This Month's Contest:
Andy and Bob are changing planes at O'Hare International Airport. As they descend to the underground tunnel that will take them from Terminal B to Terminal C, they decide to do an experiment. Andy will run on the moving walkway while Bob runs alongside on the floor. Then they will reverse direction. Andy will run against the direction of the moving walkway (like a salmon swimming against the current), while Bob runs on the floor. If Andy and Bob run at the same speed (and assuming no other passengers), who will reach the beginning of the moving walkway first, Bob or Andy? Or will they finish at the same time?
Three logicians get into an argument and decide to settle things with a three-way duel. The duelists, who shall be known as A, B, and C, each have a pistol with an unlimited amount of ammunition. They will shoot, in order, one at a time until only one person is standing. The duelists all acknowledge that A and B are expert marksmen who will always hit their targets, but C is only a moderate shot and hits his targets only two-thirds of the time. The logicians draw straws to determine the order. The rules are as follows:
- A, B, and C each stand 40 feet apart from each other.
- They take one shot based on the order determined by the draw.
- After each person takes a single shot at the opponent of his choice, it's the next person's turn to shoot.
Of the three logicians, which has the best chance of winning the duel? Solution to “Three-Way Duel” is below.
SOLUTION TO PREVIOUS PUZZLER: TWO BALL ROULETTE
To recap: You're playing on a roulette wheel with 38 slots. Two balls are released at once. What's the probability of both balls dropping into the same slot?
Solution: The probability is still one out of 38.
We received over 70 entries with about half getting the right solution and the other half solving for problems other than what the puzzle called for. (The most common, if incorrect, solution was 1/1444.) This month's winner, selected randomly from all correct responses, is Douglas Wahl, wealth management advisor, Wahl Group Financial Advisors (Merrill Lynch), Myrtle Beach, S.C. Wahl explains: “The first ball will drop in any slot with probability 100%, so we are simply trying to measure the probability that the second ball falls into that same slot. The probability that that happens is 1 in 38.” Congratulations to Douglas Wahl and good luck to all entrants for next time.
SOLUTION TO THREE-WAY DUEL: Although C is the worst shot, he has the best chance of surviving the duel, and this holds true whatever the order of shooting. Suppose A shoots first. He doesn't want to shoot C because if he does, he'll be inviting certain death from B on the next turn. So he opts to shoot B and take his chance that C will miss. With B eliminated, C shoots at A and has a two-thirds chance of hitting him. If B shoots first, then the same reasoning applies. If C is drawn to shoot first, his best bet is to fire into the ground because he doesn't want to hit either A or B; doing so would invite certain death from the other. The situation then reduces to one of the previous cases. Overall, C has a two-thirds chance of surviving the duel, while A and B each have a one-third chance.
John Kador is the author of 10 books. His latest book is Effective Apology: Mending Fences, Building Bridges, and Restoring Trust (Berrett-Koehler). www.effectiveapology.com.
Please email your solution to John Kador at [email protected] using the subject line “Moving Walkway.” Deadline is Oct. 24, 2011. One entrant will be selected to receive a signed copy of John Kador's How to Ace the Brainteaser Job Interview. Good luck.