Need help FAST!!

[jennybenny02]

ok.. Im stuck hopefully one of you can help me by tomorrow when I need this done. Sorry for the last minute. This is for my College Foundations of Math class.

Here is the problem:
4 men and a monkey gather coconuts, after going to sleep, one man awakens and decides to take his share of coconuts. He divides the coconuts into four equal piles, except for one remaining coconut, which he gives to the monkey. He then hides his share, puts the other piles back together and goes back to sleep. Each of the other men awaken during the night and does likewise, and every time there is one coconut left over for the monkey. In the morning, all the men awake, divide whats left of the coconuts into four equal piles, and again there is one left over that is given to the monkey. Find the minimum number of coconuts that could have been in the original pile.

I know the answer is 1021, But have no clue how to show my work for the answer. Each guy has a different equation Im guessing like (4x+1) :shock:

 

[jennybenny02]

I know this is a hard question and none of you probably want to take time to figure it out....

Im thinking the first guy splits up the piles (4x+1)
(4 equal piles of x coconuts + 1 remainder for the monkey)

Second guy wakes up (4y+1) - x
(4 equal piles of y coconuts (-1xpile of coconuts) + 1remainder for monkey)

3rd guy wakes up and splits the piles (4z +1) - (xpile) - (ypile)
(4 equal piles of z coconuts (- one x pile and one y pile) + 1 left over for monkey)

Would this be the right track??

I think it has to do w/ making a linear Diophantine equation

 

[Denis]

that's quite an old puzzle...
google search "monkey and coconuts"

 

[galactus]

Check this out:


http://mathworld.wolfram.com/MonkeyandC ... oblem.html

 

[jennybenny02]

Wow, Thanks a lot! That website is exactly what I was looking for :wink:

I never thought people would be so helpful online, most of the times you just find the annoying ones who dont help, haha.

Thanks again
~Jenn~