## 5. Cards

There were seven cards in a box with numbers from 3 to 9 written on them (each card had one number). Mirko randomly took three cards from the box, and Slavko took two cards, while two cards remained in the box. Mirko looked at his cards and said to Slavko: "I know that the sum of the numbers on your cards is even." What is the product of all the numbers on Mirko's cards?

Result: 192
## Solution.

The sum of the two numbers on the cards taken by Slavko can only be even if both numbers have the same parity. Among all the numbers on the cards, there are four odd and three even numbers.

If Mirko has at least one odd number among his cards, i.e., if he does not have all three even numbers, then he cannot be sure that Slavko did not take one even and one odd number.

Therefore, Mirko has cards with the numbers 4, 6, and 8, and their product is 4$\cdot$6$\cdot$8=192.