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Equally divided (Posted on 2022-05-22) Difficulty: 3 of 5
In a Senate of n Senators, itemized lists of all possible k member subcommittees were prepared.

Prove that for any k ≥ 3 the number of possible distinct subcommittees is even and the Senators are evenly divided between subcommittees with either an odd or even number of participants.

Why the constraint that k is at least 3?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (2 votes)

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Question Huh? Comment 3 of 3 |
Ady: 

I have reread the problem, and I am more confused than ever. If you mean to ask only about subcommittees with k members (instead of all the k possible subcomittees), then the question does not make sense.  If k is odd, then all the subcommittees under consideration have an odd number of members.   If k is even, then all the subcommittees under consideration have an even number of members.  For no k are Senators divided between odd-sized and even-sized subcommittees.

Clearly, what we have here is a failure to communicate

  Posted by Steve Herman on 2022-05-29 08:00:55
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