Time for MATH MINUTE! (provide your favorite theme music
here).
Get out
your paper & pencil, because I have a new puzzle for you!!
PUZZLE #87 Indiana Smith and the Museum Mirrors Mystery
A. The
Museum of Modern Sculpture was having problems.
Several
times in recent months something or someone was removing pieces of priceless
sculpture from the main gallery at night.
The
gallery was a long narrow room with mirrors down one side and windows down the
other side.
What
to do?
Call
in Indiana Smith to check out the situation of course.
One
night he quietly slipped into the gallery with his trusty torch (flashlight).
He knew from his studies of mathematics and physics that he could shine the
light on the mirror and see around and behind the sculptures.
Also,
and more importantly, he knew exactly where any objects (including those which
did not belong there) were in the gallery by the Principle of Reflection*.
This
gave him not only the exact location of something, but also the shortest route
to the something around the sculptures by going directly to the mirror at a
special point and then to the object.
How
did Indiana Smith find the shortest path to the mystery something?
Hint:
The following sketch was found on a crumpled piece of paper on the floor the
next morning. What does it mean?
- -- - - - - - - - -
- - - - - - - - - - - - - - - - --- - -
- -
- - - - - - - -- -- -- - - -- - - - - - - - - - -- - - - --- - - --
B. Indiana
Smith finds himself in the Mohave Desert without any water, and he must get
across 140 miles of desert as quickly as possible in order to rescue the
precious crystal blob from the villain NAZTY.
In
order to do this he has to get some water and fast.
He
recalls that a steam runs along side the area where he finds himself. He
estimates that he is 100 miles from the steam, the crystal blob is 40 miles
from the steam, and the distance between him and the blob is 140 miles if they
were at the stream.
What
is the shortest route to the stream and to the blob?
Hint:
Make a sketch of the geometry of the puzzle like Indiana Smith did in Part A
above.
BONUS PUZZLE: Using
the ideas from above, see if you can solve this puzzle.
A
cowgirl has her horse out in the area near the barn as below, and she wants to
take it to the barn. But first she wants to take it to the pasture to feed it
some grass, then take it to the stream to get some water, then take it to the
barn.
What
is the shortest route to accomplish this sequence of tasks?
*Principle
of Reflection: When a ray of light bounces off a flat mirror the angle of the
incoming ray with the perpendicular to the mirror is equal to the angle of the outgoing
ray with the perpendicular to the mirror. This means that the angles of the ray
with the mirror are also equal.
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).