An integer k is a “half square” if 2k is the square of a positive integer, for example, 18 is a half square because 2×18= 36= 6^2. What is the smallest half square that is greater than 100?

Start by finding the smallest whole square that’s bigger than 200. 15^2 = 225 is the smallest, but half of that isn’t an integer, so go to 16^2 = 256.

Half of that is 256/2 = 128. That’s the smallest “half square” bigger than 100.