Brain teasers from Work
1. There are 25 horses. Each horse runs at a unique constant speed. You would like to determine which are the three fastest horses. You are allowed to race 5 at a time. You cannot time the races; you can only observe relative order of finish. What is the minimum number of races necessary to identify the top 3 with certainty? How?
2. You are given the opportunity to play a game that begins by flipping a fair coin. If it comes up tails, you lose. If the first flip comes up heads, your prize is $2 and the coin is flipped again.
The game continues until tails comes up, and your prize doubles on every flip, paying out when tails appears. So, for the sequence "heads, tails" you are paid $2 and for "heads, heads, heads, tails" you are paid a total of $8.
What is the Expected Value (EV) of this game (the amount you should mathematically expect to win or lose for each dollar risked)?
How much would you pay to be able to play this game one time?
2. You are given the opportunity to play a game that begins by flipping a fair coin. If it comes up tails, you lose. If the first flip comes up heads, your prize is $2 and the coin is flipped again.
The game continues until tails comes up, and your prize doubles on every flip, paying out when tails appears. So, for the sequence "heads, tails" you are paid $2 and for "heads, heads, heads, tails" you are paid a total of $8.
What is the Expected Value (EV) of this game (the amount you should mathematically expect to win or lose for each dollar risked)?
How much would you pay to be able to play this game one time?