Question

Four men were shipwrecked on an island. Having no food, they went to work gathering pineapples. After gathering pineapples, they were tired and all fell asleep. After another while, one of the men awoke and was very hungry so he ate 1/3 of the pineapples - more than his proper share. He then went back to sleep. The second man awoke and being hungry, ate 1/3 of the remaining pineapples and went back to sleep. The third man did the same. When the fourth man awoke, he took only his rightful share of the remaining pineapples. Then there were 6 pineapples left. How many pineapples did the men gather?

Answer 1

Working backward from the fourth man's share, we can calculate that the men gathered 41 pineapples originally. They each took 1/3 of the pineapples in turn, resulting in 6 remaining after all had eaten.

Step-by-step explanation:

Calculating the Number of Pineapples

Let's solve the problem by working backward to find out the original number of pineapples the men had gathered. When the fourth man ate his share, 6 pineapples were left. These 6 pineapples represent 1/3 of the pineapples left after the third man ate his share, because if he ate 1/3, 2/3 would remain. Thus, before the third man ate, there would be 6 × 3 = 18 pineapples.

Repeating this process, we know the second man also ate 1/3, leaving 2/3 of the pineapples before he ate. So before the second man ate, there would be 18 × 3/2 = 27 pineapples. Using the same logic, we find that before the first man ate his 1/3 share, the total number of pineapples would be 27 × 3/2 = 40.5. Since we cannot have half a pineapple in this context, we round up to 41. Therefore, the men initially gathered 41 pineapples.