Pirate Portions
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: Reader Sudipta Das.
Solution
Mail to Ken