+A row of five black square tiles is to have a number of its tiles replaced with
+coloured oblong tiles chosen from red (length two), green (length three), or
+If red tiles are chosen there are exactly seven ways this can be done.
+If green tiles are chosen there are three ways.
+And if blue tiles are chosen there are two ways.
+Assuming that colours cannot be mixed there are 7 + 3 + 2 = 12 ways of
+replacing the black tiles in a row measuring five units in length.
+How many different ways can the black tiles in a row measuring fifty units in
+length be replaced if colours cannot be mixed and at least one coloured tile
+NOTE: This is related to problem 117.
+use Math::GMP qw(:constant);
+ my ($tile_len, $total_len) = @_;
+ foreach my $len (0 .. $tile_len-1)
+ for my $len ($tile_len .. $total_len)
+ push @counts, $counts[-$tile_len]+$counts[-1];
+ # We need to exclude the all-black-squares one which is:
+ # 2. Should not be included.
+ return count(2, $total_len) + count(3, $total_len) + count(4, $total_len);
+print count_for_234(50), "\n";