Marquette University

Department of Mathematics, Statistics and Computer Science

Wim Ruitenburg's Fall 2016 MATH 1300-101 homeworks plus due dates

Last updated: November 2016
Comments and suggestions: Email   wim.ruitenburg@marquette.edu

Unless otherwise stated, all homework must be in handwritten form. Justify your answers.

Due date
 
Project description
30 November
 

This problem set has unrelated parts. Show your work.
  • "Our math teacher has more than a million good ideas," says Alli. "He does not," says Emily, "he has fewer good ideas." "He has at least one good idea," says Brigid. If only one of the 3 statements is true, how many good ideas does our math teacher have?
  • Two women mathematicians are sitting at a roadside cafe, talking about family. One mentions that she has 3 daughters the product of whose ages equals 36. Remarkably, she mentions, the sum of their ages equals the number on the house across the street. The other replies that this is not enough information to find the ages of the 3 daughters. True, says the one, but note that my oldest daughter has beautiful eyes. Ah, says the other, but then I know your daughter's ages. What are the ages of the 3 daughters?
  • Click on this link to see this puzzle.
  • On an island in the Pacific there live 850 women. Four percent of them wear one earring. Of the remaining 96 percent half wear no earrings and the other half wears two earrings. How many earrings do the women together wear?
  • Hunter Jack wants to shoot a bear. He leaves his camp, and walks 10 miles south where he perceives bear tracks. Jack follows the bear tracks for 10 miles east, where he sees the bear and takes a shot at it. He misses. Then Jack walks 10 miles north and is back at camp. What is the color of the bear?
12 October
 

This problem set has unrelated parts. Show your work.
  • The collection of four integers 1, 3, 8, and 120 is such that the product of any two of them is 1 less than a perfect square. Find a fifth number so that this property still holds when this fifth number is added to the collection.
  • A woman travels 2500 kilometers by car, with one spare tire. Occasionally she rotates tires so that each tire is used an equal number of kilometers. For how many kilometers is each of the tires in use?
  • Five couples meet at a dance competition for pairs. Michelle and Barry are one of the couples. All shake hands with some of the members of the other couples. No-one shakes hands twice with the same person. Barry asks all other people including Michelle with how many people they shook hands. Surprisingly they all gave a different answer. Question: With how many people did Michelle shake hands?
  • Click on this link to see 8 figures. Complete the last row to continue the pattern of the 1st and 2nd row.