73. On the board, there were five integers. By adding them in pairs, the following ten numbers were obtained:

$$
0,2,4,4,6,8,9,11,13,15
$$

What five numbers were written on the board? Can the following ten numbers be obtained in this way:

$$
12,13,14,15,16,16,17,17,18,20 ?
$$
73. Adding all 10 sums, we get 72. Since each of the five original numbers appears in four sums, the sum of the desired numbers is $72: 4=18$. The sum of the two smallest, obviously, is 0, and the sum of the two largest is 15. Therefore, the third largest number is $18-0-15=3$. In the sequence of sums, the second place is occupied, obviously, by the sum of the first and third. 62

Therefore, this sum is 2, and the smallest number is $2-3=-1$. It is clear that the second number is $0-(-1)=1$. Similarly, we find that the two largest numbers are 5 and 10.

In the second case, the sum of the ten given numbers is 158. The sum of the desired numbers should equal $158: 4$, which is impossible since the desired numbers are integers. Therefore, the answer to the second question of the problem is negative.