In the pond, 30 pikes were released, which gradually eat each other. A pike is considered full if it has eaten no less than three pikes (full or hungry). What is the maximum number of pikes that can become full?
The number of pikes eaten is not less than three times the number of satiated pikes.

## Solution

Let $s$ be the number of satiated pikes. Then they together have eaten no fewer than $3s$ pikes. Since each pike can only be eaten once, and at least one pike remains at the end, $3s < 30$. Therefore, $s \leq 9$.

We will provide an example where exactly 9 pikes are satiated. Suppose 7 pikes (from the 3rd to the 9th) ate 21 pikes (from the 10th to the 30th; each ate 3 pikes). After this, 9 pikes remain. The first and second pikes can become satiated by eating 6 pikes (from the 4th to the 9th).

## Answer

9 pikes.