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## The Math Department Annual Dinner

Logic puzzles require you to think. You will have to be logical in your reasoning.

 Puzzle ID: #45446 Fun: (2.67) Difficulty: (1.71) Category: Logic Submitted By: dalfamnest

My department needs a new Social Coordinator! You see, we were going to have a Chinese New Year dinner but the seating plan proved to be too much for the organizer, who has now resigned. Math teachers can be hard to please!

The restaurant had big round tables for 10 people, (perfect for our department size), with chairs placed evenly around. Everyone was going to attend, and a fun evening seemed assured ... until the problems began.

[A] Ding wanted to sit as far as possible away from Dong.

[B] Walter wanted to sit opposite Wira, who insisted on sitting closer to Dong than to Ding.

[C] Wynn, Dan and Walter always sit together, in that order, anticlockwise (something about feng shui, they claimed.)

[D] Wira only wanted to sit between Liza and Fozz, who always sits with Rita!

Work out the seating plan and discover which teachers I sat between so everyone's preferences could be satisfied.

Starting with me and going clockwise, there was Walter on my left, Dan, Wynn, Dong, Liza, Wira, Fozz, Rita, and then Ding on my Right.

SOLUTION:
If we number all the seats clockwise starting with Walter = 1, then Dan = 2 and Wynn = 3 [C]. From [B], Wira is at 6.

That leaves only 4 and 9 or 5 and 10 for Dong and Ding [A], and from [B] we find that Dong must be at 4 or 5. Dong can not be at 5 [D] so Dong = 4 and Ding = 9.

That leaves only 7 and 8 for Fozz and Rita respectively [D] so Liza = 5 [D] and I come in at 10.

It's not an easy life teaching, is it? Maybe that's why we decided on an Indian restaurant for next year! I'll report on that later.

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