MathDB

Baron Munchhausen has a collection of stones, such that they are of

1000

distinct whole weights,

2^{1000}

stones of every weight. Baron states that if one takes exactly one stone of every weight, then the weight of all these

1000

stones chosen will be less than

2^{1010}

, and there is no other way to obtain this weight by picking another set of stones of the collection. Can this statement happen to be true?
(М. Антипов)
Thanks to the user Vlados021 for translating the problem.

Problem Statement