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?
I see that this puzzle has already been solved but since I spent so much time on it I decided to post my own solution just for the heck of it. Warning, long post.
Solution:
The solution to this puzzle was not difficult given that the clues themselves eliminate many possibilities. The first thing to do is try to figure out the order everyone sat in and then find what seats they could or could not sit in. We'll start off with clues 2,7, and 9. Clue 7 shows first of all that the hare had to come first or second, since he moves all 3 times. Also from 2 and 9 we are given the following order: rabbit,I,hatter,mouse. We still don't know where to place Alice but clue 4 suggests she goes after the hatter. If this is so then the only two that can go first or second are the hair and rabbit. So now where do they sit? Clue 1 says that one of them must sit in chair 1. Clue 9 says that after the first move no one is yet on side B. Thus the second guest has to sit in chair 2. For the hair this works out fine but we have a problem with the rabbit. Looking at clue 5 we see that the rabbit can't sit in a chair less then 3. If he does he won't be able to reach chair 6. So the rabbit can't be first or second. The only other one that could fit is Alice, since clue 9 clearly says that “I” and the hatter come later and we already know the mouse comes last. The order suggested in clue 4 must then be interpreted ”loosely”. Now we need to decide who goes first? It's either the hare and Alice or the other way round. Instead of using brute force we can use clues 8 and 10. Since clue 4 had to be a “loose” order we will give the same leeway for 8. Now per clue 8 we can get either: hair,Alice,mouse or mouse, Alice, hair. Since the mouse sits last Alice and the hair will have made a total of 2 advances in their chair positions when he sits. The possiblities then are: 1,2,Alice,hair,5,6 or 1,2,hair,Alice,5,6. Clue 10 says the mouse has to sit in an odd numbered chair so the first possiblity is ruled out. The hare must then come first followed by Alice. At this stage we have concluded the following: the hare goes first in chair 1 followed by Alice in chair 2. The remaining guests then sit in the order: rabbit,“I”,hatter,mouse. Furthermore the rabbit can't sit in chair 1 or 2.
We then have:
First guest sits.
Order: hare,2,3,4,5,6
Second guest sits.
Order: hare,Alice,3,4,5,6
Everyone moves: 1,hare,Alice,4,5,6
Now since according to clue 8 Alice is between the hare and mouse the rabbit can't sit in a chair next to her. Also clues 5 and 6 indicate that the rabbit and “I” must be next to each other and that “I” had to start on the B side. From this we see that the rabbit must be in chair 5 and “I” in chair 6. So we can proceed.
Third guest sits.
Order: 1,hare,Alice,4,rabbit,6
Fourth guest sits.
Order: 1,hare,Alice,4,rabbit,I
Everyone moves: I,2,Hare,Alice,5,rabbit
Again according to clue 8 the hatter can't sit next to Alice. The only chair he can sit in then is 2.
Fifth guest sits.
Order: I,hatter,hare,Alice,5,rabbit
Sixth guest sits.
Order: I,hatter,hare,Alice,mouse,rabbit
Everyone moves: rabbit,I,hatter,hare,Alice,mouse
Answering the original question “I” ended in chair 2. The order in which everyone sat in was: the Hare in chair 1, Alice in chair 2, the rabbit in chair 5, “I” in chair 6, the hatter in chair 2 and the mouse in chair 5. The final position was: rabbit,I,hatter,hare,Alice,mouse.
My own solution.
