RogerBW's Blog

I’ve been doing the Perl Weekly Challenges. The latest was about allocating numbers to rings and generating self-descriptive numbers.

The difficulty with the first problem was in working out what was meant to be going on. After that it was just a matter of allocating each number to each slot and checking the result. No clever coding here, and since giving code would spoil the problem, I won't. I found three solutions that satisfy the constraint.

For the second, I used an iterative approach for bases 4 and 5 (start with "1" followed by a relevant number of "0", count digits and construct a new number, repeat until stable). For bases 7+, the initial seed is changed to a known good result, because starting with 1000… doesn't necessarily converge on a valid answer.

my @n=(0) x $base;

$n[0]=1;

if ($base>6) {
  $n[0]=$base-4;
  $n[1]=2;
  $n[2]=1;
  $n[$base-4]=1
}
while (1) {
  my @o=@n;
  my %o;
  map {$o{$_}++} @o;
  foreach my $i (0..$#o) {
    $n[$i]=$o{$i} || 0;
  }
  if (join('',@o) eq join('',@n)) {
    last;
  }
}