Beach Day by Rodger Bliss
May 2024

Super Size My Riddle

A fast food restaurant sells chicken nuggets in orders of 6, 9, and 20.

What is the first largest number of chicken nuggets you cannot order from this restaurant?

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5 guesses to Super Size My Riddle

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  • Crabman

    I don’t understand “first largest”.

  • I’ll tell you what. Here’s the answer.
    Answer: 43
    Now, explain how I arrived at that figure.

  • craig

    Any number above 43 can be made up of different combonations of boxes. 44 nuggets can be made by 1 box of 20 nuggets and 4 boxes of 6. 45 nuggets can be made of 6 boxes of 6 nuggets and 1 box of 9.

  • Craig, you are today’s winner!
    After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6’s and 9’s). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained.
    43 is the last number that doesn’t fall into one of these categories.