**B. 3881.** Let *a*, *b*, *c* denote rational numbers, such that is also rational. Prove that at least two of the numbers *a*, *b*, *c* must be zero.

Suggested by *E. Fried,* Budapest

(5 points)

**C. 838.** Mihály Tímár (the hero of a famous Hungarian novel) is in a trouble. The red crescent that marked the sack containing the treasure has come off. He knows, however, that the heaviest of the four sacks hides the treasure. From three measurements, he has found out that the first sack together with the second one are lighter than the other two, the first and third together are equal in weight to the other two, and the first and fourth sacks together are heavier than the other two. Which sack hides the treasure?

(5 points)

**K. 69.** Out of the digits of a three-digit number of different digits, all the possible two-digit numbers of different digits are formed, and these two-digit numbers are added. Given that the sum is equal to the original three-digit number, find all such three-digit numbers.

(6 points)

This problem is for grade 9 students only.