Pirate Puzzle
A handful of pirates distributed some golden coins among themselves, such that:
- the share of Pirate 1 plus half the total share of the rest (all pirates
except #1)
- = the share of Pirate 2 plus 1/3 of the share of the rest (all pirates
except #2)
- = ...
- = the share of Pirate N plus 1/(N + 1) of the share of the rest (all
pirates except #N)
Captain Cutthroat, the puzzle-loving pirate, informed his captive Jolly Rogers
of this strange method of distribution. Moreover, he promised to set Jolly free
if he could correctly tell him the share of each pirate.
"The total number of coins is less than 1000, and more than 50% of us received
an odd number of coins."
Jolly Rogers got to work immediately, and after some time, asked the Captain,
"Can you give me a little hint?"
"The least a pirate got is this number."
Jolly Rogers was still not sure until the Captain boasted, "And I got more than
10 times that fellow."
Can you guess the number of pirates and the share of each?
Source:
http://www.ken.duisenberg.com/potw/archive/arch01/010925sol.html
and Sudipta Das
Click here for the answer.
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