 The Second Oldest Chess Riddle Bishopcrw Posers and Puzzles 15 Feb '06 18:49
1. 15 Feb '06 18:49
Now that every one on the site is the wiser about how many squares on a chess board, I thought I would pose this question.

How many rectangles are on a chess board?

P.M. your answers to me and I will let you know if you are correct or not.

Then after a day or two I will post the solution.

Have fun 😀
2. 15 Feb '06 19:51
Originally posted by Bishopcrw
Now that every one on the site is the wiser about how many squares on a chess board, I thought I would pose this question.

How many rectangles are on a chess board?

P.M. your answers to me and I will let you know if you are correct or not.

Then after a day or two I will post the solution.

Have fun 😀
1296, of which 204 are squares.🙂
3. 15 Feb '06 20:03
Originally posted by excalibur 8
1296, of which 204 are squares.🙂
I concur.
4. 15 Feb '06 20:22
5. 15 Feb '06 20:26
Originally posted by Bishopcrw
So what? We're right. And for the record, I only concurred with the answer already given.
6. 15 Feb '06 20:39
Originally posted by Bishopcrw
I am right, and you risk being a pedant.
7. 15 Feb '06 21:03
If there were ever a game for pedants it would be Chess.
The constant correction of the slightest flaws insearch of exacting perfection.

May be that is why my rating is so low😵

Your skin might need a little thickening if you are going to make it in this or any other forum. For there are certainly a lot more people who are willing to correct you for much less.

But very well,
Yes, you did get the right answer. Very Good!😀

Since this thread already had the spoiler post. If anyone does not think this is the correct answer and would like to discuss their answer and receive some clues as to what to fix please feel free to post.
8. 16 Feb '06 09:10
Nothing wrong with the thickness of my skin, and have no desire to 'make it' (whatever that means) in the forums.

For me, chess is simply entertaining, and reading these forums is sometimes educational and occasionally hilarious; in short, not to be taken too seriously. Thanks for the riddle.
9. 16 Feb '06 11:581 edit
In general, for positive integers m and n, how many rectangles are there on an mXn 'chessboard'?

10. 17 Feb '06 23:072 edits

There are 1296 rectangles on the chess board.
The reason there are so many more rectangles than just squares is due to two attributes.
1). Dimension
2). Orientation

We will now build on the squares puzzle.
We need to determine the dimention of the rectangles:
So we identify the sides of the board with x and y, respectively.
For a 1 by 2 rectangle, you can fit 8 on side x and 7 long on side y.
for a 1 by 3, there are 8 on x and 6 on y: as seen below
8 * 7 = 56
8 * 6 = 48

To simplify things a little we will do the following.
8*(7+6+5+4+3+2+1) = 224
7*(6+5+4+3+2+1) = 147

Notice two things quickly
1). the dimensions that would cause a square are excluded(8 by 8, or 7 by 7)
2). the y dimension is one shorter than the previous line. This is because we already counted the 1x and 2y rectangles in the first line.
This pattern will continue through out.

6*(5+4+3+2+1) = 90
5*(4+3+2+1) = 50
4*(3+2+1) = 24
3*(2+1) = 9
2*(1) = 2
____________________________
Now we add them up and get = 546

This is the total of rectangles with varying dimensions. And because they have varying dimensions they can also face the other direction on the board (Orientation), meaning we just counted all the x, y rectangles but now need all the y,x rectangles.

So we multiply by 2 = 1092

And now we add in our squares of 204. Since the are the same in dimension in both x,y and y,x they were excluded from the above calculation. (and yes squares are rectangles, but not all rectangles are squares, Rectangle - geometrical shape with four right angles and opposite sides equal in length, squares also have adjacent sides equal in length)

And get a total amount of rectangles of = 1296

11. 25 Feb '06 03:15
Originally posted by Bishopcrw

There are 1296 rectangles on the chess board.
The reason there are so many more rectangles than just squares is due to two attributes.
1). Dimension
2). Orientation

We will now build on the squares puzzle.
We need to determine the dimention of the rectangles:
So we identify the sides of the board with x and y, respectively.
...[text shortened]... in length)

And get a total amount of rectangles of = 1296

Thats why you win so many games!😵
12. 06 Mar '06 05:44
Originally posted by excalibur 8
I am right, and you risk being a pedant.
Well if he is just at risk, he should wear a condomint.
13. 08 Mar '06 17:57
Originally posted by Trains44
Thats why you win so many games!😵
Thank you Trains!
Alhtough it didn't seem to help in our last game😛

As my wife tells me:

"Flattery will get you everywhere!"

Care for another?