[ Examples and counterexamples. Constructions ]

Can 40 candies be distributed among six children so that each has a different number of candies and any two together have less than half of all the candies?
For example, $10+9+8+7+5+1=40$, while the largest sum of any two is $10+9=19<20$.

There are other examples as well.

## Answer

it can be done.