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