The puzzler page offers real-world puzzles and their solutions based on brainteasers that recruiters use in actual job interviews. Also featured is a puzzle contest, the solution to be published the next time we run a puzzler, in the February issue. The winners will receive a free copy of How to Ace the Brainteaser Job Interview (McGraw-Hill), signed by the author and Registered Rep. contributing editor John Kador.
THIS MONTH's CONTEST:
Risk And Uncertainty: The Russian Roulette Puzzle
The interviewer says: “Let's play a game of imaginary Russian Roulette. We start with a revolver with six chambers, all empty. Note how I put two bullets into adjacent chambers in the cylinder. Now we spin the cylinder and pull the trigger. Click! The chamber is empty.
At this point, we want to pull the trigger one more time. If we want to avoid discharging a bullet, are we better off spinning the cylinder first, and then pulling the trigger — or should we pull the trigger without spinning the cylinder?
Note: No job applicants were hurt in the making of this puzzle.
BRAINTEASER #2: THE CHECKERBOARD
My son, Dan Kador, a quality assurance engineer for a San Francisco-based software company, is occasionally called on to do some recruiting. At a recent job fair hosted by his alma mater, University of Illinois at Champaign-Urbana, he presented this puzzle:
Let's say you have a standard 8×8 checkerboard and a pile of dominoes, each of which covers exactly two adjacent squares. Now imagine that some ruffian comes along, and cuts off one square in each of the two corners that are diagonally opposite from each other.
Is it possible to place dominoes on the now-mutilated checkerboard such that all the squares are covered? If so, how many dominoes will be required? If not, can you prove that it cannot be done?
By the way, the dominoes must always cover exactly two adjacent squares, and must be placed either horizontally or vertically (never diagonally). They must also never overlap or hang over the edge of the board.
Solution: It is impossible to cover the checkerboard modified as described. “Most job candidates quickly come to this conclusion,” Dan reports, “but few do a good job proving it — which is the core of the problem. Really, all I'm looking for is somebody who asks me good questions about the problem. Sure, it's great if somebody nails the solution right away, but most candidates can't. The distinguishing factor is whether candidates are inquisitive, and seem to actually want to solve the problem, as opposed to those who just want to impress me on their interview.”
Here's The Proof: The missing checkerboard squares are always the same color. That means the checkerboard has two more squares of one color than the other. Given that every domino must necessarily cover two squares of opposite colors, it is not possible to cover all the squares. There will always be two squares of the same color left over.
Winners Of The Previous Puzzler
The previous contest, published in our April issue, asked readers to solve the following problem:
Stockbroker Alex has a quota of 4,000 trades per week. When Alex doesn't get his bonus, he goes on a slow-down strike: 99 trades the first hour, 98 trades the second hour, 97 trades the third hour, and so on. The puzzle was: How long will it take for Alex to meet his weekly quota of 4,000 trades?
We received over 50 solutions to the puzzler. Most readers correctly selected answer B (about 56 hours). But answer E (Alex will never meet the quota) is also correct if Alex works a 40-hour week. Joel Darrow of Darrow Associates, points out: “If you assume Alex will only work five eight-hour days per week, and must transact 4,000 trades within a single week, he will never meet the quota. He cannot transact 4,000 trades by doing less than an average of 100 trades per hour within one 40-hour week of trading.”
Congratulations, and a signed book goes to each of the following winners:
Joel Darrow, Darrow Associates, Ramsey, N.J.
Marc L. Pushkin, Pushkin & Pushkin, Inc., Timonium, Md.
Please email your solution to email@example.com by January 15, using the subject line “December 2007 Puzzler.” 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. Good luck.