December 2010

Challenge

Coffee, Cream, and Making a Wish

We have looked at several solutions to the classic Coffee and Cream mixture problem:

Suppose you have a cup of coffee and a cup of cream. If you take a spoonful of cream, mix it up with the coffee, then take a spoonful of that mixture and add it back to the cream, is there more cream in the coffee, or more coffee in the cream?

I offered a solution that begins by making a wish. That is, I wished that each cup initially contained 10 spoonfuls of liquid; then I proceed to solve the problem algebraically, by following spoonfuls of liquid back and forth between cups. To illustrate the real power of the make-a-wish strategy, though, let’s wish that each cup started with one spoonful of liquidIn this case, the act of transferring one spoonful of cream into the coffee amounts to pouring all the cream in the coffee. Now, mix it up. The mixture on the left is obviously half coffee and half cream. Now, pour a spoonful of the mixture, or half, back into the empty cup. The two cups now contain exactly the same solution: half coffee, and half cream! So the answer to the question is obviously that there are equal amounts of cream in the coffee and coffee in the cream!

Be sure to check out the elegant solution to the problem, as well!

Challenge Resources

Inforgraphic Competition

Visualisation Magazine, which seems to specialize in Data Representation and Information Graphics, is holding a homemade, handmade Infographic Contest.

The contest is apparently open to anyone, and the publishers are emphasizing handmade techniques. The winner will make the cover of the next volume of their magazine. I leafed through their volume on Circles (screenshot above) and there were some good looking infographics in there.

There is a flickr group set up for submissions, which you can check out here: http://www.flickr.com/groups/vismaghandmadecontest.

By patrick honner, 14 years8 years ago

Challenge NYT

Math Quiz: NYT Learning Network

Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:

http://learning.blogs.nytimes.com/2010/12/01/test-yourself-math-dec-1-2010/

This problem was based on estimating and comparing the yearly salaries of union workers who in Pennsylvania who recently agreed to restructure their contracts.