Four squirrels ate a total of 2020 nuts, each at least 103 nuts. The first squirrel ate more nuts than any of the other three squirrels. The second and third squirrels ate a total of 1277 nuts.

How many nuts did the first squirrel eat?

(L. Hozová)
We will indicate the possibilities for how many hazelnuts the second and third squirrels could have eaten, i.e., the number 1277 will be decomposed into two addends, each of which is at least 103:

$$
1277=1174+103=\ldots=640+637=639+638 .
$$

From this, it follows that the first squirrel ate at least 640 hazelnuts (she ate more than any of the other squirrels).

For the first and fourth squirrels, there were $2020-1277=743$ hazelnuts left. Again, we will indicate the possibilities for how many hazelnuts the first and fourth squirrels could have eaten:

$$
743=640+103=639+104=\ldots
$$

From this, it follows that the first squirrel ate at most 640 hazelnuts.

The first squirrel ate exactly 640 hazelnuts.

Evaluation. 2 points for each of the indicated lists; 2 points for the conclusion.