Time for MATH MINUTE! (provide your favorite theme music
here).
Get out
your paper & pencil, because I have a new puzzle for you!!
PUZZLE #99 How far is it?
When
you compute the distance from one place to another you usually just use the
straight line distance. But there are cases where this will not work.
A. Suppose
you are at point A in the imaginary city Metropolis, and you wish to drive your
car to your friends house at point B.
Notice
that all of the streets are one-way streets in this city, except for the main
crossing streets Douglas and Broadway.
What
is the shortest distance?
Also,
what is the route with the least number of turns?
B. Now suppose
you are an insect looking for food. Then your world looks very different from
ours.
Here
are some cases where you (an insect) are on a box at point Y and the food is at
point F.
Suppose
you have to crawl to the food on the box, and the dimensions of the box are 1in.
x 2in. x 3in., and the food is in the center of the 1x2 side, and you are 1in.
from the left end of the 1x3 side, but in the center width-wise as indicated?
What
is the shortest distance from you to the food?
Suppose
you are on one of the 1in. x 3in. sides of the box and the food is on the
opposite side as indicated below, where the food is 1in. from the left back
side, and you are 1in. from the right front side, both points are in the center
width-wise.
Now
what is the shortest distance from Y to F?
Hint:
In each case you can cut the box open and lay it flat to find the shortest route
Have
fun!
Send
your comments, ideas and solutions before Monday to the email below, and
in the subject line be sure to put
MM in the subject line
Visit
us here online at:
http://www2.potsdam.edu/parksjm/MM1.1.htm
to see the results every Friday.
See you next time on MATH MINUTE! (theme music fades out here).