# Number Rotations

*Author: Shlomi Fish*

https://projecteuler.net/problem=168

Consider the number 142857. We can right-rotate this number by moving the last digit (7) to the front of it, giving us 714285. It can be verified that 714285=5×142857. This demonstrates an unusual property of 142857: it is a divisor of its right-rotation.

Find the last 5 digits of the sum of all integers n, 10 < n < 10^100, that have this property.

Source code: prob168-shlomif.pl

use v6; sub MAIN(Bool :$verbose = False) { my $sum = 0; # $multiplier is "d" for 1 .. 9 -> $multiplier { for 1 .. 99 -> $L { # $digit is m. for 1 .. 9 -> $digit { my $n = (((10 ** $L - $multiplier)*$digit)/(10*$multiplier - 1)); my $number_to_check = $n * 10 + $digit; if ($n.chars() == $L and ($multiplier * $number_to_check == $n + $digit * 10 ** $L)) { print "Found $number_to_check\n" if $verbose; $sum += $number_to_check; print "Sum = $sum\n" if $verbose; } } } } if $verbose { say "Last 5 digits of the final sum are: ", "$sum".substr(*-5); } else { say "$sum".substr(*-5); } }