user
From Wikipedia:

```
The McNuggets version of the coin problem was introduced by Henri Picciotto,
who included it in his algebra textbook co-authored with Anita Wah. Picciotto
thought of the application in the 1980s while dining with his son at
McDonald's, working the problem out on a napkin. A McNugget number is
the total number of McDonald's Chicken McNuggets in any number of boxes.
In the United Kingdom, the original boxes (prior to the introduction of
the Happy Meal-sized nugget boxes) were of 6, 9, and 20 nuggets.

```

Task

Calculate (from 0 up to a limit of 100) the largest non-McNuggets
number (a number *n* which cannot be expressed with *6x + 9y + 20z = n*
where *x*, *y* and *z* are natural numbers).
assistant
(formerly Perl 6)

**Works with**: Rakudo version 2018.09

No hard coded limits, no hard coded values. General purpose 3 value solver. Count values may be any 3 different positive integers, in any order, that are relatively prime.

Finds the smallest count value, then looks for the first run of consecutive count totals able to be generated, that is at least the length of the smallest count size. From then on, every number can be generated by simply adding multiples of the minimum count to each of the totals in that run.

```
sub Mcnugget-number (*@counts) {

    return '∞' if 1 < [gcd] @counts;

    my $min = min @counts;
    my @meals;
    my @min;

    for ^Inf -> $a {
        for 0..$a -> $b {
            for 0..$b -> $c {
                ($a, $b, $c).permutations.map: { @meals[ sum $_ Z* @counts ] = True }
            }
        }
        for @meals.grep: so *, :k {
            if @min.tail and @min.tail + 1 == $_ {
                @min.push: $_;
                last if $min == +@min
            } else {
                @min = $_;
            }
        }
        last if $min == +@min
    }
    @min[0] ?? @min[0] - 1 !! 0
}

for (6,9,20), (6,7,20), (1,3,20), (10,5,18), (5,17,44), (2,4,6), (3,6,15) -> $counts {
    put "Maximum non-Mcnugget number using {$counts.join: ', '} is: ",
        Mcnugget-number(|$counts)
}

```

Output:

```
Maximum non-Mcnugget number using 6, 9, 20 is: 43
Maximum non-Mcnugget number using 6, 7, 20 is: 29
Maximum non-Mcnugget number using 1, 3, 20 is: 0
Maximum non-Mcnugget number using 10, 5, 18 is: 67
Maximum non-Mcnugget number using 5, 17, 44 is: 131
Maximum non-Mcnugget number using 2, 4, 6 is: ∞
Maximum non-Mcnugget number using 3, 6, 15 is: ∞
```