Think & Derive

Chris Long's monthly mathematical puzzle column for Central New Jersey Mensa's Forvm.

What is Think & Derive?

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.

Think & Derive, September 2000

Puzzle #1: The Easy Way

Waldo and Basil are playing a game involving a single normal die. They take turns rolling it, adding the number appearing to their score, and the winner is the first person to total 100 points or more (totals greater than 100 are counted as 100). During the course of a game, which number is the least like to appear among either Waldo's or Basil's subtotals?

Puzzle #2: The Hard Way

Waldo and Basil get tired of that game, and instead decide to play a similar game involving throwing two regular dice with the marathon goal of scoring 10,000 points or more. Estimate the probability Waldo, Basil, or both score exactly 9,000 points during the course of the game.

August Bonus: Reretired

Given a vehicle with M wheels together with N tires with x_1, x_2, ..., x_N miles of tread (x_1 ≤ x_2 ≤ ... ≤ x_N), what is the longest trip that the vehicle could make?


http://math.rutgers.edu/~clong/