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Killing squares


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#1 bonanova

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Posted 05 April 2013 - 09:18 PM

Forty toothpicks form a 4x4 checkerboard as shown in the figure.

What is the smallest number of toothpicks that if removed will break

the perimeter of every square: the 16 unit squares, the 9 order-2 squares,

the 4 3x3 squares and of course the outside border?

toothpicks.gif

If you like, extend the problem to

  1. prove your answer is smallest possible.
  2. destroy every rectangle (including the squares) with fewest removals.
  3. extend the size of the square to 5x5, 6x6, 7x7 and 8x8.
  4. derive an expression for the fewest removals.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 k-man

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Posted 05 April 2013 - 10:23 PM

Spoiler for #1

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