Question

The Pirates and the Diamond A band of 10 pirates are going to disband. They have divided up all of their gold, but there remains one GIANT diamond that cannot be divided. To decide who gets it the captain puts al of the pirates (including himself) in a circle. Ther he points at one person to begin. This person steps out of the circle, takes his gold, and leaves. The person on his left stays in the circle, but the next person steps out. This continues​

Answer 1

The captain, being pirate number 1, should point at the 9th pirate. This ensures that in the elimination process, the captain remains the last pirate and gets the diamond.

How this conclusion was arrived at.

Let's use strategy of "counting out"

The captain, being number 1, must eliminate every second pirate. If he starts with the 9th pirate.

The captain (Pirate 1) starts by pointing at the 9th pirate.The 9th pirate leaves, and the 10th pirate remains in the circle.The next pirate to leave is the 2nd pirate.This elimination process continues, with every second pirate leaving the circle.

1 (Captain), 2, 3, 4, 5, 6, 7, 8, 9 (Captain eliminates), 10 (Captain remains), 1 (Captain eliminates).

This process continues until only the captain remains, securing the diamond for himself. If the captain starts with any other pirate, the outcome would not guarantee him the diamond.