Problem 1388. Numbered lottery balls into cells

Created by James
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Difficulty:Rate

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You are running a lottery, and have a number of different balls numbered 1 to N. Your job is to figure out how many different ways these balls can go into k different buckets. The only stipulation is that each bucket must have at least one ball in it.

For example, if you have 4 balls and 2 buckets, you can divide them up seven different ways:

123, 4
124, 3
134, 2
234, 1
12, 34
13, 24
14, 23

The order of the buckets does not matter, so (12, 34) is the same as (34, 12). Likewise, the order of the balls does not matter, so (12, 34) is the same as (21, 43). Good luck!

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Last Solution submitted on Jun 08, 2024

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James on 29 Mar 2013

Great catch! That one is now fixed. That happened when I was copying the results of the array of values from 1-12 for lottery(12,x). I guess the values for 11 and 12 were on the next line, and I accidentally deleted one of the 6s in 66 for lottery(12,11). I'll double check the rest of them when I get back on my machine that has MATLAB on it. I'm rescoring now.

GeeTwo on 8 Jun 2024

Stirling numbers of the second kind.

Christian Schröder on 8 Jun 2024

Can we please stop banning keywords such as "if" in test suites? I know it's intended to crack down on cheating and look-up solutions, but it also interferes with legitimate solutions that need case distinctions.

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Sequences & Series I

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