Grandpa Vendelin went with his two grandsons Cyril and Metoděj to buy fishing rods. The price of the rods caught the attention of both Cyril and Grandpa. It was a four-digit number, where the first digit was one greater than the third digit, but one less than the last digit. The sum of all four digits was 6. Cyril also noticed that the first two-digit number represented a two-digit number that was 7 greater than the second two-digit number. However, what caught Grandpa's attention was that the number was the product of his age and the ages of both grandsons, with each grandson being older than one year.

How old was Grandpa Vendelin and how old were his grandsons?

(L. Hozová)
The number representing the price of rods is a four-digit number, where the first digit is one greater than the third digit and one less than the fourth. The three mentioned digits are therefore distinct, and the sum of all four digits is 6. The only numbers that satisfy the above conditions are 2013 and 1302. However, in the first case, the first two-digit number is 7 greater than the second two-digit number - thus, the price of the rods was 2013.

Expressing 2013 as a product of three numbers, none of which is equal to one, can only be done in one way:

$$
2013=3 \cdot 11 \cdot 61 \text {. }
$$

Grandpa Vendelín was 61 years old, and his grandchildren were 3 and 11 years old.

Evaluation. 3 points for discovering the number 2013 including justification; 3 points for the factorization of the number and the answer.