Question 119
King Hiero has 11 metal pieces indistinguishable in appearance. The King knows that their weights (in some order) are $1, 2, \ldots, 11$ kg. Also the King has a bag that breaks if it contains more than $11$ kg. Archimedes knows the weight of each piece, and he wants to prove to Hiero that the first piece weighs $1$ kg. By a move Archimedes can put several pieces into the bag demonstrating to the King that the bag is still not broken (it is prohibited to break the bag!). Find the least number of moves needed for Archimedes to prove his claim.