do  -- 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

    local maxNuggets <const> = 100
    local sum = {}
    for i = 0, maxNuggets do sum[ i ] = false end
    for x = 0, maxNuggets, 6 do
        for y = x, maxNuggets, 9 do
            for z = y, maxNuggets, 20 do
                sum[ z ] = true
            end
        end
    end
    -- show the highest number that cannot be formed
    local largest = maxNuggets
    while sum[ largest ] do largest -= 1 end
    print( $"The largest non McNugget number is {largest}" )

end