Problem 1873. Break it up! Break it up!

Created by James

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You have N pennies. Write a Matlab script that will reveal how many different ways you can break up those pennies. For example, with 5 pennies, there are seven different ways you can divide them:

(1,1,1,1,1)
(2,1,1,1)
(2,2,1)
(3,2)
(3,1,1)
(4,1)
(5)

The order of the coins does not matter, so (2,2,1) is considered the same combination as (2,1,2). You can assume that N will always be a positive integer.

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Last Solution submitted on Dec 16, 2025

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Tim on 17 Sep 2013

Test case p(300)=9253082936723604 exceeds the maximum integer that can be represented exactly as a double precision number (namely, 2^53=9007199254740992); the fact that some solutions work for this case is just luck.

James on 18 Sep 2013

Changed to p(299), which is <2^53. Thanks for the heads up.

James on 18 Sep 2013

Interestingly, p(299) had some issues as well. Changed again to p(199), which seems to be working OK.

ChrisR on 23 Apr 2022

If I ever want to learn something, I dial up a problem from James.

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Problem 1873. Break it up! Break it up!

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Problem 1873. Break it up! Break it up!

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Problem Recent Solvers79

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