Mr. Dolphin and Mr. Shark were skilled fishermen. Once, they caught 70 fish together. Five ninths of the fish caught by Mr. Dolphin were trouts. Two seventeenths of the fish caught by Mr. Shark were carps.

How many fish did Mr. Dolphin catch?

(L. Hozová)
The number of fish caught by Mr. Dolphin was a multiple of 9 and did not exceed 70. Therefore, Mr. Dolphin could have caught

$$
9, \quad 18, \quad 27, \quad 36, \quad 45, \quad 54, \quad 63
$$

fish. The number of fish caught by Mr. Shark was a multiple of 17 and did not exceed 70. Therefore, Mr. Shark could have caught

$$
17, \quad 34, \quad 51, \quad 68
$$

fish. Together, they caught 70 fish, which can be expressed from the given numbers only as

$$
70=36+34 .
$$

Mr. Dolphin caught 36 fish.

Note. It is not necessary to try all possible sums (of which there are $7 \cdot 4=28$). It is sufficient to consider the four possible numbers of fish caught by Mr. Shark, determine the corresponding number of fish for Mr. Dolphin (the difference from 70), and verify whether this number is divisible by 9:

| $\check{z}$ | 17 | 34 | 51 | 68 |
| :---: | :---: | :---: | :---: | :---: |
| $d=70-\check{z}$ | 53 | 36 | 19 | 2 |
| $9 \mid d ?$ | no | yes | no | no |