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#!/Users/colincrain/perl5/perlbrew/perls/perl-5.32.0/bin/perl
#
# piles-of-pennies.pl
#
# Penny Piles
# Submitted by: Robbie Hatley
# You are given an integer, $n > 0.
#
# Write a script to determine the number of ways of putting $n
# pennies in a row of piles of ascending heights from left to right.
#
# Example
# Input: $n = 5
# Output: 7
#
# Since $n=5, there are 7 ways of stacking 5 pennies in ascending
# piles:
#
# 1 1 1 1 1
# 1 1 1 2
# 1 2 2
# 1 1 3
# 2 3
# 1 4
# 5
#
# method:
#
# The question is a rephrasing of a number theory problems
# known as integer partitions. It's a tricky business. We are
# computing the number of ways to section a positive integer
# into smaller (positive) integers that sum to the original
# value. The various orderings are considered multisets, with
# no implicit ordering, and rearrangements of the same elements
# are considered equivalent. Element values within the grouping
# can be duplicated, as illustrated by the example above.
#
# There is no known closed-form solution to the integer partition problem.
#
# Wea are not asked to enumerate the partitions, only count
# them. But why not? What are they trying to hide? WHAT DON'T
# THEY WANT US TO KNOW???
#
# I SAY, FREE THE PATTERNS!
#
# Once we expose the truth, the world will be able to see the
# patterns for what they are: piles of money, growing higher, a
# literal stairway to heaven, built on the backs of the
# proletraiat.
#
# © 2022 colin crain
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
use warnings;
use strict;
use utf8;
use feature ":5.26";
use feature qw(signatures);
no warnings 'experimental::signatures';
use Math::Prime::Util qw( forpart partitions );
my $value = shift @ARGV // 19;
my $count;
forpart { $count++; say "@_" } $value ;
say "\nfound $count arrangements of pennies";
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