SOLUTION: The number of squares that can be formed on a chess board is-: a)204 b)304 c)1296 d)1024 I want to say that when the questions related to permutations and combinations etc co

Question 1088468: The number of squares that can be formed on a chess board is-:
a)204
b)304
c)1296
d)1024
I want to say that when the questions related to permutations and combinations etc come to me, I get stucked. So please can you explain how every permutations and combinations problems can be done with a simple logic?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I would say that you can make squares can be made out of contiguous squares chosen from the 64 squares of the chessboard.
There are obviously 1X1 squares, and 8X8 square,
but how many 2X2, 3X3, 4X4, 5X5, 6X6, and 7X7 squares can be made?
It is obvious that an 8X8 square will uses all 8 rows and all 8 columns of the chessboard, so the topmost, leftmost chessboard square must be included, but you can choose to leave some rows and columns out for smaller squares.
The topmost, leftmost chessboard square of a 7X7 square could be on the first row, or on the second row, and it could be in either ogf the leftmost columns. That is choices for topmost row, and choices for leftmost column, for a total of 7X7 squares.
Similarly, you can make 6X6 squares,
5X5 squares,
4X4 squares,
3X3 squares,
2X2 squares,
and as we already knew 1X1 squares.
The total is
.
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