perplexus.info :: Numbers : Pirates Ahoy!

Pirates Ahoy! (Posted on 2023-10-26)

A handful of pirates distributed some gold coins amongst themselves such that:
• The share of Pirate 1 plus half the total share of the rest = the share of Pirate 2 plus 1/3rd of the share of the rest = the share of Pirate N plus 1/(N+1) of the share of the rest.

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 the pirates 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?

Note: "the share of Pirate N plus 1/(N+1) of the share of the rest" mean S(N)+((S(1)+S(2)+....+S(N-1)+ S(N+1)+ S(N+2)+...)/(N+1)

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

4 pirates with shares: 5, 95, 125, 140.
EXPLANATION:
The only proportions that satisfy the conditions bulleted in the problem are:
2 pirates: 3:4 3 pirates: 5:11:13 4 pirates: 1:19:25:28
Thus, any solution must be multiple of one of the above properties.
The first statement "more than 50%" rules out 2 pirates and restricts the other proportions to odd multiples.
The second statement "the least ....." forces the multiple for the 4-pirate proportion to be 5, 15, etc( so that the possible solutions have the same minimum value.) If the multiple is greater than 13, then the total number of coins is greater than 1000, so the multiple can only be 5.
The last statement "...more than 10 times..." forces the solution to be that for 4 pirates.
Given the rest of the conditions, the answer is:
4 pirates with shares: 5, 95, 125, 140.

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