### Brain Teasers

# A 100 Player Game

100 players are lined up in a circle labeled a number 1-100. Player number 1 can either eliminate player 2 or no one. Then player 2 (assuming they're in) can choose to eliminate player 3. This continues until player 100. Player 100 can choose to eliminate player 1 and the cycle repeats until there are two players left , who are the winners. Assuming everyone played perfectly, who won?

### Hint

Start from one player, work up from there.### Answer

No one did. Let's say 95 players are eliminated, leaving 5, 19, 23, 78, and 90; well if 5 eliminates 19 then 23 eliminates 78 and 90 eliminates 5, so 5 wouldn't do that. 19, 23, 78, and 90 also have the same problem, so no one would ever win.Every combination of five players results in a stalemate. (The rule for this is: 2*(number of winners)+1=(number of players when a stalemate occurs), so setting the number of winners to five will not fix the problem.)

Hide Hint Show Hint Hide Answer Show Answer

## What Next?

View a Similar Brain Teaser...

If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.

### Solve a Puzzle

Comments hidden to avoid spoilers.

## Follow Braingle!