Key idea. Assume every cage stays below the claimed number.

1. Suppose no cage contains 11 or more rabbits. Then every cage contains at most 10.

2. Across 10 cages, that would allow at most \(10\cdot10=100\) rabbits.

3. But there are 102 rabbits. The supposition is impossible, so some cage contains at least 11.

Remember. Forcing a large group can be proved by calculating the capacity when all groups are smaller.