Math problem for the genius

Three travelers arrived tired and hungry at a lonely inn. The innkeeper apologized and said he could only offer them a meal of potatoes. When he brought in the dish, all men were asleep. After a while, one of the three woke up, ate a third of the potatoes, and went back to sleep. Soon afterward another woke up, ate a third of the potatoes that remained, and promptly fell asleep again. Then the third man did likewise. When the innkeeper came back, he found eight potatoes were left. How many had he put on the dish?

first guy eats 1/3 so 2/3 remain, the second guy eats another third, so you divide the 2/3 by 3 and then multiply by 2, that get´s you 4/9, repeat this and after the third guy ate you have 8/27 of the original amount left.

so 8/27 of one full portion = 8 potatoes (you multiply by 27)

8 full portions = 216 potatoes (you divide by 8)

1 full portion = 27 potatoes

we then check if the calculation´s correct

2/3 of 27= 18
2/3 of 18 = 12
2/3 of 12 = 8

So yeah, it´s correct!!!

The third man ate 1/3 of the potatoes he found, so leaving 2/3 or 8 potatoes
If 8 pots is 2/3 then the 3/3 he found on the plate was 12 potatoes

The second man ate 1/3 of his plateful, leaving 2/3 or 12 pots
If 12 pots is 2/3 then the 3/3 he found on the plate was 18 potatoes

The first man ate 1/3 of the potatoes he found, so leaving 2/3 or 18 potatoes
If 18 pots is 2/3 then the 3/3 he found was 27 pots.

Check ....................
Start with 27, 1/3 of 27 = 9, so 18 left
1/3 of 18 = 6, so 12 left
1/3 of 12 = 4, so 8 left

If only the innkeeper had woken them all when he brought in their potatoes!

In more Mathematical terms, let the original number of potatoes be x
The first man ate 1/3 of them, which means he left (2/3)x
The second man also left 2/3 of what he found, so he left (2/3)(2/3)x
The third man also left 2/3 of what he found, so he left (2/3)(2/3)(2/3)x = 8