Question

Yi and Sue play a game. They start with the number $42000$. Yi divides by a prime number, then passes the quotient to Sue. Then Sue divides this quotient by a prime number and passes the result back to Yi, and they continue taking turns in this way.

For example, Yi could start by dividing $42000$ by $3$. In this case, he would pass Sue the number $14000$. Then Sue could divide by $7$ and pass Yi the number $2000$, and so on.

The players are not allowed to produce a quotient that isn't an integer. Eventually, someone is forced to produce a quotient of $1$, and that player loses. For example, if a player receives the number $3$, then the only prime number (s)he can possibly divide by is $3$, and this forces that player to lose.

Answer 1

I need help

Answer 2

Yeh?

Answer 3

Yah

Answer 4

Can you help me

Answer 5

K?

Answer 6

Yay

Answer 7

The prime factors of 42000 are 2^2, 3^1, 5^4, 7^1 so there are 9 prime factors and whoever goes on the 9th turn will loose so Yi goes 1st, Sue goes second, Yi goes 3rd, Sue goes 4th, Yi goes 5th, Sue 6th, Yi goes 7th, Sue goes 8th, and Yi goes 9th. Yi will lose because she is on the 9th turn. Yi will go first and do 42000÷7=6000. Then Sue will go next and do 6000÷5=1200. Yi will go next and do 1200÷5=240. Then Sue does 240÷5=48. Yi will do 48÷3=16. Sue will do 16÷2=8. Yi will do 8÷2=4. Sue will do 4÷2=2. And Yi will do 2÷2=1. Sue wins!

Answer 8

Oh, I see

Answer 9

So you do 2^2, 3^1, 5^4, 7^1 for the prime factors and whoever goes on the 9th turn will loose because there are 9 prime factors?

Answer 10

Yah

Answer 11

Now do you see?

Answer 12

Yah thanks

Answer 13

Bye

Answer 14

i g2g

Answer 15

BYE!