Question 3158: I'd appreciate your help.
Three men went fishing one day. They put all the fish in one basket. Then they left for a rest. When the first man came back, he divided the fish into three equal parts with one fish left over. He threw away that one, and left with his ration. When the second man was back, assuming that he was the first one coming back, he divided the remaining fish into three equal parts of one fish left over. He threw away that one, and left with his ration. When the third man was back, assuming that he was the first one back, he did the same thing as the first two.
a.) What is the minimal number of fish they caught in total? And justify your answer.
b.) Let T be the number of fish they caught in total, and let x be the number of fish the third person took. Express T in terms of x.
c.) What would be next two numbers of fish they caught in total? (hint: use formula in (b))
Answer by drglass(89)   (Show Source):
You can put this solution on YOUR website! To solve this problem work from the last fisherman forward. How many fish were in the basket when the last fisherman got there?
Since the last fisherman was able to divide the number in the basket by 3 with a remainder of 1, the number of fish must have been:
Where x is the number of fish taken by the last fisherman.
The second fisherman removed 1 then took 1/3 of the fish leaving 2/3 for the last fisherman. To construct that number we have to undo this operation, that is we multiply N by 3/2 then add 1, or:
Likewise, the first fisherman removed 1 and left 2/3 in the basket for the second fisherman so
If we try n = 0 we cannot construct a valid number because T would not be a whole number. Likewise, n = 1 and n = 2 do not work, but n = 3 does. So, with x = 3, the number of fish in the basket when the second fisherman took his turn was:
 ,
which means he took  fish. When the first fisherman gets to the basket there are:
The fishermen caught 25 fish.
To construct the total number of fish, we created an equation for T in terms of x, which is what part b of the question wants. So,
see above
Now, to find the next numbers in the sequence start with values of n greater than 3. You should quickly realize that even numbers won't work. To give you an idea of how long this will take, the value of n is 11 which makes T = 79.
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