Problem 5.4. Alyona, Borya, Vera, and Polina were collecting apples in the garden. Someone collected 11 apples, another - 17, a third - 19, and the fourth - 24. It is known that

- one of the girls collected 11 apples;
- Alyona collected more apples than Borya;
- the total number of apples collected by Alyona and Vera is divisible by 3.

Who collected how many apples?
(a) Alyona collected
(1) 11 apples.
(b) Borya collected
(2) 17 apples.
(c) Vera collected
(3) 19 apples.
(d) Polina collected
(4) 24 apples.
Answer: a3 b2 c1 d4.

Solution. The total number of apples collected by Alyona and Vера is divisible by 3. Thus, if Alyona collected 24 apples, the number of apples collected by Vера must also be divisible by 3; but among our numbers, there are no others that are multiples of 3, so this is impossible.

Since Alyona collected more apples than Borya, she must have collected either 17 or 19 apples. But if she collected 17 apples, then Borya must have collected 11 apples, and according to the problem, 11 apples were collected by one of the girls.

Therefore, Alyona collected 19 apples, and Borya collected 17. Of the remaining two numbers, only 11, when added to 19, gives a number divisible by 3. Thus, Vера collected 11 apples, and Polina collected 24 apples.