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Here's a different posing of the problem: This figure is a rectangle sub-divided into 10 different-sized squares, each with a different integer (counting number) side length. What are the dimensions of the rectangle? Is the rectangle really a square? How many solutions are there? How do you know?

A lovely 3D visualization problem

A YouTube version of the same proof

Another cool approach to this problem is to reflect either the hole or the ball over one of the sides and see if there is a direct line shot. Stripping down problems from all the textbook chatter is a grand way to get students thinking. And students defining their own problems is brilliant!