BRAINTEASER: THREE-COIN TOSS

YOU HAVE THREE COINS IN YOUR POCKET. THEY ARE IDENTICAL IN EVERY WAY EXCEPT TWO ARE FAIR COINS (HEADS ON ONE SIDE, TAILS ON THE OTHER) AND ONE IS AN UNFAIR COIN (BOTH SIDES ARE HEADS).

YOU DIG INTO YOUR POCKET AND PULL OUT ONE COIN AT RANDOM. WITHOUT INSPECTING IT, YOU FLIP THE COIN THREE TIMES. YOU GET HEADS ALL THREE TIMES. WHAT IS THE PROBABILITY THAT THE NEXT TOSS OF THIS COIN WILL ALSO BE HEADS?

Please email your solution to this month's contest to John Kador at jkador@jkador.com by September 15, with “Three-Coin Toss” in the subject line. We will select two winners from all correct entries, with extra consideration given to offbeat or elegant solutions. Winners will receive a signed copy of John Kador's How to Ace the Brainteaser Job Interview (McGraw Hill), signed by the author and Registered Rep. Contributing Editor John Kador. Good luck.

Kador, the author of 10 books, published Charles Schwab: How One Company Beat Wall Street and Reinvented the Brokerage Industry in 2003. His website is www.jkador.com

PREVIOUS PUZZLER FROM OUR APRIL ISSUE:

In the April Puzzler, I presented the “Trapped in a Blender” brainteaser, a puzzle that was being used in Google interviews. (It has since adopted new puzzles — stay tuned!) That puzzle posed the following question:

Imagine that you are shrunk and trapped in a blender whose blades will turn on in 60 seconds. What do you do?

We received over 30 replies. As there is no right or wrong answer to this puzzle, solutions were judged in terms of creativity, elegance and originality. The two winners are Ernest A. Laird, associate VP, Morgan Stanley, Mobile, Ala.; and Richard “Nick” Horning, financial advisor, Merrill Lynch Global Private Client Group, Modesto, Calif. Congratulations to both.

THE WINNERS:

Ernest A. Laird offered 10 solutions. “Shrinkage is not defined here, so several options appear possible based on size,” he writes. Five of Laird's solutions are:

  • Yell for someone to unplug the blender.

  • Wedge straight legged and back against the tapered wall of the blender container above the blades.

  • Rock the container off the base of the blender.

  • Curve into the space under the blender blades.

  • Yell for someone to fill the blender with warm water to create a whirlpool bath so as to float above the blades.

Richard “Nick” Horning offered two courses of action and, if neither worked, a coup de grace:

  • If I were small enough to lie under the blades and curl around the part that supports the blades, holding on tightly to avoid any suction would be my strategy.

  • If I were too large for strategy one, I would attempt to position myself in the center of the blade mechanism to minimize the centrifugal force (like standing in the middle of a merry-go-round). Sure, you would be dizzy as heck — but you'd live.

“If options one and two were not available, and I was in a total Kobayashi Maru scenario, Horning continues, “then I would simply make peace with my dear and fluffy lord.” (Editor's note: The Kobayashi Maru, a Star Trek spaceship, is the precipitating element in a simulated no-win training scenario.)

FEBRUARY'S RED BULL PUZZLE: SOLUTION

Although we received over 20 replies to the February 2008 Puzzler and had many creative solutions, no one actually got the right answer. This turned out to be the trickiest puzzle yet. So, no prizes awarded, but here it is again with the solution.

A brokerage has to deliver 3,000 cans of Red Bull to desperate colleagues in a retail office exactly 1000 miles away. The firm hires a driver to transport the Red Bull. The driver can carry up to a maximum of 1,000 cans at a time. Moreover, the driver must consume one can for every mile he drives. What is the maximum number of cans of Red Bull that can be delivered?

SOLUTION: The answer is about 533 cans. The solution to this puzzle calls for two insights: First, the driver must “stage” the delivery, leaving some cans at an intermediate stop and going back for others before going forward again. The second insight is that there comes a point at every stage where the driver does not need to go back. For a lengthier explanation, please check our website: http://registeredrep.com/puzzler_feb_solution.