Last night I was randomly awake and I thought up of a random math game and was wondering if there was a way to actually win it. It is based off a game we used to play as children, and it goes a little something like this:

Objective: Be the person to have said the highest number.

Starting out: Person A says 1. Person B says 2. Person A then says 3. Person B then says 4. etc.

So the question is, is there a way for either person A or person B to actually win this game if they were to go on for an infinite amount of time?

Now what usually happens is one of us (usually me) gets tricky and says:

Person A “My number is whatever you said last +1”

Which usually warrants a response such as: Person B “Well, my number is whatever you said last +2”

So next question becomes, in this case, is there a clear winner or does it still end up with an undecided ending?

This continues though, to become:

Person A “My number is whatever you said last *2”

Which, again, gets the response: Person B “My number is whatever you said last *3”

So the next question is, is there a clear winner in this case or do they still end up with an undecided ending?

And finally the question becomes, is there a mathematical formula that will cause one of the two players to automatically win once it is stated and the other person can’t rebuttal no matter what they come up with?

So there are my 4 questions of the day. If you have any thoughts, please leave a comment. Who knows, this may end up being my theory that I try and prove if I get accepted into grad school.

Philosophically,

-The Cali Garmo