A tough problem, an oldie
I am going to repeat an old problem that first appeared in a weekly newspaper, where riddles were posted by no other than the great M. Gardner. A prize of 100$ was later promised for a solution.
"Five men
find themselves shipwrecked on an island, with
nothing edible in sight but coconuts, plenty of these, and
a monkey
. They agree to split the coconuts into five equal
integer lots, any remainder going to the monkey.
Man 1 suddenly feels hungry in the middle of the night
and decides to take his share of coconuts at that very
moment. He finds the remainder to be one after division
by five, so he gives this remaining coconut to the monkey
and takes his fifth of the rest, lumping the coconuts that
remain back together. A while later, Man 2 wakes up
hungry too, and does exactly the same - takes a fifth of the
coconuts, gives the monkey the remainder, which is again
one, and leaves the rest behind. So do men 3, 4, and 5.
In the morning they all get up, and no one mentions anything
about his coconut-affair the previous night. So they share
the remaining lot in five equal parts finding, once again, a
remainder of one left for the monkey. Find the initial number
of coconuts.
"
The problem is HARD, so don't think there's something wrong with you if you can't solve it. The first solution was hard labour. Allegedly, it was Paul Dirac himself who provided the clever solution which is in fact very elegant and simple. Also allegedly, this had to do with his then current work on anti-electrons. Now there's a clue in there..
)
