6 February 2015

Chessboard puzzle

Here is a simple or complex – depending upon your perspective – puzzle. It is complex if you try to enumerate all possibilities. There is a very simple and elegant way though.

As always, if you are reading this on FB, do not post your answer on Comments section. Sent me a message.

Question: In a simple 8 by 8 chessboard, how many rectangles are there?

As you can imagine a rectangle can be one square by one square – and there are 64 of them – (squares are rectangles) or two squares by one square (and there are quite a few of them) or three squares by five squares and such….



Posted February 6, 2015 by Rajib Roy in category "Puzzles

10 COMMENTS :

  1. By Rajib Roy on

    The answer to the puzzle is extremely simple.
    What we have to realize is that any rectangle in a chessboard is formed by choosing two vertical lines from the 9 vertical lines available (to form 8 columns, you need 9 lines) and two horizontal lines from the 9 horizontal lines available. Any such choice will give you a rectangle and all rectangles are necessarily one of those choices.
    So the answer is the ways you can pick 2 vertical lines multiplied by the ways you can pick 2 horizontal lines.
    In other words, 9C2 * 9C2 = 36*36 = 1296

    Reply
  2. By Rajib Roy on

    The answer to the puzzle is extremely simple.
    What we have to realize is that any rectangle in a chessboard is formed by choosing two vertical lines from the 9 vertical lines available (to form 8 columns, you need 9 lines) and two horizontal lines from the 9 horizontal lines available. Any such choice will give you a rectangle and all rectangles are necessarily one of those choices.
    So the answer is the ways you can pick 2 vertical lines multiplied by the ways you can pick 2 horizontal lines.
    In other words, 9C2 * 9C2 = 36*36 = 1296

    Reply

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