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Problem of the Week
Problem D
What’s in That Square?

Fourteen squares are placed in a row forming the grid below. Each square is to be filled with a positive integer, according to the following rules.

  1. The product of any four integers in adjacent squares is \(120\).

  2. Integers may appear more than once in the grid.

Four of the squares are already filled with a positive integer, as shown. Determine all possible values of \(x\).

The third square has a 2, the sixth square has a 4, the ninth square has the variable x, and the twelfth square has a 3. The remaining squares are empty.