Chess with Maths

🎯Brain teaser ‼️

• 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).Cancel means possibilities of capture.

Can you answer this question with logic?  

This question is based on permutation concept ? Am I correct ?

Well in the old Scots math means good, so...

I think so, there are two queens and 64 squares , According to me the answer would be 2^8 .

Yes

No

Suppose you have placed your queen on a1 then for another queen to arrange position no neither a square nor 1 square file and the diagonal square would be left for another queen

So, the better way to solve this would be , to left either queen untouched and move another queen , so this will happen in every square on the board , such that it cover all the square and positions .

We can observe that in some cases the numbers are increasing and decreasing .

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

Hello

Nice to see you after long time...

Hi, do we know each other? You must excuse my memory.

I've always tried to do this on a chessboard but never could!

At max I could put 7 queens not attacking each other, 8 is very hard.

Yet, very surprised that there are 42 ways 🤯

Yes correct and you logically proved 👏

Congrats

I think you misunderstood the question , there are only two queens on board

Yes

Isn't it just a multiplication problem?

(64 - (8*3))*64 = 2560?...

Oh... I changed my mind...

Just out of curiosity, what does "never get cancel by each other" mean in the puzzle? Everyone seems to understand it, but I don't.