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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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.
Changed to p(299), which is <2^53. Thanks for the heads up.
Interestingly, p(299) had some issues as well. Changed again to p(199), which seems to be working OK.
If I ever want to learn something, I dial up a problem from James.