# Why do I always lose? [duplicate]

As always, good luck!

Sarah is really good at math. I mean, really good at math. Every now and then we play this game where we take turns picking random numbers between 1 and 10, and we add these guesses up until someone reaches 100.

The problem is, she always wins! Somehow, every single game we end up with it being my turn at the number 89, at which time there is no choice I can make to win, but any choice she makes after will give her the win.

I took the time to record our guesses from the last time we played, but I can’t figure out how she’s doing it. It all seems random!

1, 5, 6, 3, 8, 9, 2, 7, 4, 4, 7, 1, 10, 8, 3, 6, 5, 4, 7

Sarah won, like she always does! She made the first move this time, but each time we play, we alternate who goes first, and she still wins!

How does Sarah keep winning?

• The correct answer explains this mathematically.

## 1 Answer

Ok, well it goes like this:

She started with number 1, each of any next following numbers summs up to 11 (5+6, 3+8, 9+2, ..). After each turn (of 2 people), You will receive total score 1+(n*11) = (1, 12, 23, 34, 45, ...). At some point, You will reach 100 points.