The Problem Poser

by Don Scheuer

Walking in a Winter Wonderland

Doing activities centered around Pascal's triangle, probability concepts and time-distance-rate ideas has led me to discover some interesting "walking" problems which are fun to solve. In this column, I will share some of these with you.

A city is arranged with all of the streets at right angles to each other. One set of streets bears letter designations, A, B, C, etc., while the other set is numbered 1, 2, 3, etc. If someone who lives on E and 4th wants to walk to J and 8th, how many different routes are possible if the person always goes to higher letters of the alphabet and larger numbers? (A sketch might help!)

Here's a second problem: some hikers leave at 9:00 a.m. and return at 3:00 p.m. Their walking rate uphill is 3 mph, downhill 6 mph and on flat land 4 mph. If they follow the same route out and back, how far do they hike?

Now, back to the city of the first problem‹another person is walking from 10th and H to 16th and M, always going to letters farther along in the alphabet and larger numbers. The police have blocked off the street between 13th and K and 13th and L. What is the probability that a randomly chosen route would include this blocked-off street?

After mulling over these conundrums for a while, you might want to take a walk to clear your head. Enjoy!

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