The Chicken Nugget Theorem, AKA the Postage Stamp Problem, states that for any two relatively prime positive integers $m,n$, the greatest integer that cannot be written in the form $am + bn$ for nonnegative integers $a, b$ is $\ mn-m-n$. (AoPS definition).

So, let's say you worked at a shop that sold cookies in packets of $13$ and $9$. What would be the largest number of cookies that you couldn't buy?

$m = 13$

$n = 9$

$(13 \times 9) - 13 - 9$

$=117 - 13 - 9$

Ans: $95$ cookies.

Origin:

A long time ago, in a galaxy far, far away...

McDonalds had sold Chicken McNuggets in packets of $9$ and $20$. Some wise person wondered what was the largest number of chicken nuggets that one couldn't buy. Later, the answer was found to be $151$ McNuggets. And thus, the Chicken McNugget Theorem had been formed.

~Brian

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

$</code> ... <code>$</code>...<code>."> Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in $</span> ... <span>$ or $</span> ... <span>$ to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestInteresting. I didn't know that McDonalds had branches in other galaxies.

As an exercise, try to prove the theorem.

Log in to reply

Considering that Dominos plans to open branch on the moon, I would not be surprised if McDonalds has branches on the Death Star. Those stormtroopers must have something to eat.

Log in to reply

Frobenius numbers?

Log in to reply

Precisely. The chicken mcnugget theorem is a popularized version of frobenius though.

Log in to reply

That's amazing.

Log in to reply

Hypothetically, if they sold two packs of 2 and 2 (sounds odd, but yeah) then according to the theorem you can't buy 0 nuggets. But the actual answer is 1(obviously)

Log in to reply

the two numbers has to be relatively prime to each other.

Log in to reply

Ah..Thanks, my bad.

Log in to reply

I feel sorry for McD... They will never be able to sell 151 nuggets by and large...

Log in to reply

Then they decided to add 4 and 6 number of nuggets in a packet. So, what do I do? (weep...)

Log in to reply

Hah! They still cannot sell 151 nuggets!

Log in to reply

This is awesome..

Log in to reply

Applied math!

Log in to reply