How deserve to you usage 50 American coins to include up to a dollar? The coins obtainable are a penny (1 cent), a nickel (5 cents), a dime (10 cents), a 4 minutes 1 (25 cents), and a half-dollar (50 cents).

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If you have not do the efforts to fix it, have actually a go now. For anyone else, the price is after the break.You need to use is 40 pennies, 8 nickels (40 cents) and 2 dimes (20 cents). Did you resolve it? any kind of other answers?

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I did fix it, however only through trial and also error. Feels favor there must be a tidy formula to reach the result

tibo says:
Eddie says:
Smylers says:

I wrote a fast Perl regime to find all the means of making $1 out of those coins, then screen just those which consist the 50 coins.

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There’s fixed anything to the algorithm: many of that it just dividing it down into simpler situations that can be solved trivially — view the comments because that details.

Running it finds both solutions:

$ ./50_coins50 coins: 45 × 1¢ + 2 × 10¢ + 1 × 25¢ + 2 × 5¢50 coins: 40 × 1¢ + 2 × 10¢ + 8 × 5¢

Here’s the program, greatly commented:

#! /usr/bin/perl

# 50_coins## do $1 out of 50 coins:

use v5.10;use warnings;use strict;

use List::AllUtils qw;

# discover all the means 100 deserve to be damaged down into the obtainable coins:foreach my $count (breakdown(100, (50, 25, 10, 5, 1)))

# count the complete coins used, and also display if there’s 50: my $coins = amount values %$count; speak qq<$coins coins: >, sign up with q< + >, map qq<$count->$_ × $_¢> sort keys %$count if $coins == 50;

sub breakdown# returns all the ways of make $target utilizing

# If the target is zero, then we deserve to make that (using no coins): return if $target == 0;

# Otherwise if there space no coins we can’t do anything: return if !

# If the target has actually gone below zero then it’s impossible to carry out anything: return if $target # at the very least one). The the feasible ways of make $target, they one of two people involve # the first coin or they don't — for example ways of making $1 have the right to be split # into those that use at the very least one 25¢ and also those the don't usage 25¢ at all. # work out every of those sets separately, and also return the merged list. # # use this function again to deal with each of the smaller troubles — which may # in turn involve invoking that again, and so on, till it reaches one of the # basic cases above. Stop Perl worrying the it'll never end: no warnings qw;


# The methods of make $1 utilizing at least one 25¢ coin is the exact same as including # one 25¢ coin to every of the ways of do 75¢ utilizing those coins # (including potentionally more 25¢ coins). So discover all the methods of # make that smaller target using the very same coins, and add one counting of the # very first coin into each the the breakdowns: map $_->$coin<0>++; $_ breakdown($target – $coin<0>,

# The means of making $1 there is no using any 25¢ coins is similar to that coin # had actually never been had in the list of enabled coins in the an initial place. # So uncover all the methods of making the very same target but without making use of the # first coin: breakdown($target,