Mmmmm.....Coconuts

[AllPrimesAreOdd]

A ship in the ocean sinks, and 5 sailors are stranded on a desert island with a monkey. The monkey's name is Clarence. THe island is covered with coconut trees. All day, the 5 sailors gather a huge pile of coconuts. They plan to split it the next day.
That night, one of the sailors decides to take a cut of the pile. After splitting the coconuts into 5 equal piles with 1 coconut left over, he takes one of the piles, and gives the extra coconut to the monkey.
AFter this sailor is done and returns to sleep, a second sailor does the same thing. He splits the coconuts into 5 equal piles with one coconut left over which he gives to the monkey, and he takes one of the piles.
The 3rd, 4th, and 5th sailors do the same.
In the morning, all the sailors notice that the pile is much smaller (and the monkey is much fatter) than the day before (but none of them mention anything because they are all guilty.) THey take the remaining coconuts and split them amongst themselves equally, 5 ways.

What is the smallest possible number of coconuts in the original pile?

[AllPrimesAreOdd]

i was just informed that an identical problem was posted not long ago (with very interesting replies.)

excuse my ignorance ops:

[xilman]

Originally Posted by AllPrimesAreOdd

What is the smallest possible number of coconuts in the original pile?

There were -4 coconuts. At the first iteration, the pile was split into five equal piles each containing -1 coconuts. Five times -1 is -5, which is one fewer than the original pile; this extra coconut was given to the monkey. The sailor takes away his -1 coconut, leaving -4 in the pile ready for the next sailor to repeat the process.

8-)


Paul

P.S. I can't really take credit for this answer. It's an old chestnut --- or is that coconut?

[graeme]

Incidently Paul Dirac is allegedly the one who came up the the -4 coconuts solution. He invented the concept of what we now call anti-matter, so I suppose it was fairly natural for him to think of anti-coconuts.

(as with all good stories, no-one is really sure if he did or not, not even him! )

[ET_]

as with all good stories, no-one is really sure if he did or not, not even him!

call it Uncertainty Principle...

Is there room for a joke? Here it is:

A biologist, a phisicist and a mathematician look at the door of a laboratory.

A man and a woman suddenly enter the lab and close the door.
After a while the door opens again, and the man and his assistant come out, together with a technician.

"It's a matter of life, they reproduced" says the biologist.
"No, there are only two of them, the third person is a fallacy in the data gathered" added the phisicist.
"Don't mind about it" says the mathematician, "the room will become empty as soon as someone enters that lab..."

Luigi

[trif]

Originally Posted by ET_

call it Uncertainty Principle...

Is there room for a joke? Here it is:

A biologist, a phisicist and a mathematician look at the door of a laboratory.

A man and a woman suddenly enter the lab and close the door.
After a while the door opens again, and the man and his assistant come out, together with a technician.

"It's a matter of life, they reproduced" says the biologist.
"No, there are only two of them, the third person is a fallacy in the data gathered" added the phisicist.
"Don't mind about it" says the mathematician, "the room will become empty as soon as someone enters that lab..."

Luigi

And the human resources director castigates them for assuming the woman was the man's assistant and sends them for gender sensitivity training.

[ET_]

Trif, it has been hard enough to transtale it from Italian...

I took it from an old book of math, they still did not know about political correctness... I apologize.

Luigi :(

[cheesehead]

[Edit: On third thought, no comment.]