document.write( "Question 1088468: The number of squares that can be formed on a chess board is-:
\n" ); document.write( "a)204
\n" ); document.write( "b)304
\n" ); document.write( "c)1296
\n" ); document.write( "d)1024
\n" ); document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #702729 by KMST(5328) $\"\"$ $\"About$

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I would say that you can make $\"highlight%28204%29\"$ squares can be made out of contiguous squares chosen from the 64 squares of the chessboard.
\n" ); document.write( "There are obviously $\"64\"$ 1X1 squares, and $\"1\"$ 8X8 square,
\n" ); document.write( "but how many 2X2, 3X3, 4X4, 5X5, 6X6, and 7X7 squares can be made?
\n" ); document.write( "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.
\n" ); document.write( "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 $\"2\"$ leftmost columns. That is $\"2\"$ choices for topmost row, and $\"2\"$ choices for leftmost column, for a total of $\"2%2A2=2%5E2=4\"$ 7X7 squares.
\n" ); document.write( "Similarly, you can make $\"3%5E2\"$ 6X6 squares,
\n" ); document.write( " $\"4%5E2\"$ 5X5 squares,
\n" ); document.write( " $\"5%5E2\"$ 4X4 squares,
\n" ); document.write( " $\"6%5E2\"$ 3X3 squares,
\n" ); document.write( " $\"7%5E2\"$ 2X2 squares,
\n" ); document.write( "and as we already knew $\"8%5E2=64\"$ 1X1 squares.
\n" ); document.write( "The total is
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