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# McNuggets Problem

McNuggets Problem
You are encouraged to solve this task according to the task description, using any language you may know.
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.
```

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).

`with Ada.Text_IO; use Ada.Text_IO; procedure McNugget is   Limit : constant                      := 100;   List  : array (0 .. Limit) of Boolean := (others => False);   N     : Integer;begin   for A in 0 .. Limit / 6 loop      for B in 0 .. Limit / 9 loop         for C in 0 .. Limit / 20 loop            N := A * 6 + B * 9 + C * 20;            if N <= 100 then               List (N) := True;            end if;         end loop;      end loop;   end loop;   for N in reverse 1 .. Limit loop      if not List (N) then         Put_Line ("The largest non McNugget number is:" & Integer'Image (N));         exit;      end if;   end loop;end McNugget;`
Output:
```The largest non McNugget number is: 43
```

## ALGOL 68

`BEGIN    # Solve the McNuggets problem: find the largest n <= 100 for which there #    # are no non-negative integers x, y, z such that 6x + 9y + 20z = n       #    INT max nuggets = 100;    [ 0 : max nuggets ]BOOL sum;    FOR i FROM LWB sum TO UPB sum DO sum[ i ] := FALSE OD;    FOR x FROM 0 BY 6 TO max nuggets DO        FOR y FROM 0 BY 9 TO max nuggets DO            FOR z FROM 0 BY 20 TO max nuggets DO                INT nuggets = x + y + z;                IF nuggets <= max nuggets THEN sum[ nuggets ] := TRUE FI            OD # z #        OD # y #    OD # x # ;    # show the highest number that cannot be formed                          #    INT largest := -1;    FOR i FROM UPB sum BY -1 TO LWB sum WHILE largest := i; sum[ i ] DO SKIP OD;    print( ( "The largest non McNugget number is: "           , whole( largest, 0 )           , newline           )         )END`
Output:
```The largest non McNugget number is: 43
```

## AppleScript

Generalised for other set sizes, and for other triples of natural numbers. Uses NSMutableSet, through the AppleScript ObjC interface:

`use AppleScript version "2.4"use framework "Foundation"use scripting additions  on run    set setNuggets to mcNuggetSet(100, 6, 9, 20)     script isMcNugget        on |λ|(x)            setMember(x, setNuggets)        end |λ|    end script    set xs to dropWhile(isMcNugget, enumFromThenTo(100, 99, 1))     set setNuggets to missing value -- Clear ObjC pointer value    if 0 < length of xs then        item 1 of xs    else        "No unreachable quantities in this range"    end ifend run -- mcNuggetSet :: Int -> Int -> Int -> Int -> ObjC Seton mcNuggetSet(n, mcx, mcy, mcz)    set upTo to enumFromTo(0)    script fx        on |λ|(x)            script fy                on |λ|(y)                    script fz                        on |λ|(z)                            set v to sum({mcx * x, mcy * y, mcz * z})                            if 101 > v then                                {v}                            else                                {}                            end if                        end |λ|                    end script                    concatMap(fz, upTo's |λ|(n div mcz))                end |λ|            end script            concatMap(fy, upTo's |λ|(n div mcy))        end |λ|    end script    setFromList(concatMap(fx, upTo's |λ|(n div mcx)))end mcNuggetSet  -- GENERIC FUNCTIONS ---------------------------------------------------- -- concatMap :: (a -> [b]) -> [a] -> [b]on concatMap(f, xs)    set lng to length of xs    set acc to {}    tell mReturn(f)        repeat with i from 1 to lng            set acc to acc & |λ|(item i of xs, i, xs)        end repeat    end tell    return accend concatMap  -- drop :: Int -> [a] -> [a]-- drop :: Int -> String -> Stringon drop(n, xs)    set c to class of xs    if c is not script then        if c is not string then            if n < length of xs then                items (1 + n) thru -1 of xs            else                {}            end if        else            if n < length of xs then                text (1 + n) thru -1 of xs            else                ""            end if        end if    else        take(n, xs) -- consumed        return xs    end ifend drop -- dropWhile :: (a -> Bool) -> [a] -> [a]-- dropWhile :: (Char -> Bool) -> String -> Stringon dropWhile(p, xs)    set lng to length of xs    set i to 1    tell mReturn(p)        repeat while i ≤ lng and |λ|(item i of xs)            set i to i + 1        end repeat    end tell    drop(i - 1, xs)end dropWhile -- enumFromThenTo :: Int -> Int -> Int -> [Int]on enumFromThenTo(x1, x2, y)    set xs to {}    repeat with i from x1 to y by (x2 - x1)        set end of xs to i    end repeat    return xsend enumFromThenTo -- enumFromTo :: Int -> Int -> [Int]on enumFromTo(m)    script        on |λ|(n)            if m ≤ n then                set lst to {}                repeat with i from m to n                    set end of lst to i                end repeat                return lst            else                return {}            end if        end |λ|    end scriptend enumFromTo -- foldl :: (a -> b -> a) -> a -> [b] -> aon foldl(f, startValue, xs)    tell mReturn(f)        set v to startValue        set lng to length of xs        repeat with i from 1 to lng            set v to |λ|(v, item i of xs, i, xs)        end repeat        return v    end tellend foldl -- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: First-class m => (a -> b) -> m (a -> b)on mReturn(f)    if class of f is script then        f    else        script            property |λ| : f        end script    end ifend mReturn -- sum :: [Num] -> Numon sum(xs)    script add        on |λ|(a, b)            a + b        end |λ|    end script     foldl(add, 0, xs)end sum -- NB All names of NSMutableSets should be set to *missing value*-- before the script exits.-- ( scpt files can not be saved if they contain ObjC pointer values )-- setFromList :: Ord a => [a] -> Set aon setFromList(xs)    set ca to current application    ca's NSMutableSet's ¬        setWithArray:(ca's NSArray's arrayWithArray:(xs))end setFromList -- setMember :: Ord a => a -> Set a -> Boolon setMember(x, objcSet)    missing value is not (objcSet's member:(x))end setMember`
Output:
`43`

## AWK

` # syntax: GAWK -f MCNUGGETS_PROBLEM.AWK# converted from GoBEGIN {    limit = 100    for (a=0; a<=limit; a+=6) {      for (b=a; b<=limit; b+=9) {        for (c=b; c<=limit; c+=20) {          arr[c] = 1        }      }    }    for (i=limit; i>=0; i--) {      if (!arr[i]+0) {        printf("%d\n",i)        break      }    }    exit(0)} `
Output:
```43
```

## C

`#include <stdio.h> intmain() {    int max = 0, i = 0, sixes, nines, twenties; loopstart: while (i < 100) {        for (sixes = 0; sixes*6 < i; sixes++) {            if (sixes*6 == i) {                i++;                goto loopstart;            }             for (nines = 0; nines*9 < i; nines++) {                if (sixes*6 + nines*9 == i) {                    i++;                    goto loopstart;                }                 for (twenties = 0; twenties*20 < i; twenties++) {                    if (sixes*6 + nines*9 + twenties*20 == i) {                        i++;                        goto loopstart;                    }                }            }        }        max = i;        i++;    }     printf("Maximum non-McNuggets number is %d\n", max);     return 0;}`
Output:
```Maximum non-McNuggets number is 43
```

## C#

` using System; public class McNuggets{   public static void Main()   {      bool[] isMcNuggetNumber = new bool;       for (int x = 0; x <= 100/6; x++)      {         for (int y = 0; y <= 100/9; y++)         {            for (int z = 0; z <= 100/20; z++)            {               int mcNuggetNumber = x*6 + y*9 + z*20;               if (mcNuggetNumber <= 100)               {                  isMcNuggetNumber[mcNuggetNumber] = true;               }            }         }       }       for (int mnnCheck = isMcNuggetNumber.Length-1; mnnCheck >= 0; mnnCheck--)      {         if (!isMcNuggetNumber[mnnCheck])         {            Console.WriteLine("Largest non-McNuggett Number less than 100: " + mnnCheck.ToString());            break;         }      }   }} `
Output:
```Largest non-McNuggett Number less than 100: 43
```

## Clojure

`(defn cart [colls]  (if (empty? colls)    '(())    (for [more (cart (rest colls))          x (first colls)]      (cons x more)))) (defn nuggets [[n6 n9 n20]] (+ (* 6 n6) (* 9 n9) (* 20 n20))) (let [possible (distinct (map nuggets (cart (map range [18 13 6]))))      mcmax (apply max (filter (fn [x] (not-any? #{x} possible)) (range 101)))]  (printf "Maximum non-McNuggets number is %d\n" mcmax))`
Output:
`Maximum non-McNuggets number is 43`

## Dart

`import 'dart:math';main() {  var nuggets = List<int>.generate(101, (int index) => index);  for (int small in List<int>.generate((100 ~/ (6 + 1)), (int index) => index)) {    for (int medium in List<int>.generate((100 ~/ (9 + 1)), (int index) => index)) {      for (int large in List<int>.generate((100 ~/ (20 + 1)), (int index) => index)) {        nuggets.removeWhere((element) => element == 6 * small + 9 * medium + 20 * large);      }    }  }  print('Largest non-McNuggets number: \${nuggets.reduce(max).toString() ?? 'none'}.');}`
Output:
`Largest non-McNuggets number: 43.`

## Dyalect

Translation of: Go
`func mcnugget(limit) {    var sv = Array.empty(limit + 1, false)    var s = 0    while s <= limit {        var n = s        while n <= limit {            var t = n            while t <= limit {                sv[t] = true                t += 20            }            n += 9        }        s += 6    }    for i in limit..0 {        if !sv[i] {            print("Maximum non-McNuggets number is \(i)")            return        }    }} mcnugget(100)`
Output:
`Maximum non-McNuggets number is 43`

## Elixir

Uses MapSet and Comprehension

`defmodule Mcnugget do  def solve(limit) do    0..limit    |> MapSet.new()    |> MapSet.difference(      for(        x <- 0..limit,        y <- 0..limit,        z <- 0..limit,        Integer.mod(x, 6) == 0,        Integer.mod(y, 9) == 0,        Integer.mod(z, 20) == 0,        x + y + z <= limit,        into: MapSet.new(),        do: x + y + z      )    )    |> Enum.max()  endend Mcnugget.solve(100) |> IO.puts `
Output:
`43`

## F#

` // McNuggets. Nigel Galloway: October 28th., 2018let fN n g = Seq.initInfinite(fun ng->ng*n+g)|>Seq.takeWhile(fun n->n<=100)printfn "%d" (Set.maxElement(Set.difference (set[1..100]) (fN 20 0|>Seq.collect(fun n->fN 9 n)|>Seq.collect(fun n->fN 6 n)|>Set.ofSeq))) `
Output:
```43
```

## Factor

`USING: backtrack kernel math.ranges prettyprint sequences sets ;101 <iota> [ 0 6 9 20 [ 100 swap <range> amb-lazy ] [email protected] ] bag-of diff last .`
Output:
```43
```

## FreeBASIC

` Dim As Integer l(100), a, b, c, nFor a = 0 To 100/6    For b =  0 To 100/9        For c = 0 To 100/20            n = a*6 + b*9 + c*20            If n <= 100 Then l(n) = true        Next c    Next bNext aFor n = 100 To 1 Step -1    If l(n) = false Then Print "El mayor número que no sea McNugget es:"; n: Exit ForNext nEnd `
Output:
```El mayor número que no sea McNugget es: 43
```

## Go

`package main import "fmt" func mcnugget(limit int) {    sv := make([]bool, limit+1) // all false by default    for s := 0; s <= limit; s += 6 {        for n := s; n <= limit; n += 9 {            for t := n; t <= limit; t += 20 {                sv[t] = true            }        }    }    for i := limit; i >= 0; i-- {        if !sv[i] {            fmt.Println("Maximum non-McNuggets number is", i)            return        }    }} func main() {    mcnugget(100)}`
Output:
```Maximum non-McNuggets number is 43
```

`import Data.Set (Set, fromList, member) gaps :: [Int]gaps = dropWhile (`member` mcNuggets) [100,99 .. 1] mcNuggets :: Set IntmcNuggets =  let size = enumFromTo 0 . quot 100  in fromList \$     size 6 >>=     \x ->        size 9 >>=        \y ->           size 20 >>=           \z ->              let v = sum [6 * x, 9 * y, 20 * z]              in [ v                 | 101 > v ] main :: IO ()main =  print \$  case gaps of    x:_ -> show x    []  -> "No unreachable quantities found ..."`

Or equivalently, making use of the list comprehension notation:

`import Data.Set (Set, fromList, member) gaps :: [Int]gaps = dropWhile (`member` mcNuggets) [100,99 .. 1] mcNuggets :: Set IntmcNuggets =  let size n = [0 .. quot 100 n]  in fromList       [ v       | x <- size 6        , y <- size 9        , z <- size 20        , let v = sum [6 * x, 9 * y, 20 * z]        , 101 > v ] main :: IO ()main =  print \$  case gaps of    x:_ -> show x    []  -> "No unreachable quantities found ..."`
`43`

## J

Brute force solution: calculate all pure (just one kind of box) McNugget numbers which do not exceed 100, then compute all possible sums, and then remove those from the list of numbers up to 100 (which is obviously a McNugget number), then find the largest number remaining:

`   >./(i.100)-.,+/&>{(* [email protected]>[email protected]%~&101)&.>6 9 20 43`

Technically, we could have used 100 in place of 101 when we were finding how many pure McNugget numbers were in each series (because 100 is obviously a McNugget number), but it's not like that's a problem, either.

## Java

`public class McNuggets {     public static void main(String... args) {        int[] SIZES = new int[] { 6, 9, 20 };        int MAX_TOTAL = 100;        // Works like Sieve of Eratosthenes        int numSizes = SIZES.length;        int[] counts = new int[numSizes];        int maxFound = MAX_TOTAL + 1;        boolean[] found = new boolean[maxFound];        int numFound = 0;        int total = 0;        boolean advancedState = false;        do {            if (!found[total]) {                found[total] = true;                numFound++;            }             // Advance state            advancedState = false;            for (int i = 0; i < numSizes; i++) {                int curSize = SIZES[i];                if ((total + curSize) > MAX_TOTAL) {                    // Reset to zero and go to the next box size                    total -= counts[i] * curSize;                    counts[i] = 0;                }                else {                    // Adding a box of this size still keeps the total at or below the maximum                    counts[i]++;                    total += curSize;                    advancedState = true;                    break;                }            }         } while ((numFound < maxFound) && advancedState);         if (numFound < maxFound) {            // Did not find all counts within the search space            for (int i = MAX_TOTAL; i >= 0; i--) {                if (!found[i]) {                    System.out.println("Largest non-McNugget number in the search space is " + i);                    break;                }            }        }        else {            System.out.println("All numbers in the search space are McNugget numbers");        }         return;    }}`
Output:
`Largest non-McNugget number in the search space is 43`

## JavaScript

`(() => {    'use strict';     // main :: IO ()    const main = () => {        const            size = n => enumFromTo(0)(                quot(100, n)            ),            nuggets = new Set(                size(6).flatMap(                    x => size(9).flatMap(                        y => size(20).flatMap(                            z => {                                const v = sum([6 * x, 9 * y, 20 * z]);                                return 101 > v ? (                                    [v]                                ) : [];                            }                        ),                    )                )            ),            xs = dropWhile(                x => nuggets.has(x),                enumFromThenTo(100, 99, 1)            );         return 0 < xs.length ? (            xs        ) : 'No unreachable quantities found in this range';    };      // GENERIC FUNCTIONS ----------------------------------     // dropWhile :: (a -> Bool) -> [a] -> [a]    const dropWhile = (p, xs) => {        const lng = xs.length;        return 0 < lng ? xs.slice(            until(                i => i === lng || !p(xs[i]),                i => 1 + i,                0            )        ) : [];    };     // enumFromThenTo :: Int -> Int -> Int -> [Int]    const enumFromThenTo = (x1, x2, y) => {        const d = x2 - x1;        return Array.from({            length: Math.floor(y - x2) / d + 2        }, (_, i) => x1 + (d * i));    };     // ft :: Int -> Int -> [Int]    const enumFromTo = m => n =>        Array.from({            length: 1 + n - m        }, (_, i) => m + i);     // quot :: Int -> Int -> Int    const quot = (n, m) => Math.floor(n / m);     // sum :: [Num] -> Num    const sum = xs => xs.reduce((a, x) => a + x, 0);     // until :: (a -> Bool) -> (a -> a) -> a -> a    const until = (p, f, x) => {        let v = x;        while (!p(v)) v = f(v);        return v;    };     // MAIN ---    return console.log(        main()    );})();`
Output:
`43`

## jq

Translation of: Clojure
`[ [range(18) as \$n6  |  range(13) as \$n9  |  range(6)  as \$n20 |  (\$n6 * 6 + \$n9 * 9 + \$n20 * 20)] | unique | . as \$possible | range(101) | . as \$n | select(\$possible|contains([\$n])|not)] |max`
Output:
`43`

## Julia

Simple brute force solution, though the BitSet would save memory considerably with larger max numbers.

`function mcnuggets(max)    b = BitSet(1:max)    for i in 0:6:max, j in 0:9:max, k in 0:20:max        delete!(b, i + j + k)    end    maximum(b)end println(mcnuggets(100)) `
Output:
```
43

```

## Kotlin

Translation of: Go
`// Version 1.2.71 fun mcnugget(limit: Int) {    val sv = BooleanArray(limit + 1)  // all false by default    for (s in 0..limit step 6)        for (n in s..limit step 9)            for (t in n..limit step 20) sv[t] = true     for (i in limit downTo 0) {        if (!sv[i]) {            println("Maximum non-McNuggets number is \$i")            return        }    }} fun main(args: Array<String>) {    mcnugget(100)}`
Output:
```Maximum non-McNuggets number is 43
```

## Locomotive Basic

`100 CLEAR110 DIM a(100)120 FOR a=0 TO 100/6130   FOR b=0 TO 100/9140     FOR c=0 TO 100/20150       n=a*6+b*9+c*20160       IF n<=100 THEN a(n)=1170     NEXT c180   NEXT b190 NEXT a200 FOR n=0 TO 100210   IF a(n)=0 THEN l=n220 NEXT n230 PRINT"The Largest non McNugget number is:";l240 END`
Output:
`The largest non McNugget number is: 43`

## Lua

` function range(A,B)    return function()        return coroutine.wrap(function()            for i = A, B do coroutine.yield(i) end        end)    endend function filter(stream, f)    return function()        return coroutine.wrap(function()            for i in stream() do                if f(i) then coroutine.yield(i) end            end        end)    endend function triple(s1, s2, s3)    return function()        return coroutine.wrap(function()            for x in s1() do                for y in s2() do                    for z in s3() do                        coroutine.yield{x,y,z}                    end                end            end        end)    endend function apply(f, stream)    return function()        return coroutine.wrap(function()            for T in stream() do                coroutine.yield(f(table.unpack(T)))            end        end)    endend function exclude(s1, s2)    local exlusions = {} for x in s1() do exlusions[x] = true end    return function()        return coroutine.wrap(function()            for x in s2() do                if not exlusions[x] then                    coroutine.yield(x)                end            end        end)    endend function maximum(stream)    local M = math.mininteger    for x in stream() do        M = math.max(M, x)    end    return Mend local N = 100local A, B, C = 6, 9, 20 local Xs = filter(range(0, N), function(x) return x  % A == 0 end)local Ys = filter(range(0, N), function(x) return x  % B == 0 end)local Zs = filter(range(0, N), function(x) return x  % C == 0 end)local sum = filter(apply(function(x, y, z) return x + y + z end, triple(Xs, Ys, Zs)), function(x) return x <= N end) print(maximum(exclude(sum, range(1, N)))) `
Output:
```43
```

## Mathematica

`Complement[Range,   Select[6 #[] + 9 #[] + 20 #[] & /@     Tuples[Range[0, 17], 3], # < 101 &]][[-1]]`
Output:
```43
```

## MiniZinc

` %McNuggets. Nigel Galloway, August 27th., 2019var 0..99: n;constraint forall(x in 0..16,y in 0..11,z in 0..5)(6*x + 9*y + 20*z!=n);solve maximize n;output [show(n)] `
Output:
```43
----------
==========
```

## Perl

Translation of: Raku
Library: ntheory
`use ntheory qw/forperm gcd vecmin/; sub Mcnugget_number {    my \$counts = shift;     return 'No maximum' if 1 < gcd @\$counts;     my \$min = vecmin @\$counts;    my @meals;    my @min;     my \$a = -1;    while (1) {        \$a++;        for my \$b (0..\$a) {            for my \$c (0..\$b) {                my @s = (\$a, \$b, \$c);                forperm {                    \$meals[                        \$s[\$_] * \$counts->                      + \$s[\$_] * \$counts->                      + \$s[\$_] * \$counts->                    ] = 1;                } @s;            }        }        for my \$i (0..\$#meals) {            next unless \$meals[\$i];            if (\$min[-1] and \$i == (\$min[-1] + 1)) {                push @min, \$i;                last if \$min == @min            } else {                @min = \$i;            }        }        last if \$min == @min    }    \$min ? \$min - 1 : 0} for my \$counts ([6,9,20], [6,7,20], [1,3,20], [10,5,18], [5,17,44], [2,4,6], [3,6,15]) {    print 'Maximum non-Mcnugget number using ' . join(', ', @\$counts) . ' is: ' . Mcnugget_number(\$counts) . "\n"}`
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: No maximum
Maximum non-Mcnugget number using 3, 6, 15 is: No maximum```

### Perl using Regex

`use strict;use warnings; \$_ = 1 . 0 x 100;1 while s/ (?=1) (?:.{6}|.{9}|.{20}) \K 0 /1/x;/01*\$/ and print "Maximum non-Mcnugget number is: \$-\n";`
Output:
`Maximum non-Mcnugget number is: 43`

## Phix

Translation of: Go
`constant limit=100sequence nuggets = repeat(false,limit+1)for sixes=0 to limit by 6 do    for nines=sixes to limit by 9 do        for twenties=nines to limit by 20 do            nuggets[twenties+1] = true        end for    end forend forprintf(1,"Maximum non-McNuggets number is %d\n", rfind(false,nuggets)-1)`
Output:
```Maximum non-McNuggets number is 43
```

Also, since it is a bit more interesting, a

Translation of: Raku
`function Mcnugget_number(sequence counts)     if gcd(counts)>1 then return "No maximum" end if     atom cmin = min(counts)    sequence meals = {}    sequence smin = {}     integer a = -1    while true do        a += 1        for b=0 to a do            for c=0 to b do                sequence s = {a, b, c}                for i=1 to factorial(3) do                    sequence p = permute(i,s)                    integer k = sum(sq_mul(p,counts))+1                    if k>length(meals) then meals &= repeat(0,k-length(meals)) end if                    meals[k] = 1                end for            end for        end for        for i=1 to length(meals) do            if meals[i] then                if length(smin) and smin[\$]+1=i-1 then                    smin = append(smin,i-1)                    if length(smin)=cmin then exit end if                else                    smin = {i-1}                end if            end if        end for        if length(smin)=cmin then exit end if    end while    return sprintf("%d",iff(smin?smin-1:0))end function constant tests = {{6,9,20}, {6,7,20}, {1,3,20}, {10,5,18}, {5,17,44}, {2,4,6}, {3,6,15}}for i=1 to length(tests) do    sequence ti = tests[i]    printf(1,"Maximum non-Mcnugget number using %s is: %s\n",{sprint(ti),Mcnugget_number(ti)})end for`
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: No maximum
Maximum non-Mcnugget number using {3,6,15} is: No maximum
```

## PicoLisp

`(de nuggets1 (M)   (let Lst (range 0 M)      (for A (range 0 M 6)         (for B (range A M 9)            (for C (range B M 20)               (set (nth Lst (inc C))) ) ) )      (apply max Lst) ) )`

Generator from fiber:

`(de nugg (M)   (co 'nugget      (for A (range 0 M 6)         (for B (range A M 9)            (for C (range B M 20)               (yield (inc C)) ) ) ) ) )(de nuggets2 (M)   (let Lst (range 0 M)       (while (nugg 100)         (set (nth Lst @)) )      (apply max Lst) ) )`

Test versions against each other:

`(test   T   (=      43      (nuggets1 100)      (nuggets2 100) ) )`

## PowerShell

Translation of: UNIX Shell
`\$possible = @{}For (\$i=0; \$i -lt 18; \$i++) {  For (\$j=0; \$j -lt 13; \$j++) {    For ( \$k=0; \$k -lt 6; \$k++ ) {      \$possible[ \$i*6 + \$j*9 + \$k*20 ] = \$true    }  }} For ( \$n=100; \$n -gt 0; \$n-- ) {  If (\$possible[\$n]) {    Continue  }  Else {    Break  }}Write-Host "Maximum non-McNuggets number is \$n"`
Output:
`Maximum non-McNuggets number is 43`

## Python

### Python: REPL

It's a simple solution done on the command line:

`>>> from itertools import product>>> nuggets = set(range(101))>>> for s, n, t in product(range(100//6+1), range(100//9+1), range(100//20+1)):	nuggets.discard(6*s + 9*n + 20*t)  >>> max(nuggets)43>>> `

Single expression version (expect to be slower, however no noticeable difference on a Celeron B820 and haven't benchmarked):

`>>> from itertools import product>>> max(x for x in range(100+1) if x not in...   (6*s + 9*n + 20*t for s, n, t in...     product(range(100//6+1), range(100//9+1), range(100//20+1))))43>>> `

### Using Set Comprehension

Translation of: FSharp
` #Wherein I observe that Set Comprehension is not intrinsically dysfunctional. Nigel Galloway: October 28th., 2018n = {n for x in range(0,101,20) for y in range(x,101,9) for n in range(y,101,6)}g = {n for n in range(101)}print(max(g.difference(n))) `
Output:
```43
```

A composition of pure functions, including dropwhile, which shows a more verbose and unwieldy (de-sugared) route to list comprehension, and reveals the underlying mechanics of what the (compact and elegant) built-in syntax expresses. May help to build intuition for confident use of the latter.

Note that the innermost function wraps its results in a (potentially empty) list. The resulting list of lists, some empty, is then flattened by the concatenation component of bind.

Works with: Python version 3.7
`'''mcNuggets list monad''' from itertools import (chain, dropwhile)  # mcNuggetsByListMonad :: Int -> Set Intdef mcNuggetsByListMonad(limit):    '''McNugget numbers up to limit.'''     box = size(limit)    return set(bind(box(6))(        lambda x:         bind(box(9))(            lambda y:             bind(box(20))(                lambda z: (                     lambda v=sum([x, y, z]): (                        [] if v > limit else [v]                    )                )()))))  # Which, for comparison, is equivalent to: # mcNuggetsByComprehension :: Int -> Set Intdef mcNuggetsByComprehension(limit):    '''McNuggets numbers up to limit'''    box = size(limit)    return {        v for v in (            sum([x, y, z])            for x in box(6)            for y in box(9)            for z in box(20)        ) if v <= limit    }  # size :: Int -> Int -> [Int]def size(limit):    '''Multiples of n up to limit.'''    return lambda n: enumFromThenTo(0)(n)(limit)  # TEST -----------------------------------------------------------def main():    '''List monad and set comprehension - parallel routes'''     def test(limit):        def go(nuggets):            ys = list(dropwhile(                lambda x: x in nuggets,                enumFromThenTo(limit)(limit - 1)(1)            ))            return str(ys) if ys else (                'No unreachable targets in this range.'            )        return lambda nuggets: go(nuggets)     def fName(f):        return f.__name__     limit = 100    print(        fTable(main.__doc__ + ':\n')(fName)(test(limit))(            lambda f: f(limit)        )([mcNuggetsByListMonad, mcNuggetsByComprehension])    )  # GENERIC ABSTRACTIONS ------------------------------------ # bind (>>=) :: [a] -> (a -> [b]) -> [b]def bind(xs):    '''List monad injection operator.       Two computations sequentially composed,       with any value produced by the first       passed as an argument to the second.    '''    return lambda f: list(        chain.from_iterable(            map(f, xs)        )    )  # enumFromThenTo :: Int -> Int -> Int -> [Int]def enumFromThenTo(m):    '''Integer values enumerated from m to n       with a step defined by nxt - m.    '''    def go(nxt, n):        d = nxt - m        return range(m, n - 1 if d < 0 else 1 + n, d)    return lambda nxt: lambda n: list(go(nxt, n))  # FORMATTING ---------------------------------------------- # fTable :: String -> (a -> String) ->#                     (b -> String) -> (a -> b) -> [a] -> Stringdef fTable(s):    '''Heading -> x display function -> fx display function ->                     f -> xs -> tabular string.    '''    def go(xShow, fxShow, f, xs):        ys = [xShow(x) for x in xs]        w = max(map(len, ys))        return s + '\n' + '\n'.join(map(            lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),            xs, ys        ))    return lambda xShow: lambda fxShow: lambda f: lambda xs: go(        xShow, fxShow, f, xs    )  # MAIN ---if __name__ == '__main__':    main()`
Output:
```List monad and set comprehension - parallel routes:

mcNuggetsByComprehension -> 43```

## Racket

Translation of: Python
(one of them)
`#lang racket(apply max (set->list (for*/fold ((s (list->set (range 1 101))))                                 ((x (in-range 0 101 20))                                  (y (in-range x 101 9))                                  (n (in-range y 101 6)))                        (set-remove s n))))`

## Raku

(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 == [email protected]min            } else {                @min = \$_;            }        }        last if \$min == [email protected]min    }    @min ?? @min - 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: ∞```

## REXX

This REXX version generalizes the problem (does not depend on fixed meal sizes),   and also checks for:

•   a meal that doesn't include McNuggets   (in other words, zero nuggets)
•   a meal size that includes a double order of nuggets
•   a meal size that includes a single nugget   (which means, no largest McNugget number)
•   excludes meals that have a multiple order of nuggets
•   automatically computes the high value algebraically instead of using   100.
`/*REXX pgm solves the  McNuggets problem:  the largest McNugget number for given meals. */parse arg y                                      /*obtain optional arguments from the CL*/if y='' | y=","  then y= 6 9 20                  /*Not specified?  Then use the defaults*/say 'The number of McNuggets in the serving sizes of: '    space(y)\$=#= 0                                             /*the Y list must be in ascending order*/z=.       do j=1  for words(y);      _= word(y, j)  /*examine  Y  list for dups, neg, zeros*/       if _==1               then signal done    /*Value ≡ 1?  Then all values possible.*/       if _<1                then iterate        /*ignore zero and negative # of nuggets*/       if wordpos(_, \$)\==0  then iterate        /*search for duplicate values.         */            do k=1  for #                        /*   "    "  multiple     "            */            if _//word(\$,k)==0  then iterate j   /*a multiple of a previous value, skip.*/            end   /*k*/       \$= \$ _;      #= # + 1;     \$.#= _         /*add─►list; bump counter; assign value*/       end        /*j*/if #<2                     then signal done      /*not possible, go and tell bad news.  */_= gcd(\$)        if _\==1  then signal done      /* "     "       "  "   "    "    "    */if #==2   then z= \$.1 * \$.2  -  \$.1  -  \$.2      /*special case, construct the result.  */if z\==.  then signal doneh= 0                                             /*construct a theoretical high limit H.*/       do j=2  for #-1;  _= j-1;       _= \$._;       h= max(h, _ * \$.j  -  _  -  \$.j)       end   /*j*/@.=0       do j=1  for #;    _= \$.j                  /*populate the  Jth + Kth   summand.   */         do a=_  by _  to h;           @.a= 1    /*populate every multiple as possible. */         end   /*s*/          do k=1  for h;  if \@.k  then iterate         s= k + _;       @.s= 1                  /*add two #s;   mark as being possible.*/         end   /*k*/       end     /*j*/        do z=h  by -1  for h  until \@.z          /*find largest integer not summed.     */       end     /*z*/saydone:  if z==.  then say 'The largest McNuggets number not possible.'                else say 'The largest McNuggets number is: '          zexit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/gcd: procedure; \$=;    do j=1  for arg();  \$=\$ arg(j);  end;  \$= space(\$)     parse var \$ x \$;     x= abs(x);       do  while \$\=='';  parse var \$ y \$;  y= abs(y);  if y==0  then iterate         do  until y==0;  parse value  x//y  y   with   y  x;  end       end;              return x`
output   when using the default inputs:
```The number of McNuggets in the serving sizes of:  6 9 20

The largest McNuggets number is:  43
```

## Ring

` Nuggets = list(100) for six = 0 To 100/6    for nine =  0 To 100/9        for twenty = 0 To 100/20            n = six*6 + nine*9 + twenty*20            If n <= 100 and not (six = 0 and nine = 0 and twenty = 0)               Nuggets[n] = true             ok        next    nextnext for n = 100 to 1 step -1    if Nuggets[n] = false       ? "Maximum non-McNuggets number is: " + n       exit    oknext `
Output:
```Maximum non-McNuggets number is: 43
```

## Ruby

Translation of: Go
`def mcnugget(limit)  sv = (0..limit).to_a   (0..limit).step(6) do |s|    (0..limit).step(9) do |n|      (0..limit).step(20) do |t|        sv.delete(s + n + t)      end    end  end   sv.maxend puts(mcnugget 100)`
Output:
```43
```

Generic solution, allowing for more or less then 3 portion-sizes:

`limit = 100nugget_portions = [6, 9, 20] arrs = nugget_portions.map{|n| 0.step(limit, n).to_a }hits = arrs.pop.product(*arrs).map(&:sum)p ((0..limit).to_a - hits).max # => 43`

## Rust

No hard limits. Generalization of Rødseth’s Algorithm explained in post. Working code: Rust playground.

`fn main() {    let test_cases = vec![        [6, 9, 20],        [12, 14, 17],        [12, 13, 34],        [5, 9, 21],        [10, 18, 21],        [71, 98, 99],        [7_074_047, 8_214_596, 9_098_139],        [582_795_988, 1_753_241_221, 6_814_151_015],        [4, 30, 16],        [12, 12, 13],        [6, 15, 1],    ];    for case in &test_cases {        print!("g({}, {}, {}) = ", case, case, case);        println!(            "{}",            match frobenius(case.to_vec()) {                Ok(g) => format!("{}", g),                Err(e) => e,            }        );    }} fn frobenius(unsorted_a: Vec<i64>) -> Result<i64, String> {    let mut a = unsorted_a;    a.sort();    assert!(a >= 1);    if gcd(gcd(a, a), a) > 1 {        return Err("Undefined".to_string());    }    let d12 = gcd(a, a);    let d13 = gcd(a / d12, a);    let d23 = gcd(a / d12, a / d13);    let mut a_prime = vec![a / d12 / d13, a / d12 / d23, a / d13 / d23];    a_prime.sort();    let rod = if a_prime == 1 {        -1    } else {        // Rødseth’s Algorithm        let mut a1 = a_prime;        let mut s0 = congruence(a_prime, a_prime, a_prime);        let mut s = vec![a1];        let mut q: Vec<i64> = vec![];        while s0 != 0 {            s.push(s0);            let s1 = if s0 == 1 { 0 } else { s0 - (a1 % s0) };            let q1 = (a1 + s1) / s0;            q.push(q1);            a1 = s0;            s0 = s1;        }        let mut p = vec![0, 1];        let mut r = (s * a_prime - p * a_prime) / a_prime;        let mut i = 1;        while r > 0 {            let p_next = q[i - 1] * p[i] - p[i - 1];            p.push(p_next);            r = (s[i + 1] * a_prime - p_next * a_prime) / a_prime;            i += 1;        }        let v = i - 1;        -a_prime + a_prime * (s[v] - 1) + a_prime * (p[v + 1] - 1)            - (a_prime * s[v + 1]).min(a_prime * p[v])    };    Ok(rod * d12 * d13 * d23 + a * (d23 - 1) + a * (d13 - 1) + a * (d12 - 1))} fn gcd(a: i64, b: i64) -> i64 {    if b == 0 {        a    } else {        gcd(b, a % b)    }} fn congruence(a: i64, c: i64, m: i64) -> i64 {    // Solves ax ≡ c mod m    let aa = a % m;    let cc = (c + a * m) % m;    if aa == 1 {        cc    } else {        let y = congruence(m, -cc, aa);        (m * y + cc) / aa    }}`
Output:
```g(6, 9, 20) = 43
g(12, 14, 17) = 61
g(12, 13, 34) = 79
g(5, 9, 21) = 22
g(10, 18, 21) = 65
g(71, 98, 99) = 1307
g(7074047, 8214596, 9098139) = 48494282357
g(582795988, 1753241221, 6814151015) = 173685179295403
g(4, 30, 16) = Undefined
g(12, 12, 13) = 131
g(6, 15, 1) = -1
```

## Swift

`func maxNugget(limit: Int) -> Int {  var (max, sixes, nines, twenties, i) = (0, 0, 0, 0, 0)   mainLoop: while i < limit {    sixes = 0     while sixes * 6 < i {      if sixes * 6 == i {        i += 1        continue mainLoop      }       nines = 0       while nines * 9 < i {        if sixes * 6 + nines * 9 == i {          i += 1          continue mainLoop        }         twenties = 0         while twenties * 20 < i {          if sixes * 6 + nines * 9 + twenties * 20 == i {            i += 1            continue mainLoop          }           twenties += 1        }         nines += 1      }       sixes += 1    }     max = i    i += 1  }   return max} print(maxNugget(limit: 100))`
Output:
`43`

## Tailspin

` templates largestNonMcNuggetNumber  @: { largest: 0, mcNuggetNumbers: [1..\$+20 -> 0] };  @.mcNuggetNumbers([6,9,20]): 1..3 -> 1;  1..\$ -> #  [email protected] !  when <?([email protected](\$) <=0>)> do @.largest: \$;  otherwise @.mcNuggetNumbers([\$ + 6, \$ + 9, \$ + 20]): 1..3 -> 1;end largestNonMcNuggetNumber 100 -> largestNonMcNuggetNumber -> !OUT::write `
Output:
```43
```

## UNIX Shell

Translation of: Clojure
Works with: bash
Works with: ksh
Works with: zsh
`possible=()for (( i=0; i<18; ++i )); do  for (( j=0; j<13; ++j )); do    for (( k=0; k<6; ++k )); do      (( n = i*6 + j*9 + k*20 ))      if (( n )); then        possible[n]=1      fi    done  donedone for (( n=100; n; n-- )); do  if [[ -n \${possible[n]} ]; then    continue  fi  breakdone printf 'Maximum non-McNuggets number is %d\n' \$n`
Output:
`Maximum non-McNuggets number is 43`
Works with: sh
`possible=i=0while [ \$i -lt 18 ]; do  j=0  while [ \$j -lt 13 ]; do    k=0    while [ \$k -lt 6 ]; do      possible="\${possible+\$possible }"`expr \$i \* 6 + \$j \* 9 + \$k \* 20`      k=`expr \$k + 1`    done    j=`expr \$j + 1`  done  i=`expr \$i + 1`done n=100while [ \$n -gt 0 ]; do  if echo "\$possible" | tr ' ' '\n' | fgrep -qx \$n; then    n=`expr \$n - 1`    continue  fi  breakdoneecho "Maximum non-McNuggets number is \$n"`
Output:
`Maximum non-McNuggets number is 43`

## Wren

Translation of: Go
`var mcnugget = Fn.new { |limit|    var sv = List.filled(limit+1, false)    var s = 0    while (s <= limit) {        var n = s        while (n <= limit) {            var t = n            while (t <= limit) {                sv[t] = true                t = t + 20            }            n = n + 9        }        s = s + 6    }    for (i in limit..0) {        if (!sv[i]) {            System.print("Maximum non-McNuggets number is %(i)")            return        }    }} mcnugget.call(100)`
Output:
```Maximum non-McNuggets number is 43
```

## zkl

Translation of: Python
`nuggets:=[0..101].pump(List());	// (0,1,2,3..101), mutableforeach s,n,t in ([0..100/6],[0..100/9],[0..100/20])   { nuggets[(6*s + 9*n + 20*t).min(101)]=0 }println((0).max(nuggets));`
Output:
```43
```