6.1. On the board, there are 5 integers. By adding them in pairs, the following set of 10 numbers was obtained: $-1,4,6,9,10,11,15,16,20,22$. Determine which numbers are written on the board. In your answer, write their product.
Answer: -4914 (numbers on the board: $-3,2,7,9,13$).

Solution. The sum of the numbers in the obtained set is 112. Each of the original five numbers appears 4 times in this sum. Therefore, the sum of the required numbers is $112: 4=28$. The sum of the two smallest numbers is -1, and the sum of the two largest numbers is 22. Therefore, the middle number (the third largest of the five) is $28-22-(-1)=7$. In the set given in the problem, the second number is equal to the sum of the first and third required numbers, from which the first number is $4-7=-3$, and the second is 2. Similarly, we obtain that the fourth number is 9, and the fifth is 13. Thus, the numbers on the board are $-3,2,7,9,13$, and their product is -4914.