Strategies and Hints

1. ₆₄C₂=

2. The numbers on the grid are the first 64 perfect squares.

3. An integer that is both a perfect square and a perfect cube is a perfect sixth power.

Solution

There are four integers less than or equal to 4096 (4⁶) that are perfect sixth powers. The probability of choosing two of these is ₄C_{2 64}C₂ = .