Problem 49 (difficulty: 6/10)

Show that for all positive integer \(\displaystyle n\geq 6\) a square can be divided into \(\displaystyle n\) squares.

Solution:

Dividing a square into for ones of half the side we see that if a square can be divided into \(\displaystyle n\) squares, then it can also be divided into \(\displaystyle n+3\) squares. On the other hand we have the solutions for \(\displaystyle 1, 6\) and \(\displaystyle 8\):

(The right-most picture shows another possible construction.)

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