Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142. I need help with this problem, and I was thinking in this way:
$$ x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} + x_{7} = 332 $$
and I need to find three of these which sum is at least 142.
But I don't know what next. 
Any help would be appreciated

You can form $\binom{7}{3}$ triplets, i.e. 35 triplets. Every men participates in $\binom{6}{2}$ triplets, i.e 15. So the sum of all 35 triplets is $15 \times 332 = 4980$, which means the average is $\frac{4980}{35} = 142.427...$ so there has to be at least one triplet with total age of at least 142. Actually since all years are integers this proves that there has to be a triplet with total sum of at least 143.
