[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 101

 

Why can't the proportion be 123:456 ?

 
He copied his opponent's moves on one board to the other and vice versa. :-)
 
Yurixx >>:
Он копировал ходы противника на одной доске на другую и наоборот. :-)


it was already just about passengers on the train :-)
 
Yurixx >>:

А почему нельзя разбить в пропорции 123:456 ?

Can you be more specific? The full formula, please?


2 Mathemat: I've known the Ostap problem and the answer since I was a kid.

Do it again.

 

OK, hilarious. These are the ones I can't solve:

Vasya has a chessboard, from which the corner squares a1 and h8 (the outermost on the diagonal) are cut out. Vasya also has 31 dominoes of the size of two squares of the chessboard each. Can Vasya cover the whole board with dominoes?


 

It won't work. Each domino can only cover a couple of fields of different colours. And we have two more white squares than black.

Just cut another corner instead of one of the stated ones.


ps. By the way, a good example from the boson-fermion theme.

 

OK, cut the other one off (top left instead of right).

P.S. Well, yeah, that'll work here. OK, remove the middle row from the board.

P.P.S. The board will be bad. Well, then: take a 7x8 board and remove the squares as before.

 

Mathemat писал(а) >>

OK, let's remove the middle row from the board.

:)

Oh, that's more interesting. Let's see.

 
MetaDriver >>:

:)

О, тут поинтереснее. Ща посмотрим.

Easy. I'm too lazy to even draw an example. It's fine - let the people indulge themselves.

 
MetaDriver >>:

Лехко. Даже лень пример рисовать. Да и ладно - пусть народ побалуется.

But if you remove two rows from the middle (one vertical and one horizontal), then it's deadlocked again. For it's odd...

Reason: