Presented by Cold Stone Creamery(R)

The Department of Mathematics Challenge of the Week

A solution and a new problem is posted every Monday evening during fall and spring semesters at www.cs.colostate.edu/~rmm/mathChallenge

One winner each week is eligible for a free ice cream and topping, courtesy of Cold Stone Creamery.

Email your solutions to solution@math.colostate.edu. Indicate your status (undergrad/grad/faculty/other) and school affiliation or city of residence if you are not affiliated with a school.

Email ideas for future challenges to Ross McConnell (rmm@cs.colostate.edu)



Solution to Challenge 15, Fall '04

(Last challenge of the semester)


This week's challenge is a continuation of Challenge 14 (see below). You are one of the unfaithful wives. You just happen to be walking by the missionary's place in time to hear him ask the question and see all the husbands' hands go up. Being infinitely smart yourself, you know that this spells trouble for you.

Suppose that there are at least two other unfaithful wives. What action can you take to keep from getting caught?

Solution

Solutions that worked were given by Chris Hoover, Kyle Thayer (undergrad, CSU), Gabriel Somlo, Priya Venkataraman (grad students, CSU), Andrew Johnson (grad student, Colorado School of Mines), Florian Hulpke (grad student, University of Heidelberg), Robert France (CSU faculty), Doug Beeman, Nicolae Popescu (Fort Collins). Chris, Gabriel, Priya, and Florian, who is visiting Ft. Collins later in the month, got the ice-cream prizes.


Solution to Challenge 14

The problem again: There is an island where all the natives are married. All of the husbands are jealous. The natives like to gossip, so if a wife is unfaithful, everybody except her husband will know about it.

The natives are infinitely adept at solving logic problems. If a husband figures out that his wife has been unfaithful, he will wait until dark, put his chagrined spouse in a canoe, and paddle away to a new island. The next day, when everybody discovers that the two have moved, they will know that the husband found out. All of this is common knowledge on the island.

One day, a missionary gathers the husbands together and asks them to raise their hands if they know of at least one unfaithful wife on the island. They all raise their hands. Nothing further is said about it. However, as a result of this incident, all the husbands of unfaithful wives, and only these husbands, figure out that their spouses have not kept to their vows.

How can this be? With your solution, include an answer to this question: If there are k unfaithful wives, how long does it take for their husbands to figure it out?

Solution

Correct solvers were Britta Eckhardt, Chris Hoover, Dan Covill, Brian Roy (CSU Undergrads) Mark Rogers, Monica Chawathe (CSU grad students), Andrew Johnson (Colorado School of Mines grad student), Maggie Loe (CSU Alum, Calgary), Gary Rubinstein (Stuyvesant High School faculty), Nicolae Popescu (Fort Collins), Lou Cairoli (Cleveland), Rocke Verser (Loveland). Britta Eckhardt gets the ice cream.


Previous Challenges, Fall '04

Challenge 1

Challenge 2

Challenge 3

Challenge 4

Challenge 5

Challenge 6

Challenge 7

Challenge 8

Challenge 9

Challenge 10

Challenge 11

Challenge 12

Challenge 13

If you would like to receive a weekly email reminder about the Challenge Problem, send an email to solution@math.colostate.edu

The Department of Mathematics Challenge Problem is sponsored by the Cold Stone Creamery, which is providing all the prizes.

If more than one correct solution is submitted, one prize winner will be chosen from among the correct solutions. Submissions from CSU faculty and people not affiliated with CSU are encouraged, but they are ineligible for the prizes.

For questions, comments or suggestions for future challenge problems: please e-mail Ross McConnell, rmm@cs.colostate.edu.