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?

This is what I got:

clues:
(1,3) ...so 1st sits in chair 1, and 2nd sits in chair 2.
(5) ...so R is to the right of I.
(6) ...so I is not 1st or 2nd.
(7) ...so H is either 1st or 2nd.
(8) ...so A is 2nd and M chooses chair 5, or A is to the left of H, and M chooses chair 4.
(9) ...so R is 1st, 2nd or 3rd; I is 3rd or 4th, and T is 4th or 5th.
(10) ...so, per clue (8), A is 2nd and M, who is 6th, chooses chair 5.

now the reasoning:
A is 2nd and chooses chair 2, so T also chooses chair 2.
If A is 2nd, H must be 1st, per clue (7)
If H is 1st and A is 2nd, clue (9) tells us that R is 3rd, I is 4th, and T is 5th. And M, of course, is still 6th.
So the penultimate position (in which T and M take their seats) has H already sitting in chair 3, A already sitting in chair 4, T taking his seat in chair 2, and M sitting down in chair 5.
Which leaves chairs 1 and 6 open for I and R. Since their positions will never be reversed throughout the time described in the problem, and since we know that I sits in chair 1 at some point--while R is sitting in chair 6--the full seating arrangement must be:

    I T H
A: 1 2 3
B: 6 5 4
    R * A

...then everyone moves one space, so the final arrangement is:
    R I T
A: 1 2 3
B: 6 5 4
    M A H

The narrator ends in chair 2.

But I still don't know who "I" is.

Posted by Carole on 2005-05-19 00:37:52