Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 12

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Mathemat:

Read my post, I supplemented it. Read it carefully.


Yep, that's it, I'm done recalculating.)
 

By the way, here's the answer to the circle cutter:

True, it's too small to see anything :)

P.S. I can't remember if it was there or not (weight 4):

In a magical land lived brave knights, fierce dragons and beautiful princesses. The knights killed the dragons, the dragons ate the princesses, and the princesses tortured the knights to death. In total there were 100 knights, 99 princesses and 101 dragons. An ancient spell cast on everyone forbids killing those who have killed an odd number of victims. Now there is only one inhabitant left in this land. Who is it and why?

 
TheXpert: Princess is out of the question :) they're tough bastards :)
Prove it. Dragons eat them and don't pay attention to their survivability.
 
TheXpert: Oops... Taki dragon.
One scenario of mutual annihilation doesn't prove anything, you know. You have to prove that it can't be otherwise in any scenario that leaves one/one/one alone.
 
Mathemat:
One scenario of mutual annihilation does not prove anything, you see. You have to prove that it can't be otherwise.
Yes, there is proof. I'll rub it in :)
 
TheXpert:
Yes, there is proof. I'll rub it in :)
Fine, I do. Let others think.
 

(Weight 4)

On an initially empty 1x81 board, two megabrainers play a game.

The first MM puts a white or a black chip on any field of the board each turn. The second MM can swap any two chips on the board or skip his turn.
If after 81 moves of each player the chips on the board are symmetrically placed, the second player wins, otherwise the first player wins.
Who will win?
 
Mathemat:

(Weight 4)

On an initially empty 1x81 board, two megabrainers play a game.

The first MM puts a white or a black chip on any field of the board each turn. The second MM may swap any two chips on the board or skip his move.
If after 81 moves of each player the chips on the board are symmetrically placed, the second player wins, otherwise the first player wins.
Who wins?

What's four points for? It's a freebie. :)

Let's play a better game. For example, on a reduced board of 11x1 (doesn't change the point).


Dibs on me being second. ;)

 
MetaDriver:

Dibs on the second one. ;)

You're so sneaky :) All you have to do is keep the difference 1 if there's no stone in the centre and 0 if there is.
 
TheXpert:
You're so sneaky :) All you need to do there is to keep the difference 1 if there's no stone in the centre, and 0 if there is.
Yes, you have to minimize asymmetry with every move. If there is no centre stone, zero won't always work, but sooner or later you'll have to put the first one in the centre as well.
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