Pascal's Bomb

Revision as of 14:48, 25 November 2020 by Jcjc (talk | contribs) (Pascal's Bomb)


In the year 69, Munkey man first developed the idea. It was then sent to Gmaas for review, approved by Gmaas, and became published.

Forgotten by the year 696, it was later re-discovered. In the year 4269, bestzack66 got on FTW and said "Pascal's" and MathHayden said "Bomb". Thus, it became a real theorem.

Later on, bestzack66 and MathHayden contributed to mankind by re-publishing the theorem, this time onto the AoPS wiki. It is now here for all AoPS users to learn from.




Suppose that MathHayden has $69$ apples. He needs to distribute them among $2$ of his very distinguished friends(not including himself). Each friend must get at least $14$ apples. How many $Possible$ distributions are there?

Solution 1

By applying the Pascal's Bomb, we Munkey it and get an answer of $\boxed{42}$.

Solution 3(slower)

We first proceed to give each friend $14$ apples. We then have $41$ apples left to distribute among the two friends. The first one can have $0 \leq x \leq 41$ apples and the second will have $41-x$ apples. There are $\boxed{42}$ $Possible$ values of $x$, from $0$ to $41$, and that is the answer.


All credits go to Munkey Man

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