The Puzzler #8

Try these brainteasers that recruiters use in actual job interviews.



As you may know, an odd lot is a block of fewer than 100 shares of a stock. And this Puzzler concerns a stockbroker with a very odd sense of selling stock indeed: He will sell stock only in lots of six, nine or 20 shares. In other words, if a customer wants to buy any other number of shares, he or she must be able to combine one or more of the three odd lots that the broker offers, or the broker will refuse the order. So, for example, a customer is allowed to buy 12, 15 or 40 shares, but they can't buy seven or 19 shares.

The Puzzler this month asks: What is the largest number of shares of stock that a customer cannot buy under these odd lot restrictions?



Registered Rep. readers did very well with this probability problem. (Quickly: You are given three coins, one of which has heads on both sides. You take one coin at random and flip it three times, which results in three heads; what's the probability that the next toss of this coin will also be heads?)

I received over 50 replies, about three-quarters of which had the right answer. The correct answer is two-thirds or 66.67 percent.


Alan M. Hughes, Morgan Keegan & Company, Raleigh, N.C., who wittily explained: “As any financial advisor worth [his] weight can tell you, ‘Past results do not guarantee future performance;' therefore, any previous results from preceding tosses must be forgotten. As a result, you are left with three coins — each of which has two possible outcomes. That results in six possible outcomes: two tails and four heads. The expected result of any future toss would be 66.67 percent chance heads. Given the current state of financial markets and financial assets in general, I would like to find someone with the liquidity left to rattle three quarters in their pocket. As Gordon Gekko in the movie Wall Street said, “Without liquidity you cannot piss in the tall weeds with the big dogs.”

Randy Matteson, Edward Jones, in Owings, Md., had the following answer: On an optimistic day, I would assume the probability of the next toss also being heads to be 100 percent. (Meaning I chose the double header.)

On a pessimistic day, I would assume the probability of the next toss also being heads to be 50/50. (Meaning I chose a standard coin.)

But on an indifferent day, I would assume the probability of the next toss also being heads to be 66.66 percent. (Meaning I did the math: I random flip with 6 possible outcomes; four heads and two tails = 66 percent heads. Or, think of it as a 50/50 flip with the additional chance of choosing the double header at 16 percent). Thanks to everyone for your participation. Good luck with this month's Puzzler!

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

Please email your solution to John Kador [email protected] using the subject line ”Odd Lots.” The deadline is November 15, 2008. Two responses will be selected, based on originality and creativity, to receive a signed copy of John Kador's How to Ace the Brainteaser Job Interview. Good luck!

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