Question 10
The pirate law establishes that, in order to divide the coins of a treasure, the captain must choose a group of pirates (excluding himself). Then the captain must distribute the same amount of coins to each of the pirates in this group, in such a way that it is not possible to give each of them any of the remaining coins (respecting the fact that each pirate receives the same amount). The remaining coins are then given to the captain. On Captain Barbaroxa's ship there are 100 pirates (not including the captain). Barbaroxa must share a treasure that contains less than 1000 coins. If he chooses 99 pirates, he will have 51 coins, but if he chooses 77 pirates, he will have 29 coins.
a) How many coins does the treasure contain?
b) How many pirates should choose Barbaroxa to get as many coins as possible?
a) How many coins does the treasure contain?
b) How many pirates should choose Barbaroxa to get as many coins as possible?