This Month's Contest:
There are three envelopes, each containing a cashier's check for a random number of dollars. Your goal is to choose the envelope with the biggest check. The rules are as follows: You can open any envelope and look at the check. If you believe this is the biggest check among the three, the game is over. You get to cash it. Otherwise you can discard that check and go for one of the two remaining envelopes. If you prefer the check in the second envelope you select, it's yours. But if you're still not satisfied, you can discard that second envelope, and then your selection is the check in the last envelope. You can't go back to a check you've discarded. What's the best strategy for getting the highest payout?
Please email your solution to John Kador [email protected] using the subject line “Biggest Check.” Deadline is April 22, 2011. One entrant will be selected to receive a signed copy of John Kador's How to Ace the Brainteaser Job Interview. Good luck.
Your client wants to buy three equities, spending exactly $1,000 in the process. The stocks and prices are as follows: AAA is $150.00 per share; BBB is $10.00 per share; CCC is $2.50 per share. You are to buy at least one of each stock and spend exactly $1,000. How many shares of each stock must you buy? (Solution below.)
SOLUTION TO PREVIOUS PUZZLER: TAKE THE BEE TRAIN
To recap: Two freight trains 150 miles apart are rushing toward each other. The first train goes 60 mph; the second train at 90 mph. A bee goes back and forth until the trains collide. How far does the bee travel?
Solution: 120 miles. The two trains are 150 miles apart. Their combined speed is 150 mph. Therefore, no matter how you split the bee's travel segments between the two trains, the bee only has 1 hour of total flight time. Assuming the bee maintains a constant speed of 120 mph for the 1 hour flight time, it would have traveled 120 miles.
We received over 75 entries. Almost all entries had the correct solution. Hint to those who came up with very elegant solutions using calculus: keep it simple. These are brainteasers, not higher order math problems! The winner, selected randomly from all correct responses, is Omar Chyou, senior vice president/wealth advisor, Wells Fargo Private Bank, Palo Alto, Calif. Congratulations to Omar Chyou. Good luck to all entrants for next time.
SOLUTION TO SPECIFIC ORDER: The best way to solve this problem is by trial and error. Solving by algebra doesn't work because you have three variables but only one equation. Start with the most expensive stock. There are a number of possible solutions. One solution is 3 AAA, 40 BBB, and 60 CCC.
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.