The Map of Mathooli

Posted September 2 - 8, 1996

The cities could be arranged like this:C A BIn this scenario, C is 10 miles from A, A is 30 miles from B, and C is 40 miles from B.Or you could have this scenario:

A B CIn this situation, A is 30 miles from B, C is 40 miles from B, and A is 70 miles from C. Thus, the maximum distance apart the two cities can be is 70 miles.

Abraham Nevado Zazo [abraham@bitmailer] of Madrid, Spain sent Minus the map he created to solve the problem. Check it out!

I send you a graphic which shows the distribution of Mathooli's Map. I put C city and then I put D city, in two possible ways East and West from C city, I continue doing this with all the cities. Then I find the largest way from color green to red. I understand that the largest way between C and A is 70 Miles, so the solution is 70 Miles.We don't know how Anne Castle [acastle@d.umn.edu] knew that Trolls live in City D, but she must be familiar with Mathooli because she came up with this solution:

The maximum distance possible between cities A and C is 70 miles. Since the cities are in a straight line, you can maximize the distance by putting B between A and C. Then 30 + 40 = 70.Mickie Geri (of third period algebra 305) came up with a clever way of solving this problem:If A was between B and C, the distance would be only 10 miles.

C cannot be between A and B (it won't fit!).

D doesn't matter because only the Trolls live there?!

Derek Perry also came up with an answer of 70 miles.30 38 2 I----------------I-------------------------I---------I A B D CSince A-B is 30 miles, B-D is 38 miles and D-C is 2 miles, the total (maximum) distance between city A and city C is 70 miles.

Minus something to chew on!