Solution to Problem 129

Congratulations to this week's winner

Nathan Pauli

Other solutions were submitted by Shaun Lewis, Scott Baker. Further solutions were submitted by Philippe Fondanaiche, Scott Powell, Scott Baker, Sudipta Das, Alexey Vorobyov.

Yes, there are sets of lines whose intersections form a square. Here are two such possible choices:
a) y = x, y = x - 1, y = -x + b, y = -x + b + 1;
b) y = -x, y = x - 1, y = x + b, y = -x + b + 1.
The first one is sketched on the left; it can be reflected through the line x = 1/2 to get another one.

Nathan Pauli showed that the problem admits a general solution under the (obvious) necessary condition that no three points are colinear.

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