# 2016-7’s fortnightly maths prize winners

# STEP I-2015-3

A prison consists of a square courtyard of side b bounded by a perimeter wall and a square building of side a placed centrally within the courtyard. The sides of the building are parallel to the perimeter walls.

Guards can stand either at the middle of a perimeter wall or in a corner of the courtyard.

If the guards wish to see as great a length of the perimeter wall as possible, determine which of these positions is preferable.

You should consider separately the cases b < 3a and b > 3a.

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