Endpiece: The Puzzler #11

Think You're Smart? Try these brainteasers that recruiters use in actual job interviews. THIS MONTH'S CONTEST A financial services firm has 10 employees. Although no one wants to divulge his or her individual salary, they all agree it would be useful if they knew the average salary of the group. Devise a way for the group to determine the average salary of the group without anybody knowing the individual

Think You're Smart? Try these brainteasers that recruiters use in actual job interviews.

THIS MONTH'S CONTEST

A financial services firm has 10 employees. Although no one wants to divulge his or her individual salary, they all agree it would be useful if they knew the average salary of the group. Devise a way for the group to determine the average salary of the group without anybody knowing the individual salaries of any other person in the group.

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

BRAINTEASER #2: COKE-PEPSI

This month, we consider a puzzle that continues to generate heated emails four years after I first wrote about it. Here's the puzzle: There are two glasses, each with the same quantity of liquid. One glass contains Coca-Cola. The other glass contains Pepsi. Take one tablespoon of the Coke and mix it with the Pepsi. Now take one tablespoon of the Pepsi-Coke mixture and transfer it back to the first glass. Is there now more Coke in the glass of Pepsi, or is there more Pepsi in the glass of Coke?

If you want to work out the answer for yourself, stop reading now. Based on my email, the intuitive answer for many people is that there is more Pepsi in the glass of Coke than Coke in the glass of Pepsi. Readers have sent me treatises on the properties of mixtures and algebraic formulas to prove it. But the answer is actually simple: There is just as much Pepsi in the glass of Coke as there is Coke in the glass of Pepsi.

Surprising? The key to solving this puzzle is to remember that the total volume of liquid at the end is the same as at the beginning. Any Coke missing from the first glass must displace an equal volume of Pepsi that has no place to go but to the glass of Coke.

Don't get distracted by the nature of the liquids. The answer is the same whether we're talking about coffee, tea, gasoline or something more discrete. For example, let's try it with boys and girls: Boys' High School is for boys and Girls' High School is for an equal number of girls. Fill a school bus with boys, drive them over to Girls' High, and let the students mingle. Then at random grab enough students of either gender to fill the school bus and drive back to Boy's High and let them out. Now, are there more boys at Girls' or more girls at Boys' High?

ANSWER: When you think about it this way, it becomes easier to see that every boy who ends up at Girls' High is replaced by one girl who ends up at Boys' High. Let's go back to the Coke and Pepsi puzzle. When the tablespoon leaves the Coke glass, it is full of Coke. When it comes back, some of the Coke has been replaced with Pepsi. How much Pepsi comes back? It doesn't matter. One unit of Pepsi comes back for each unit of Coke left behind.

SOLUTION TO PREVIOUS PUZZLER: ODD LOTS

To recap: A stockbroker sells stock only in lots of 6 shares, 9 shares or 20 shares. What is the largest number of shares of stock that a customer cannot buy under these odd lot restrictions?

The answer is 43 shares.

Please congratulate the winners of this month's Puzzler, who will receive a signed copy of How to Ace the Brainteaser Job Interview:

Michael S. Stickler, Senior Vice President
Morgan Stanley
Short Hills, N.J.

Jordan Spees, Registered Representative
AIG Financial Advisors, Inc.
San Diego, Calif.

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

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