Chess with Maths

Yes!

I spent 5 months in India when I was 24 years old, which is very nearly 50 years ago. I spent my 25th birthday climbing a snow peak in thick mist. It was only a small one, about 16000 feet.

Anyway, in that time I learned to understand some of the ways that Indian people express themselves. The way that question was phrased was probably difficult for many Westerners to understand. The idea was "how many different ways can you place a white queen and a black queen on a board in such a way that the two queens do not attack each other?" So you have to work it out for one of the queens and then you double it to cover both queens. The closer you place one queen towards the centre of the board, the less positions there are where you can place the other queen and it isn't attacked. In fact, for each square nearer the centre that you place the first queen, the number of positions you can place the second queen decreases by two, showing that a queen becomes more powerful, the nearer it gets to the centre of the board.

I didn't know any of this before I saw this question yesterday but I worked it all out in about ten minutes.

No, you misunderstood in more ways than one . The answer is 5152 ways.

He's a professional mathematician who works in engineering but he was on about maybe designing a chess engine to help him with his programming skills, so maybe he probably did think about it.

Because I forgot that the position of the queen is repeated on calculation... I therefore conclude that the answer must have an additional of 64*(3-1) = 128

2448+128 = 2576?...

Thank You for saying that I am wrong Ashvath23... without you, I made a mistake...

Then, I forgot the other queen... Thanks for optimissed... I must correct myself again...

2576*2 = 5152?

Hello ashvath

Nice to meet my all friends after long time

I've been involved in a thread here about "is chess a draw?" Well yes it is but did you know that to analyse chess completely with a modern computer would probably take longer than the present age of the universe? And that there's nowhere to store the results? According to my wife, my son's very happy in his new job. He just came up with a model that explains something that hasn't been done before and they like him. Can't say what that something is.

There are 42 ways the Qs can be placed with the white Q on a1. There are 42 ways if the white Q is on a4. If the white Q is on f4, there are 38. Logically, for all the edge squares there are 42. If on b7 there are 40, so a pattern is developing. If we divide the board into concentric tracks, the outer track contains squares all of which are 42. The next track inwards 40, the next track inwards, 38.

The final track is the centre four squares. Taking one at random, d4, there are 5x6 +6 = 36

So we have 4x36 + 12x38 + 20x40 + 28x42 = 2576

Double it and we have the answer.

5152

I don't understand why the solution is to calculate for one Queen and then double it. Surely if one Queen can take the other then the reverse is also true. So doubling is just repeating positions already calculated?

True, but the queens can be WB, WW or BB. 2576 is correct for WB but double counted for WW and BB. So the total for queens not on the same row or diagonal is double that. If you take the view that opposite coloured queens can cancel each other if they're on the same row or diagonal but same coloured queens can't ever cancel each other then the answer is 6500 as above.

If the question is about only the WB case doubling is incorrect and the answer would be 2576.

@magipi hit the nail on the head.

Nice to see you after long time

In how many ways two queens shall be placed into 8×8 chessboard such that they never get cancel by each other ( there are only two queens on board place , assume white plays first ).

The question have a unique word indeed... it says cancel by each other... I find it vague because if a piece capture another piece, the piece that capture the other piece remain on the board... It also say that white plays first, so it is still using a rule in chess which is turn based... If both of these things do not meet in the same rules, which should we trust?...

The answer might be sad... But, if I think more about it, it does not make sense...

If the riddler clarifies things for us, we might get the better look at it...

Is it just about capturing stuff?