Here is my humble contribution to I Math Carnival organized by Eliatron: a problem earlier this year by my math teacher. Do not collect any great difficulty because I'm only in 1 ยบ Bachillerato.
A group of 5 pirates shipwrecked on an island full of coconuts in the who lives only a monkey. After much thought on how to survive, choose to gather all the coconuts on the island and pile. After a hard day's work, get collect them all and decide to leave the stack intact to pass on to the next morning.
But none of the pirates is wary of others. A first pirate gets up in the middle of the night, divides the lot into 5 parts and get a . But to divide the lot into 5 parts on a coconut, so it gives the mono . Soon after, another pirate gets up and returns to divide the lot into 5 parts and takes one, all without noticing the decline of the heap initial. Again on a coconut to make the 5 groups, so it also gave the monkey. As expected, stands another third pirate and repeat. Have divided the lot into 5 parts again on another coconut. "Who do I give? Then the monkey. "The fourth pirate gets up to divide the pile of coconuts into 5 parts, and stays with it. Decides to give the monkey a coconut that was left to the 5 sub-lots. And finally, we find the fifth and last pirate. Divide the pile into 5 parts, gives the leftover coconut mono and stays on your part.
arrives the next morning and split the current bunch of coconuts into 5 parts on either without . How many coconuts were in the first lot and many are left in the morning?
The problem posed by the teacher had here. I thought maybe the number of coconuts that had each pirate could follow a final order, and so is (but obviously depends on what value is taken as the first term of the sequence).
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