I suspect so did @Optimissed, but maths is not his strong point.
Chess with Maths
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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?
Mar 15, 2024
0
#66
StockOfHey wrote:
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?
They can't be in the way of each other.
I also do not understand it myself? Is it just a mistake? Or it is made on purpose?
If I think more about it... A queen that cannot be captured by the other can remain on the square controlled by other... Is it just a glitch?
Mr_Mathematician wrote:
Optimissed wrote:
Mr_Mathematician wrote:
Optimissed wrote:
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.
He will definitely come up with great new developing skills
We can also see amazing probability concepts here like if one follows book more the chess analyser tell us about winning chances we can also calculate it since there are more than 10^ 20 total games combination we humans can't do perfectly
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.
Basically in physics there is a principle called Heisenberg uncertainty principle this same thing gets applied to all which are related to uncertainty and I think everything in this universe is uncertain.
The probability arises where uncertainty occurs thats why we go take help of statistics in analyzing games / patterns/ chances etc.
Statistics can't help in deciding if chess is drawn though. You only have to demonstrate one forced win to refute it.
Is statistics also says that extreme things can also happen no matter how small they are?
What is life?... Does it sucks or not?... LOL...
MARattigan wrote:
Optimissed wrote:
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
Double it and we have the answer.
You do if you allow the queens to be the same colour. You need to halve it for each of WW and BB because in those cases you will have double counted, so 2576.(1+½+½) in total.
All depends if two queens of the same colour can ever get to cancel each other if they're on the same row or diagonal. (Search me.)
If they can't you need to add in 4x27 + 12x25 + 20x23 + 28x21 = 1348, so 6500 in total.
Yes I had to think about that for a minute cos I'm tired but you're right. Still, could you have worked it out completely from scratch in less than 10 minutes? Maybe but I doubt it. You're quite right in your criticism though.
Because each of the solutions for one colour on a particular square have an analogous solution with the other colour on that square when the first colour is elsewhere.
StockOfHey wrote:
What is life?... Does it sucks or not?... LOL...
I hesitate to imagine why Americans constantly use the idea that if something's bad, that can be described by the metaphor of performing a presumably unnatural sexual act. I hope they grow up one day but I don't think they will. 
Sorry... I admit... I am wrong... I also think that I made a mistake... Yeah, I agree... The position of White does not disinclude the position of Black... I made a mistake that they exist without other... The truth is, they are with each other all of the time on the board... Thanks!... I know now that both of them are on the board on all configurations of position... Therefore, it is a mistake of doubling... Sorry... Thanks!...
Optimissed wrote:
StockOfHey wrote:
What is life?... Does it sucks or not?... LOL...
I hesitate to imagine why Americans constantly use the idea that if something's bad, that can be described by the metaphor of performing a presumably unnatural sexual act. I hope they grow up one day but I don't think they will.
I like it!... Thanks... 
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 ).
I found the words "that they never get cancel by each other". It is hard to get... If you did not combine the definition of the second sentence "assume white plays first", it is hard to know the real definition of the word cancel...
There are two definition:
1. decide or announce that (a planned event) will not take place.
2. (of a factor or circumstance) neutralize or negate the force or effect of (another).
The first one says that, capturing a piece is included in the problem... Because, if you cancel the effects of the other piece, you must capture it while the ones who capture remain hence "they did not cancel each other"...
The second one says that, capturing a piece is not included in the problem... Because, if you capture the other, it will not exist...
Because most of us agreed that the second definition is what we are talking about... I guess, the second definition seems more practical...
Besides, queens are not kings... are not they?
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.
AH I see. Thank you. I had in mind only one pair of Queens at a time and assumed WB