7.3 In a pond with carp, 30 pikes were released, which began to gradually eat each other. A pike is considered full if it has eaten three other pikes (hungry or full), and each full pike ate exactly one carp for dessert (hungry pikes did not eat carp). What is the maximum number of carp that could have been eaten? Justify your answer.
Solution. The maximum number of pikes eaten is 29, so no more than $29: 3=9.6666 \ldots$ pikes can be satiated, which means no more than 9 pikes (and, accordingly, no more than 9 roaches can be eaten). 9 roaches can be eaten as follows (the method is not unique). Choose 9 pikes and denote them as $A_{1}, A_{2}, \ldots, A_{9}$. First, pike $A_{1}$ eats three of the unselected (becomes satiated) and a roach, then pike $A_{2}$ eats pike $A_{1}$, two unselected, and a roach, and so on until pike $A_{9}$, which eats pike $A_{8}$, two unselected, and a roach.

Answer: 9 roaches.

| THERE IS IN THE SOLUTION | SCORE |
| :--- | :---: |
| Correct and justified answer | 7 points |
| Correct example of how 9 pikes can be satiated, without proof that 9 is the maximum number | 3 points |
| Justification that 10 pikes cannot be satiated (in the absence of an example showing 9 pikes can be satiated) | 2 points |
| Rougher estimates and examples of satiation of fewer than 9 pikes | 0 points |