The Hatter, the Hare, the Rabbit, the Mouse, Alice and I met for a Tea Party. The table had two sides, with three chairs on each side, numbered like so:

Side A: 1 2 3
Side B: 6 5 4

Chair one was across from chair 6, chair 2 across from chair 5, etc. We would sit down one at a time, in any chair we choose. The first guest to sit down was called the first guest. After the second guest sat down, however, everyone moved clockwise to the next chair. This behavior was continued after the fourth and sixth guest sat down.

My question is, after everyone had been seated, where was I seated?

(1) The first guest sat in chair 1.
(2) The mouse sat down last.
(3) After the first time everyone moved, no one had been on side B yet.
(4) The Hatter and Alice choose the same starting chair.
(5) When I was in chair 1, the Rabbit was in chair 6.
(6) I started on side B, but didn't end there.
(7) The hare moved all three times.
(8) Alice ended up between the mouse and the hare.
(9) I sat down after the rabbit but before the hatter.
(10) The mouse sat down in an odd numbered chair.

Also, a bonus question. Who am I?

Rabbit | Cheshire Cat | Hatter

Mouse | Alice | Hare

as per the figure in the question.

Why?

Fact: Mouse sat down last in an odd numbered chair.

Conclusion: After the shuffle, mouse is in even chair (2/4/6)

Fact: Alice ended up between mouse and hare.

Conclusion: For that to be physically possible, Alice would be in chairs 2 or 5. But the mouse is in an even chair, so Alice ended up in 5. At this point mouse is in 4 or 6.

Fact: The hare moved all three times.

Conclusion: Movement occured after 2nd guest sat down, so that requires the Hare to be the first to sit down.

Fact: The first Guest sat in chair 1.

Conclusion: The first guest is the Hare, since the Hare sat down first. Since the Hare moved three times, then the hare ends up in position 4.

Fact: The Hare is in position 4.

Conclusion: The mouse has to be in position 6, since the mouse was earlier concluded to be in either position 4 or 6.

Fact: I sat down after the rabbit but before the hatter.

Conclusion: Since there are only 3 spaces left on the A side, and you are in between two others. You (the Cheshire Cat), are in chair 2.

Fact: When I was in chair 1, the rabbit was in chair 6.

Conclusion: The rabbit is in chair 1 since the rabbit follows you around the table in a clockwise fashion (1 is the next chair to go to from 6 after a shuffle), and you ended up in chair 2.

Fact: Only one space left: Chair 3.

Conclusion: The Hatter is in chair 3.

 

Posted by big sjk on 2005-05-21 06:18:14