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Math 141

Assignment #1: Time

Due in class, 1/26/06

1. A shoe salesman in Berkeley, California once told me I shouldn't wear the new shoes he was selling me every day, or even wear them every other day: "You can double the lifetime of your shoes by wearing them only every third day," he told me confidently. Give two different interpretations of what the salesman meant; explain why, under the first interpretation, his advice was good advice, and why, under the other interpretation, his advice was bad advice.

2. A short obituary in the December 5, 2005 issue of The New Yorker (p. 40) read as follows:

A letter arrived the other day bearing the news that Cecille Shawn, the wife of William Shawn, who was the editor of The New Yorker from 1952 to 1987, had passed away. The letter was from one of the Shawn's three children, the composer Allen Shawn, and he wrote to say that "our mother died peacefully at home on October 30th. She was ninety-nine years old." Cecille Shawn, who was born Cecille Lyon, grew up in Chicago and, as a young woman, worked as the editor of the features page of the Chicago Daily News. She created a game using a character named Blundering Ben, in which readers scored points by finding mis-used words and phrases. When she was eighteen, Cecille was introduced to William Shawn, and he wrote in his diary, "Today I met my future wife." They married in 1928 and spent much of the next year living in Paris, where Mr. Shawn earned a living playing jazz piano in a club called La Cloche. It was their only trip overseas. When they returned to the States, the Shawns moved from Chicago to New York. The Depression was on, but Cecille was able to find a job as a freelance "fact-finder" at The New Yorker, which was in the eighth year of its existence. She asked the editors if her husband could help with the work. As Allen wrote, "She soon happily bowed out of her own job at the magazine," where her husband thrived for the next half-century.

For how many years did William court Cecille before marrying her? Express your answer as a range, in the form "More than X years but less than Y years''. Make the range as narrow as possible, given the information you have, but no narrower than logic permits you to conclude.

3. Roger and Rhonda plan to have a child together. Her menstrual cycle typically lasts 25 to 29 days, and ovulation occurs on day 12, 13, or 14 of her cycle. Rhonda wants Roger to be at home during each cycle on the day of her ovulation. If Rhonda's last cycle began on July 22 (Day 1), should Roger plan to take a business trip in the last half of September? If he absolutely needs to take the trip, what are the days in late September when he must make sure to be at home?

Note: You must indicate whom you worked on the assignment with (if you worked alone, indicate that you worked alone) and how long you spent on the assignment.

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