3. (7-8 grade) Vasya thought of 5 natural numbers and told Petya all their pairwise sums (in some order): $122,124,126,127,128,129,130,131,132,135$. Help Petya determine the smallest of the numbers Vasya thought of. Answer: 60.
Solution. By adding all 10 pairwise sums, we get the sum of all 5 numbers, multiplied by 4, since each number participates in it exactly 4 times. $122+124+126+127+128+129+130+131+132+135=1284=4 S$, therefore, $S=321$. The sum of the two smallest numbers is 122, and the sum of the two largest is 135, so the third largest number is $321-122-135=64$. Note that the number 124 can only be obtained as the sum of the smallest and the third largest, i.e., the smallest number is 124-64 $=60$.