Square Hole

Geometry Level 3

The above are 3 squares of distinct integer lengths, the smallest of which is 1.

Rearranging the 3 squares as in the diagram below, we find that the blue and yellow areas are equal. Are there any more combinations of 3 distinct squares such that ( Area of the largest ) ( Area of the medium-sized ) = ( Area of the medium-sized ) ( Area of the smallest ) ? (\text{Area of the largest}) - (\text{Area of the medium-sized}) = (\text{Area of the medium-sized}) - (\text{Area of the smallest})?

Yes, infinitely many Yes, finitely many No

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