On the table lay eight cards with numbers $2,3,5,7,11,13,17,19$. Ferda picked three cards. He added the numbers written on them and found that their sum was 1 greater than the sum of the numbers on the remaining cards.

Which cards could have remained on the table? Determine all possibilities.

(L. Hozová)

Hint. What is the sum of the numbers on all the cards?
The sum of the numbers on all eight cards is

$$
2+3+5+7+11+13+17+19=77
$$

and that is equal to $39+38$. Ferda chose three cards with a sum of 39. By trying the largest numbers first, we can find all the suitable options:

| in hand | on the table |
| :---: | :---: |
| $19,17,3$ | $13,11,7,5,2$ |
| $19,13,7$ | $17,11,5,3,2$ |