The Puzzler #17

Feb 1, 2010 12:00 PM, By John Kador

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THIS MONTH'S CONTEST
WHO's THE LIAR?

Consider these three statements:

Alice says Bob lies.

Bob says Craig lies.

Craig says both Alice and Bob lie.

Who lies and who tells the truth?

Please email your solution to John Kador jkador@jkador.com using the subject line “Who's the Liar?” Deadline is February 20, 2010. Two responses will be selected to receive a signed copy of John Kador's How to Ace the Brainteaser Job Interview. Good luck.

BRAINTEASER: HIDDEN COUNTRIES

The United Nations has 192 members. The names of two member countries are hidden in each of the ten sentences below. Can you discover which two? Example: “Interpol and the FBI discover hidden Marksmen.” POLAND and DENMARK appear in capital letters: “InterPOL AND the FBI discover hiDEN MARKsmen.”

1. Vladimir and Olga are Soviet Names.
2. Have you ever heard an animal talk in dialect?
3. In letters to the press we denounced the wholesale ban on luxury imports.
4. Evening classes may help an amateur to improve his painting.
5. Children put on galoshes to go out in the rain.
6. Rash decisions may cause trouble so thorough analysis is a necessity.
7. The viscount has not found a home yet and he regrets leaving his fine palace.
8. If your exhaust pipe rusts you just have to shrug and accept it.
9. Such a display could be either grand or rather vulgar.
10. Give the dog a bone and give him a little water.

SOLUTION TO PREVIOUS PUZZLER: 907 PRIME

To recap: To prove that 907 is a prime number, you must check to see that it not divisible by any other number, beginning with 2, 3, 5, 7 and so on. The challenge: How far do you need to go up the number line before you can conclude that 907 is in fact prime?

Solution: To prove that a given number is prime, you only need to check as far as the largest prime number that is smaller than the number's square root. The reason is that in any pair of factors for the number, one factor will be greater than the square root and the other factor will be smaller. (If the number is a perfect square, then it will have two equal factors, but it won't be prime.) If you haven't come across a factor by the time you reach the number's square root, you never will. In the case of 907, the largest whole number smaller than the square root is 30. So the largest prime you need to consider is 29.

We received over 50 entries. Congratulations to this month's winners:

Gregory W. Serbe, President, Lebenthal Municipal Asset Management, New York, NY

Sean M. Riley, Financial Advisor, Merrill Lynch, Fort Lauderdale, FL

SOLUTION TO HIDDEN COUNTRIES: 1. Iran, Vietnam; 2. Malta, India; 3. Sweden, Lebanon; 4. Panama, Spain; 5. Tonga, Togo; 6. Lesotho, Ghana; 7. Dahomey, Nepal; 8. Peru, Uganda; 9. Chad, Andorra; 10. Gabon, Mali

John Kador is the author of 10 books. His latest book is Effective Apology: Mending Fences, Building Bridges, and Restoring Trust (Berrett-Koehler). www.effectiveapology.com