- 05 Jun '04 18:12There were 4 men stranded on a dessert island once. They decided to search the whole island and find what recources they had to live off. After searching all over they discover thre's plent yo f water but the only food available was coconuts. So they decided that they would collect al the coconuts on the isalnd and then devide them up between them, so they each got a fair share of the food currently avaialble.

They spent all day doing this and built a very large pile of the big hairy nuts (). They were all very tired though so they decided to to leave the pile and devide it up in the morning....

After a while one of the them was still awake and thinking, he was worried they did not have enough to live off. He got up and devided the coconuts into 4 piles and found one left over. This he thought would cause an argument in the morning so he threw it out to sea. Looking at his pile he decided it was a little small, so he burried his pile and put the other 3 back in to a big pile and went to sleep again.

a little while later another of the men woke....and he was worried they did not have enough to live off. He got up and devided the coconuts into 4 piles and found one left over. This he thought would cause an argument in the morning so he threw it out to sea. Looking at his pile he decided it was a little small, so he burried his pile and put the other 3 back in to a big pile and went to sleep again.

soon after the third amn got up and he to got up devided the coconuts into 4 piles and found one left over. This he thought would cause an argument in the morning so he threw it out to sea. Looking at his pile he decided it was a little small, so he burried his pile and put the other 3 back in to a big pile and went to sleep again.

finaly the 4th man got up, and as the other before him had he devided the coconuts into 4 piles and found one left over. This he thought would cause an argument in the morning so he threw it out to sea. Looking at his pile he decided it was a little small, so he burried his pile and put the other 3 back in to a big pile and went to sleep again.

The next morning they all got up and looked at the ground and generally avoided each others gazes, non one comented on the pile which was now a lot smaller! They devided the the coconuts up as planned in to 4 piles and discovered there was one left over. After a suprisingly short discussion they decided to throw it in the sea and each took there piles...

My puzzle is...finaly!..... what is the smallest number of coconuts they could have started with the previous night? - 06 Jun '04 22:01

lets try...*Originally posted by TheMaster37***Occording to the story, the number of coconuts is:**

N= 4(4(4(4(4X+1)+1)+1)+1)+1 = 1024X + 341

Assuming they never take negative amounts of coconuts, or 0 coconuts, the minimum should be 1365, given i didn't make mistakes in my calculation.

first man gets up and devides in to 4 to find one left over so...

(1365-1)/4 = 341

1364 - 341 = 1023

2nd man

(1023-1)/4 = non integer

Close but no cigar! You have merely quatered the number each time (and achieved a correct reuslt for that scenario) but each man hides HIS quater but re-piles the the other 3/4 for the next man to opperate on.... - 07 Jun '04 06:02 / 1 edit

Oops, I didn't read the question properly. I thought there were 5 men.*Originally posted by THUDandBLUNDER***What coconuts?**

-4

My flippant answer ought to have been -3

The smallest positive solution with n men each throwing k coconuts into the sea after every division is given by

n^(n+1) - k(n-1)

. - 07 Jun '04 08:08

Good Job! That the answer I have too (note i was givren this problem but never the solution so thre may be a lower one but i don't think so.)*Originally posted by timebombted***1021........**

The piles go down in number as so:

1021

765

573

429

321

80 Each the next day + 1 in the ocean

Just out of curiosity how did you go about solving this? - 08 Jun '04 09:33

Yeah, same method as me*Originally posted by timebombted***Used Microsoft Excel to create the formula then copied it to infinity, after that filtered on columns with whole numbers......**

The formula is quite complex due to the number of brackets and stuff but there is no complex algebra. Dependes whether you start at the bottom or the top.... I think I said X = number they are left with and worked up...so

the pile in the moring would be (X*4) + 1

the pile the last man found would be 4/3*(X*4)+1)+1

and so on for each man....

Starting from the top X = number they start with

3(X-1)/4 is the result after the first man....

3((3(X-1)/4)-1)/4 after the second.....

This was alot more chalenging puzzle before computers made ittrative processes easier If you wanted to do this without a computer then best bet is to use the first method, if you start at 1 you only have to get to 80!