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Geometry Partition

  1. Aug 27, 2009 #1
    1. The problem statement, all variables and given/known data

    For n>14 such that n is an integer, prove that a square can be partitioned into n smaller squares...

    2. Relevant equations


    3. The attempt at a solution

    I was thinking this would be somewhat of an induction proof because we are working our way up to n. So far, I've found when n = 15, n = 17, but somehow n = 16 is eluding me at the moment. I'm just trying to see what it would look like if I were to do this visually, however my assumption is that this has to deal with modulo 3 in some form or another. How this works into a proof is also something that is eluding me. Any suggestions would be warmly welcomed!
  2. jcsd
  3. Aug 28, 2009 #2


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    I'm sorry I can't be of much help, but at first sight a proof by induction seems impossible. Because suppose you have shown that if it is possible for n, then it can also be done for n + 1.
    Clearly, for n = 4 the statement is true (or even for n = 1, if you want).

    Also, what do you mean by "partition into smaller squares"? Does that count all squares? For example, when you draw a 3x3 grid in the square, does that give 9 squares? Or does that give 9 (1x1) squares + 4 (2x2) squares = 13 in total?
    Also, can you post an image for n = 15, just to get the problem clear?
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