# Reciprocal cycles

Author: Shlomi Fish

https://projecteuler.net/problem=26

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

```1/2 =       0.5
1/3 =       0.(3)
1/4 =       0.25
1/5 =       0.2
1/6 =       0.1(6)
1/7 =       0.(142857)
1/8 =       0.125
1/9 =       0.(1)
1/10        =       0.1
```

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

Source code: prob026-shlomif.pl

```use v6;

sub find_cycle_len(Int \$n) returns Int {
my %states;

my \$r = 1;
my \$count = 0;

while ! ( %states{\$r}:exists ) {
# \$*ERR.say( "Trace: N = \$n ; R = \$r" );
%states{\$r} = \$count++;
(\$r *= 10) %= \$n;
}

return \$count - %states{\$r};
}

my \$max_cycle_len = -1;
my \$max_n;

for (2 .. 999) -> \$n {
if ((my \$cycle_len = find_cycle_len(\$n)) > \$max_cycle_len) {
\$max_n = \$n;
\$max_cycle_len = \$cycle_len;
}
}

say "The recurring cycle is \$max_n, and the cycle length is \$max_cycle_len";

```