PWC107 - Self-descriptive Numbers


Here we are with TASK #1 from the Perl Weekly Challenge #107. Enjoy!

The challenge

Write a script to display the first three self-descriptive numbers. As per wikipedia, the definition of Self-descriptive Number is

In mathematics, a self-descriptive number is an integer m that in a given base b is b digits long in which each digit d at position n (the most significant digit being at position 0 and the least significant at position b−1) counts how many instances of digit n are in m.

The questions

My first question is about what do we mean by the first three? Is the ordering following from the ascending ordering of the bases, followed by some kind of ascending order for the numbers in each base?

Another question - this quite meta, I admit - was… didn’t I already solve this?. Sure, this is a repeated challenge… but I wasn’t participating into the challenge as of PWC 43, so there had to be something different.

And last another meta question - what are these challenges about? I mean, what does it mean to win the challenge? Is it the fastest to code a solution? A working solution, or any solution? I admit that I didn’t find anything to this regard (although I do the challenge for the pure fun of doing it and learn something).

The solution

It turns out that I did indeed solve a generalization of the problem. About one year ago, I started my Autobiographical Numbers series as a way to apply a small library about Constraint Programming.

And no, I will not inflict you with another series on the same topic.

This time I’ll leverage on the fact that only three numbers are requested, and that I hope (/know) that this will only involve little bases. Hence, a brute force attack will do:

#!/usr/bin/env perl
use 5.024;
use warnings;
use experimental qw< postderef signatures >;
no warnings qw< experimental::postderef experimental::signatures >;
use List::Util 'sum';

sub nested_loops_iterator {
   my ($dims, $opts, $cb, $accumulator) = @_;
   return unless scalar @{$dims};
   ($opts, $cb) = ($cb, $opts) if ref($opts) eq 'CODE';
   my @indexes     = (-1);
   my @accumulator = (undef) x scalar @{$dims};
   return sub {
      while ((my $level = $#indexes) >= 0) {
         my $dimension = $dims->[$level];
         my $i         = ++$indexes[$level];
         if ($i > $#{$dimension}) { pop @indexes }
         else {
            $accumulator[$level] = $dimension->[$i];
            if   ($level == $#{$dims}) { return @accumulator }
            else                       { push @indexes, -1 }

sub is_self_descriptive (@sequence) {
   for my $i (0 .. $#sequence) {
      my $count = sum map { $_ == $i ? 1 : 0 } @sequence;
      return unless $count == $sequence[$i];
   return 1;

sub three_self_descriptive_numbers {
   my ($b, @found) = (1);
   while ('necessary') {
      my $it = nested_loops_iterator([map { [0 .. ($b - 1)]} 1 .. $b]);
      while (my @args = $it->()) {
         push @found, join '', @args if is_self_descriptive(@args);
         return @found if @found == 3;
   return @found[0..2];

say join(', ', three_self_descriptive_numbers());

I’m probably killing a mosquito with a cannon, but I had the cannon in the backyard and so… why not?

We iterate through the bases and then through the values, looking for numbers that comply. As soon as we find three of them we exit… so it’s brute force with a hearth!

Stay safe people!

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