Registered Rep. presents the second installment of our newest feature, The Puzzler.
Each month, the puzzle page will offer a real-world puzzle and its solution. This page will also feature a separate puzzle contest: The solution will be published the following month. The most original response to the contest will receive a free copy of Kador's career book, How to Ace the Brainteaser Job Interview (McGraw-Hill, 2004).
November's Puzzle and Solution
A stockbroker relieves tension by shaping little bulls or bears out of modeling clay. Every time he trades a round lot, he takes a one-ounce square of clay and quickly shapes it into the form of a miniature bull or a bear, depending on whether the price went up or down. During each sculpting process, a little bit of clay is left over.
In fact, for every five sculptures the stockbroker makes, there is enough extra clay to make one additional sculpture. Every day the stockbroker starts with 25 one-ounce squares of clay. What is the maximum number of model bulls or bears the stockbroker can sculpt in a five-day week?
Solution
This is a classic remainder problem. Using 25 ounces of clay, the stockbroker makes 25 sculptures per day. This process generates 25/5 or 5 ounces of excess clay every day. This extra clay can be used to make five additional sculptures. While making these five additional statues, the stockbroker generates one additional ounce of clay. This additional ounce is enough to create one more sculpture.
At this point, the maximum number of model bulls and bears the stockbroker can make is 25 plus 5 plus 1 or 31 per day. So if you said 155 sculptures (31 × 5), you get partial credit. Note that there is still one-fifth ounce of clay left over every day. At the end of five days, the stockbroker will have one additional ounce of clay to make yet one more tiny bull or bear. The solution: In five days, the stockbroker can sculpt a maximum of 156 model bulls or bears.
December's Contest
A large brokerage maintains call centers in each of the 48 contiguous states. One of the company's brokers (let's call him Joe) is ordered to inspect every call center in person. Of course, there are rules. Joe has to travel exclusively by car. He can begin his journey in any one of the 48 contiguous states and can drive to each state in whatever order he chooses. But Joe can visit each state only once. He is not allowed to go back into a state he has already visited.
Challenge: Where is the call center Joe visits last?
Please email your solution to [email protected], using the subject line, “December 2005 Puzzler.” Only one submission per reader, please. We will publish the solution we consider the most original in this space next month. Good luck.
(Entry deadline for November's Puzzler was due Nov. 25 — after Registered Rep. went to press — so November's winner will be featured in January's issue.)
Complete Puzzle Rules
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The submission should include your name, address, affiliation and email address. No purchase required.
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Entries must be received by Jan. 15, 2006. One entry per person. Employees of Registered Rep. magazine and its affiliated publications are ineligible. Void where prohibited or restricted by law. Registered Rep. is not responsible for incomplete, lost, stolen, illegible, misdirected or late entries.
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One winner will be selected on the basis of accuracy, originality and elegance, as judged by the magazine staff. In some cases, the winner will be selected in a random drawing from all eligible entries that contain a correct answer to the month's puzzle. The decision of the judges is final. We will notify the winner by email.
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The winner will get his or her solution published in Registered Rep. The winner will also receive a copy of How to Ace the Brainteaser Job Interview inscribed by the author.
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All entries become the property of Registered Rep. Each contest entrant consents to the publication of his or her name and puzzle answer, in any and all media and manner, now or hereafter known, in perpetuity without compensation. Registered Rep. is not responsible for any damages or losses relating to the puzzle or acceptance/use of any prize.
Writer's BIO: John Kador, the author of 10 books, published Charles Schwab: How One Company Beat Wall Street and Reinvented the Brokerage Industry in 2003. His Web site is www.jkador.com
