Chris Long's monthly mathematical puzzle column for Central New Jersey Mensa's Forvm.
Problem #1 in each column will range in difficulty from easy to moderate, problem #2 from difficult to impossible. Please feel free to send me solutions, comments, or problem proposals. The answers to each will be given in the following month's column.
The current Think & Derive and all back issues are available on my website, as well.
Waldo is trying to make a cross-country trip in his car, but he has an unusual car that takes unusual tires. He has eight of these, but they've been worn down quite a bit. In fact, the eight tires have, respectively, 800, 900, 1300, 1500, 1700, 1800, 2000, and 2500 miles of tread left. Is it possible for Waldo to complete a 3000 mile drive while arriving with tires that still have at least 100 miles of tread on them? If so, what's the fewest number of tire changes that he needs to make during the trip?
If Waldo had eight tires with 500, 500, 1000, 1500, 2000, 3000, 6000, and 8000 miles of tread left respectively, what would be the longest trip that he could make?
The standard cousin system works well if you don't have any inbreeding, e.g. your 2nd cousin marrying your 3rd cousin. Devise a new system for measuring degree of closeness of relationship that can handle inbreeding as well, and test your system by answering the following questions. Most people would consider your closest relatives to be your parents, siblings, and children. Does your system predict this? Most people would consider your next closest relatives to be your aunts/uncles, nieces/nephews, and grandparents. Does your system predict this? If two of your 2nd cousins (who are also 2nd cousins to each other) married, the standard cousin system would consider their child to be your 2nd cousin once removed. What does your system suggest? Hint: consider a crude genetic model.
http://math.rutgers.edu/~clong/