Brain teaser thread 2 - return of the teasers

[Ignorance]

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?

[Zero-Tau]

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.

[Ignorance]

Correct. Your turn.

[RGBVideo]

EDIT: Thanks for clearing that out. Maybe we should switch names...

[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.

[Ignorance]

Originally posted by Tuomerehu
River? Inside a bank?

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

[Adam Smith]

edit...nevermind....

[Zero-Tau]

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:

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?

[Guest]

Thats a classic one by Breyer...
you can prove the position is a draw by the 50-move rule

[Guest]

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?

[Guest]

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).

[Guest]

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.

[Guest]

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..

[One_Brow]

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.

[Urban Ranger]

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.