Mathematics Problem Of the Week

Fall 2006

POW #3

A Questionable Number

Bart has thought of a positive integer between 1 and 75 (inclusive) and wants Lisa to try to guess it by asking only yes/no questions. Lisa, who’s very good with numbers, asks the following questions and Bart answers truthfully after each one.

Is it a prime number?

Is it even?

Is it divisible by three?

Is it divisible by five?

Is it less than 25?

Lisa then announces that she’s got Bart’s number and is right. Can you also guess Bart’s number even though you don’t hear the answers as Lisa did? Be sure to explain your reasoning.

Due Friday, September 29^nd at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.