I gathered together several objects from my house which were of nearly
integer weights. (The teacher had a pretty accurate grocer's scale
which went up to 25 pounds.) I took these objects in and weighed and
tabulated them with the class. Then I concealed three objects in a
paper bag (actually I made four different bags). The students had to
weigh the bags and based on the total weight, figure out what was
inside. Of course I made it so that there was a unique solution.
To liven things up, I made up a story about Magdalena, the Master of
Mathemagic. While the bags were outside, and out of my sight,
Magdalena sneaked up and replaced a four pound orange juice carton
with a four pound container of worms. She left a note that said that
if we figured out what was in all the bags and opened the one with the
worms last, everything would be OK. So of course we did, and it was a
container of gummy worms, which we shared.
The author of the above is:
Professor Adrienne Lavine
University of California, Los Angeles
Mechanical and Aerospace Engineering Department
38-137F Engineering IV
Los Angeles, CA 90095-1597
Prof. Lavine also suggested the following puzzle.
In a certain population a given birth has the same chance of being a boy as a
girl. Couples want to have boy babies and they cease having children after their
first boy is born. If a girl is born they try again.
What is the proportion of boys in the total population?