add solution when one of the numbers doesn't end in $d

1 files changed, 13 insertions, 1 deletions

diff --git a/challenge-113/james-smith/perl/ch-1.pl b/challenge-113/james-smith/perl/ch-1.pl
index efb023fcf0..d8445c8f47 100644
--- a/challenge-113/james-smith/perl/ch-1.pl
+++ b/challenge-113/james-smith/perl/ch-1.pl
@@ -7,7 +7,7 @@ use feature qw(say);
 use Test::More;
 use Benchmark qw(timethis);
 
-my @ex = ( [25,8,0], [25,7,0], [24,7,1], [24,0,0], [10,0,1], [28,8,1], [26,8,1], [16,8,0], [441,9,1], [431,9,0] );
+my @ex = ( [25,8,0], [25,7,0], [24,7,1], [24,0,0], [10,0,1], [28,8,1], [26,8,1], [16,8,0], [441,9,1], [431,9,1] );
 
 is( represent( $_->[0], $_->[1]), $_->[2] ) foreach @ex;
 
@@ -17,6 +17,18 @@ timethis( 1_000_000, sub { represent($_->[0],$_->[1]) for @ex } );
 say '';
 sub represent {
   my($t,$n,$d) = (0,@_);
+  ## If $d is equal to 0
+  ##   Any number between 100 & 109 can be represented by itself
+  ##   For numbers over 109 we can represent these as 100-109 + a
+  ##   number ending in 0...
+  ## If $n is between 10*$d and 10*$d+9 then it can be represented as $d$x
+  ##   For numbers > than this we can do a similar trick to above
+  ##   We can reprent them as $d$x + a number ending in $d
+  return 1 if $n >= 10 * ($d||10);
+  ## Finally we get to the list of numbers less than this - as the only
+  ## digit that can contain $d is the last one we just try to see if
+  ## we can find a sum of numbers ending in $d which have the same last
+  ## digit as $n and less than or equal to $n.
   $n>=($t+=$_*10+$d) && ($n%10 == $t%10) && return 1 for 0..9;
   0;
 }