What does John like if he likes 400 but not 300; 100 but not 99; and 2500 but not 2400?

John would like the number 900. The reasoning is actually quite simple, mathematically. Each of the numbers in the problem that John likes come out to round square roots - whole numbers. If the number cannot be reduced to a simple, whole square root, John doesn’t like it. The only number that comes out to a round number when taking the square root in the answers is 900.

Let’s break it down even further. The square root of 400 is 20, but the square root of 300 is 17.3, with some other decimals behind it. The square root of 100 is 10, but the square root of 99 is 9.94 and so on. Each of the numbers has a specific square root that goes with it (rounded for sake of space), and if it’s not round, John doesn’t like it. Simple as that.