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Sunday Times Teaser 2836 – Squaring Up

by Tom Wills-Sandford

Published: 29 January 2017 (link)

Alice had a large collection of one centimetre square tiles. She used them to make a set of some larger squares of different sizes, all with sides of less than a metre. When I saw these squares I removed one corner tile from each. Then, for each mutilated shape, Alice moved the minimum number of tiles to transform it into a rectangle. Overall she moved two hundred tiles. This resulted in a set of rectangles all of whose sides were a prime number of centimetres long.

What (in increasing order) were the lengths of the sides of her original squares?

5 Comments Leave one →
  1. Brian Gladman permalink

    • geoffrounce permalink

      Excellent very fast solution – only 13 msec on my laptop , with few lines of code after excluding comments.

  2. Here’s my code:

    The library is available from [ ]

  3. Christopher Wheeler permalink

    Hello all I am totally confused by this.
    What is the answer?

    • Brian Gladman permalink

      Hello Christopher,

      The answer is “Squares with sides 30, 42, 60 and 72.”. The rationale for this solution is given in the comments on lines 12 to 19 of my Python program given above.

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