28-11-2002 01:32									#1
	Brain teaser thread 2 - return of the teasers Support Apolyton, pre-order Civilization IV

Continuation of Brain teaser thread

I'll post a new one even though One_Brow already posted unanswered one in the last thread:

Man carrying an attache case full of money falls at bank and is never seen again. What happened?

	28-11-2002 01:41									#2
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He falls at the bank of a river and tumbles into the river. Unfortunately, the current is so strong that it'd be impossible to search for his corpse.

	28-11-2002 01:43									#3
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Correct. Your turn.

	28-11-2002 01:43									#4
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EDIT: Thanks for clearing that out. Maybe we should switch names...

Last edited by VJ on 28-11-2002 at 01:50

	28-11-2002 01:47									#5
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Good. Time for another retrograde chess problem.

Take a look at the position below. What were the last 96 moves? (Yessir, that's ninety-six )

I think we'll need to work together on this one. I don't have the answer, you see.

Attachment: chess2.jpg
This has been downloaded 141 time(s).

	28-11-2002 01:48									#6
	Avatar Enlargement: We've got the solution

quote: Originally posted by Tuomerehu River? Inside a bank?

River bank is the place where river ends and ground begins. Nothing to do with money.

	28-11-2002 01:52									#7
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edit...nevermind....

	28-11-2002 02:16									#8
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OK, I'll withdraw my problem. Apparently, you even have to use the 50-move rule to prove that the moves are unique...

But I'll leave it up, just so people can see how insane things can get.

Instead, here is One_Brow's problem from the first thread:

quote: As we all know, standard Tic-Tac-Toe (3x3) ends in a draw if both sides make the best plays. If you expand the playing field to (4x3), the first player always wins. Let's now expand the game to 4-in-a-row. For the sake of ease, the grid sizes must be different by no more than one (so 3x3 and 3x4 allowed, not 3x5). What is the largest grid size in which the second player can force a tie in a game of four-in-a-row?

	28-11-2002 02:21									#9
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Thats a classic one by Breyer...
you can prove the position is a draw by the 50-move rule

	28-11-2002 02:25									#10
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Yeah i was working on Ignorance's problem
Im working on trying to prove a win on 5x5.
If it can be done then I can work done, if not, I believe that the bigger ones (except maybe 5x6) are too big to prove a win or draw by hand.
Ignorance, do you know if its doable by hand, or if computer analysis is used?

	28-11-2002 02:29									#11
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Ok, ppl, Im not sure of all yet, but If youre trying to prove a win, play the first defensive move adjacent diagonally of the first move, thats the toughest defense (as in usual TTT ironically).

	28-11-2002 02:40									#12
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Ok, Im almost certain I can guarantee a win in a 6x6
of course havnt checked all cases but looks plausible.
I think this is really hard by hand. Because if a win is possible in 5x5, you have to prove then you have to prove 4x4 and 4x5 are draws, and if not , you have to prove a win in 5x6 or 6x6 which are all really hard.

	28-11-2002 02:43									#13
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I played around a bit. A guaranteed win in 5x5 seems implausible to me.
If you start with anything but the center move, then opponent replies center move, and youre at a loss to force 3 in a row at 2 different places.
If you do reply center move, opponent replies immediate diagonal, and I cant prove a win either...
Ill try play around a bit more see if I can prove a draw for 5x5 then...
Btw anyone else trying this by hand or at all?

EDIT:
ok in 5x5, anything but a center first move cant force a win Im over 95% sure.
Let me try to prove something for the 5x5 with first center move, then well see..

	28-11-2002 03:06									#14
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LulThyme,

I don't think a formal proof is necessary. I will happily accept the explanation that a person has played it out a few times -- assuming they are correct, of course.

	28-11-2002 07:59									#15
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quote: Originally posted by Zero-Tau Good. Time for another retrograde chess problem. Take a look at the position below. What were the last 96 moves? (Yessir, that's ninety-six ) I think we'll need to work together on this one. I don't have the answer, you see.

I get a headache by just looking at it.

	28-11-2002 08:00									#16
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I need a clarification on One_Brow's problem. Does he mean that the allowed matrice sizes range from 3x4 to 5x4?

	28-11-2002 10:43									#17
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quote: Originally posted by Urban Ranger I need a clarification on One_Brow's problem. Does he mean that the allowed matrice sizes range from 3x4 to 5x4?

I think he meant that the allowed sizes are 3x4, 4x4,4x5, 5x5, 5x6, etc, going on forever. Dimensions differing from each other by more than 1 are presumably not allowed because that would give us too many cases to consider, and it would be somewhat ambiguous which of two grid sizes is "bigger" (although I guess it would be the one with the largest area).

	28-11-2002 11:09									#18
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quote: Originally posted by Zero-Tau Good. Time for another retrograde chess problem. Take a look at the position below. What were the last 96 moves? (Yessir, that's ninety-six ) I think we'll need to work together on this one. I don't have the answer, you see.

What I want to know is what kind of maniac plays Chess like that? You can't even be sure what way round the board is!

	28-11-2002 18:22									#19
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OK One brow, so its sorta of a guess
I may still try some more, but I kinda ran out of time yesterday. I would say on a 5x5 it is possible to force a draw. I cant prove a win or a draw on a 6x6. Im almost certain you can prove a win on a 7x7. So my guess would be 6x6 is the biggest board you can force a draw as the second player. (NOt counting 5x6 or 6x7)
Since I seem to be the only one actually trying you may as well put the answer or a brief explanation...

	28-11-2002 20:17									#20
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quote: Originally posted by JohnM2433 I think he meant that the allowed sizes are 3x4, 4x4,4x5, 5x5, 5x6, etc, going on forever. Dimensions differing from each other by more than 1 are presumably not allowed because that would give us too many cases to consider, and it would be somewhat ambiguous which of two grid sizes is "bigger" (although I guess it would be the one with the largest area).

Exactly so.

	28-11-2002 20:31									#21
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quote: Originally posted by LulThyme OK One brow, so its sorta of a guess I may still try some more, but I kinda ran out of time yesterday. I would say on a 5x5 it is possible to force a draw. I cant prove a win or a draw on a 6x6. Im almost certain you can prove a win on a 7x7. So my guess would be 6x6 is the biggest board you can force a draw as the second player. (NOt counting 5x6 or 6x7) Since I seem to be the only one actually trying you may as well put the answer or a brief explanation...

On a 6x6 board the first payer (black) has a forced win in six turns:

1. c3 d4 (any other corner mov allows a rotated version, you knowfrom 5x5 a corner is needed)
2. d2 b4 (white must defend the pair on b4 or e1, e1 allows the smae fllowing sequence)
3. c4 (black defends the pair)

Here we have two branches, as white can defend the c3-c4 pair on c2 or c5:

3. ... c5
4. c2 c1 (forced)
5. b2 (Black wins on either a2 or e2 next turn)

3. ... c2
4. d3 (Black forms two open pairs c3-d3 and c4-d3. He converts one to an open three next turn, as white has no pair to convert).

So, now that you know the size is smaller than 6x6...

	29-11-2002 02:30									#22
	Avatar Enlargement: We've got the solution

One_Brow, I just realized that your strategy doesn't use the f column, not even for threats. So the strategy would work on a 5 x 6 board as well.

Now we just need to figure out the 5 x 5 case.

	29-11-2002 06:46									#23
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Yeah. 5x6 is win for first player.
I can't figure out a way to win 5x5 though. Seems like that is the answer.

	29-11-2002 10:16									#24
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I tried a bit, and am almost certain 5x5 is a draw.
I just logged before I go to bed and have a hard day tomorrow, might try to post somewhat of an explanation.
As I said before, anything than a start in the middle, player 2 replies in the middle and you can quickly block all attacks. After a start in the middle (c3) reply d2 (for example) and then I divided in a lot of cases and could prove draws for most.

	30-11-2002 04:26									#25
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Yes, 5x5 is draw f the secod player pays correctly. There is no real "proof" outside of demonstration.

LulThyme did themost work on this, but since had commented recently that he had posted too many puzzles himself, I think we can let Ignorance be our next puzzler (if for no other reaon than irony).

	30-11-2002 06:44									#26
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I'm working on something, but not to waste time I'll post it when it's my turn next time.

Few riddles for now, hopefully everyone hasn't heard these before:

1:
When young, I am sweet in the sun.
When middle-aged, I make you happy.
When old, I am valued more than ever.
2:
I'm gentle enough to soothe the skin,
light enough to caress the sky,
hard enough to crack rocks.
3:
I build up castles.
I tear down mountains.
I make some men blind,
I help others to see.

	30-11-2002 06:58									#27
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1 is grapes, or wine or something.

	30-11-2002 07:01									#28
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The second one is water.

	30-11-2002 07:41									#29
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Yep.
1. Wine
2. Water

	30-11-2002 19:27									#30
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*bump*