Oh Mangoes! My FavouriteNumber Theory Level 3
One night three naughty boys stole a basket full of mangoes from a garden, hid the loot and went to sleep. Before retiring they did some quick counting and found that the fruits were less than a 100 in number. During the night one boy awoke, counted the mangoes and found that he could divide the mangoes into 3 equal parts if he first took 1 for himself. He then took 1 mango, ate it up, and took 1/3 of the rest, hid them separately and went back to sleep. Shortly thereafter another boy awoke, counted the mangoes and he again found that if he took 1 for himself the loot could be divided into 3 equal parts. He ate up one mango, bagged 1/3 of the remainder, hid them separately and went back to sleep. The third boy also awoke after some time, did the same and went back to sleep. In the morning when they all woke up, and counted their mangoes, they found that the remaining mangoes again totaled 1 more than could be divided into 3 equal parts. How many mangoes did the boys steal ?