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Four P Pentominoes (Posted on 2016-03-04) Difficulty: 3 of 5
Four copies of the P pentomino pictured below can easily be placed in a 5x5 square without overlapping.
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Prove it is impossible to put 5 copies in a 5x5 square without overlapping.

Which of the other 11 pentominoes can be included with four P pentominoes such that all five can be placed in a 5x5 square?

See The Solution Submitted by Brian Smith    
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Sq probe | Comment 2 of 4 |
If it would be possible to place 5 pentominoes in the 5x5 sq it would be also possible to place 5 squares 2x2. 

But this is not possible because when 4 squares 2x2 are placed, the arrangement of the free space is only possible in blocks of 1xn, and there is no way to place the fifth 2x2 square.

Edited on March 4, 2016, 5:38 pm
  Posted by armando on 2016-03-04 14:56:02

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