Question

Yi and Sue play a game starting with the number $42000$. They divide by prime numbers alternately. What is the result?

A. Yi wins the game.
B. Sue wins the game.
C. The game ends in a tie.
D. The result cannot be determined.

Answer 1

The result of the game where Yi and Sue divide the number $42000 by prime numbers cannot be determined without additional rules specifying which primes can be divided at each turn.

Step-by-step explanation:

To determine the outcome of the game where Yi and Sue alternatively divide the number $42000 by prime numbers, we need to examine the prime factorization of $42000. The prime factorization is as follows:

$42000 = 2^{3} \times 3 \times 5^{3} \times 7$

Since the players alternate in dividing the number by a prime factor, and there is an odd number of each prime factor (except for the prime number 3 of which there is only one), the game will end when the number reaches 1. Assuming both players make optimal moves, the player who starts will divide by 2 three times, then the other player will divide by 3 once, and so on. Given the number of times each prime factor appears, the outcome will depend on the sequence in which they divide the number. Without additional rules regarding which numbers (primes) can be divided at each turn, the result cannot be determined from the information provided. There is simply not enough information to declare a winner or ascertain if the game ends in a tie.