[ Examples and counterexamples. Constructions ]

Seven mushroom pickers collected a total of 100 mushrooms. Is it necessarily true that there will be two mushroom pickers who together collected at least 36 mushrooms, if the number of mushrooms collected by each is pairwise distinct?
Let's say, for example, the mushroom pickers collected 10, 12, 13, 14, 16, 17, and 18 mushrooms respectively. Then any pair together collected no more than 35 mushrooms, and

$10+12+13+14+16+17+18=100$

## Answer

Not necessarily.