Question 79
In Nottingham city, 100 riches reside, and each of them owns at least one million of gold coins. Robin Hood develops plans to raid them. Each plan consists in stealing same number of gold coins (not exceeding one million) from each of the riches. Prove that, no matter what wealths of the riches are, Robin Hood can develop at least 100 raiding plans such that for two different plans $P'$ and $P''$ there no two riches $B'$ and $B''$ such that $B'$ would have the same number of gold coins after the raiding plan $P'$ as $B''$ after the raiding plan $P''$.