In early seasons during the Time Hunt stage they played a game of 20 sticks - a participant played with Maître de jeu and has always been the one to make a first move.
I found out they played a variation of Nim game, which has a pretty simple mathematical solution! Which means that first mover could guarantee a win using a special tactics no matter what the opponent does:
You have to take 3 sticks to leave 17. Then leave 13, 9 and 5. The opponent will have to take 1-3 sticks, which leaves 2-4 to you and you'll take 1-3 to leave the opponent with 1 remaining stick to take. If you're the one to make a first move, the opponent cannot push you into this "17,13,9,5" death row! And your job is simple - to keep him there.
My question is - how the hell did participants manage to lose this game occasionally during multiple seasons?!
Added: Simpler and more straightforward guide:
- You start with 20 sticks and it's your move.
- Take 3 sticks (17 left).
- Your opponent takes N sticks, where N equals 1, 2 or 3.
- Take 4 - N sticks: if your opponent took 3, you take 1. If 2, take 2. If 1, take 3.
- Repeat steps 3, 4 until you win.
Also, "solution" of the game gives different benefits. Checkers had also been solved, but the solution does not allow you to win in 100% cases, only guarantees a draw.