magipi wrote:
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.
It means that the both queens won't capture each other . Both queens are in safe squares.
Chess with Maths
Sort:
After some thought... I made a mistake...
(64-(8*3))*7 = 280
(64-(8*3)-2)*5 = 190
(64-(8*3)-4)*3 = 108
(64-(8*3)-6)*1 = 34
280 + 190 + 108 +34 = 612
612 * 4 = 2448?
@stockOfHey , I am thinking that you are calculating for one queen you need to calculate for two queen .
Do you mean a queen cannot capture the other?
StockOfHey wrote:
Do you mean a queen cannot capture the other?
Yes .
Sorry, I am afraid that is my answer...
Are the number of squares controlled by a queen in different file remain the same?
Are the number of squares controlled by a queen in different rank remain the same?
Are the number of squares controlled by a queen in each diagonal on each position the same?
If the answer on all of these questions are yes, why? If not, why?
Based on observation... the squares of a file controlled by a queen remain the same...
the squares of a rank controlled by a queen remain the same...
the squares of a diagonal controlled by a queen increases by two as you move closer to center from the edge...
Are these things right? or not? Why?
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?
StockOfHey wrote:
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?
Yes, that's correct answer . 
TY!... It is hard to be duhmb... Thanks that there are people like you that I can rely on...
Mr_Mathematician 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
Yes correct and you logically proved 👏
Congrats
Thanks.
Mar 15, 2024
0
#38
Mr_Mathematician wrote:
Wind wrote:
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 🤯
I think you misunderstood the question , there are only two queens on board
Oops! Indeed, I thought it was 8 queens.
Still surprised that there are only 42 ways, very nice!
Wind wrote:
Mr_Mathematician wrote:
Wind wrote:
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 🤯
I think you misunderstood the question , there are only two queens on board
Oops! Indeed, I thought it was 8 queens.
Still surprised that there are only 42 ways, very nice!
No, you misunderstood in more ways than one . The answer is 5152 ways.
Mar 15, 2024
0
#40
Optimissed wrote:
Wind wrote:
Mr_Mathematician wrote:
Wind wrote:
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 🤯
I think you misunderstood the question , there are only two queens on board
Oops! Indeed, I thought it was 8 queens.
Still surprised that there are only 42 ways, very nice!
No, you misunderstood in more ways than one . The answer is 5152 ways.
OMG that's just fantastic!! 🤯
Chess and Math, what a fine mixture.
(64 - (8*3))*7 = 280
(64 - (8*3) -((2*1+3*2+4*3+5*2+6*1)/9))*9 = 324
(280 + 324)*4 = 2416?