==0;
+	    $xr=sprintf("%0${N2}d",($xr/2)%$M);
+	    my $xl1=sprintf("%0${N2}d",(($a2-$b2)/2)%$M);
+	    foreach my $mid($N%2==0?(''):(0..9)){
+		my $x=join '', reverse(split '', $xl1), $mid, $xr;
+		next unless $x>=$min;
+		my $y=join '', reverse(split '', $x);
+		next unless $x>$y;
+		my $s=$x+$y;
+		my $d=$x-$y;
+		next unless floor(sqrt($s))**2==$s;
+		next unless floor(sqrt($d))**2==$d;
+		say "N=$N\tx=$x\ty=$y\tx+y=$s=", sqrt($s),"**2\tx-y=$d=",sqrt($d),"**2";
+	    }
+	}
+    }
+}