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Square in a notched square (Posted on 2015-11-25) Difficulty: 3 of 5
Remove a unit square from each corner of a square of side x (with x≥2).

Find, in terms of x, the area of the largest square that can be inscribed in the remaining figure.

No Solution Yet Submitted by Jer    
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Some Thoughts A thought (spoiler) | Comment 2 of 3 |
In the case x > 4, Charlie’s post invites us to carry out the
substitution of his ‘y’ to obtain an explicit expression for
the area in terms of x.

But to avoid the complications:

we can split the area into a central inner square of side x – 2,
(with vertices at the inner corner of each square cut-out)
and four triangles each with base x – 2 and height 1:

Area      = (x – 2)2 + 4*(1/2)(x – 2)

            =  x(x – 2)

  Posted by Harry on 2015-11-27 14:50:41
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