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6 Partitioning a set

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Partitioning a set
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All the King's Wine

Reminds me of a very geeky joke:

A geek teaching at school: "Suppose we have 1000 apples. Or let's take a round number... Suppose we have 1024 apples."

Partitioning a set

The solution {1, 2} and {3,4} is one way to generate a set of disjoint sets. The question asks in how many ways. Similarly, {1,3}, {2,4} and {1,4},{2,3} also satisfy the conditions of being mutually exclusive. So we have three ways in which we could make partitions such that the said conditions are satisfied namely, 1. {1,2} {3,4} 2. {1,3} {2,4} 3. {1,4} {2,3}

Please let me know if the wording of the question is confusing because this was the problem I wanted to share i.e. the number of ways in which such groups are mutually exclusive sets could be made.

Partitioning a set

Hey Stephen,

 Thanks for pointing out a flaw which was obvious and I totally overlooked. I have re-worded the question which has added additional constraints to the problem and thus reduced your solution to mine.
 And again, thanks for pointing out the flaw.
The double-square number problem

If the number isn't restricted to 4 digits, then we have a very easy solution: 10100 :D


Submitted Puzzles 1

6 8 Partitioning a set
In how many ways can a set of r objects be partitioned into subsets of k objects such that: all subsets are mutually exclusive each of k-object subset appears in exactly one of the partitions [Partit ...