Puzzle of the Month, March 99

1) Permutation problem
Explain why when you permute the pieces a<>d and b<>c of the 5-piece puzzle shown in fig. a) you obtain 2 different squares, but if you do the same thing with the 5-piece puzzle b) nothing changes?

puzzle 1
96-99, Sarcone & Waeber, Lausanne


2) Square inclusion
Cut the green shape below (a parallelogram) into 4 identical pieces in order to form a regular polygon that encloses the red small square...

parallelogram
96-99, Sarcone & Waeber, Lausanne



Solutions

1) Permutation problem
A diagram is better than a thousand words... Well, look at the diagrams a) and b) below and you will understand the problem. Actually, in the fig. b) the puzzle pieces are kites having adjacent sides equal in pairs so that if you switch these pieces you will obtain the same square with the hole again and again!

diagram a) diagram b)

 

2) Square inclusion
Sure, there are several good solutions... But I like this one!

solution

 


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