Gold Coins In Bags
A farmer was blessed and got himself a cow that is able to produce gold liquid out of her udder. The farmer hurried to milk her and used his skill to process it into gold coins. He made 500 gold coins, Now he wants to divide them to * maximum number of bags * such that each bag will have a different amount of coins (two bags with three coins each are not allowed, also a bag with 0 coins are not allowed). How many bags did he use after the distribution?
( Hint: Start by trial and error with a small number of coins)
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1 solution
To get the maximum number of bags, put 1 coin in the first bag, 2 in the next, then 3, 4, and so on, until there are not enough coins for the next bag; the remaining coins can be dumped into the last filled bag. If we add the coins in the bags, we get 1 + 2 + 3 + . . . ≤ 5 0 0 2 n ( n + 1 ) ≤ 5 0 0 n 2 + n − 1 0 0 0 ≤ 0 n = 3 1