1. Two friends, Dushan and Nikola, met after many years. Dushan stated that he has three sons. Nikola asked how old they were. "The product of their ages is 36, and the sum is equal to the number of the bus that just passed by us," Dushan replied. Based on this information, Nikola could not determine their ages. "Only the oldest of them has a mole like me," Dushan added. With this additional information, Nikola calculated the ages of the children? (The ages are expressed as natural numbers).
Solution. The product of three natural numbers can only equal 36 in the following cases: $1 \cdot 1 \cdot 36, 1 \cdot 2 \cdot 18, 1 \cdot 3 \cdot 12, 1 \cdot 4 \cdot 9, 1 \cdot 6 \cdot 6, 2 \cdot 2 \cdot 9, 2 \cdot 3 \cdot 6$, 3.3.6. For each of these cases, the sum is equal to: $38, 21, 16, 14, 13, 13, 11, 10$ respectively. Since Nikola could not determine the ages based on the bus number, it follows that the bus number is 13. When Dushan added that the oldest son is laughing, Nikola chose the second combination from 1,6,6 and 2,2,9, because here it is known which son is the oldest.