September 2016

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Ponder This Challenge:

It is impossible to seat three people (Alice, Bob, and Charlie) in three places for six hours, while changing places each hour in such a way that each hour has a different seating permutation and no one stays in his or her chair during two consecutive hours. Here is an "almost" solution:

A B C A B C

B C A C A B

C A B B C A



The only violation is the "B B" in the middle of the third line.

Our challenge for this month is to design a seating plan for four people for 24 hours in such a way that they don't repeat the same seating arrangement, and the number of violations is minimal, where violations refer to the same person sitting in the same place he sat in during one of the two preceding hours.

Update (29/8): We count each person sitting violation separately, so ABCD-ABDC counts as two violations; and having the same person sit on the same seat for three consecutive hours count as three violations (t vs t+1; t+1 vs t+2 and t vs t+2) etc.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com