counting to specific number.

Question

In a counting game to a specific number, if the rules are

• only two players.
• I am the first player always.
• one can say at least one number and at most 2 numbers.
• the number we are counting to is bigger than 3.

for example

Player 1: 1,2

Player 2: 3,4

Player 1: 5,6

Player 2: 7

Player 1: 8

Player 2: 9

Player 1: 10

I can always win if i followed the right pattern depending on the number. Is this theory right\applicable to all numbers?

Answer 1

You can guarantee to win by following the right pattern as long as the number you are counting to is not divisible by three. If it is divisible by three however, then player 2 can guarantee to win. Whenever you say one number, he can say two, and when you say two, he can say one. This way, he will always reach every number divisible by three, including the winning number.