The Odd Card
by Werner Miller

Werner Miller is a retired teacher of mathematics, whose hobbies are recreational mathematics and magic. A magical inventor and writer, Werner has produced a prolific volume of work, mostly what he calls “semi-automatic” card tricks based on mathematical principles. He is the author of "Fast von selbst", "Alles Miller oder was", "Ratatouille", more than 300 trick contributions to various magazines and web sites and more than 30 related computer programs. In addition, Werner is also a staff member of the German magazine "Magische Welt", a columnist for the British magazine "The Magician", and regular contributor here at Visions. Werner's first English-language book, Ear-Marked, is available here.

The Odd Ball-Problem
You have a number of balls identical in size and appearance except for one which is slightly lighter or heavier. How can you determine which is the odd ball using a minimum of weighings with a balance? Is it possible to find out as well whether this ball is heavier or lighter than the others?

To become familiar with the problem, you may try with 9 balls first, one of them heavier. Strange enough, only two chances to weigh the balls are sufficient.

Usually there are 12 balls involved. After only 3 weighings you should not only know the odd ball, but also whether it is heavier or lighter.

How does it work?
If you are unable to solve the problem or want to understand the mathematical background (there is a connection to the ternary system), you may follow one of these links:

http://www.primepuzzle.com/leeslatest/12_ball_solution.html
http://www.mathsisfun.com/pool_balls.html
http://www.scientificpsychic.com/mind/balls1.html
http://www.math.washington.edu/~mbadger/pitt/math1185/12ball.html

A computerized version with playing cards
More than 40 years ago, C. W. Lakin contributed his version of the Odd Ball-Problem to the magazine "The Gen" (Vol. 23, 1967/68, p. 257). Instead of balls he used playing cards.

I extended and computerized his version. The result is a neat freeware program you can download here (Windows XP required).

To perform, you need the 13 Spade cards and a paper clip. Run the executable and ask a spectator to carry out the on-screen instructions and to answer truthfully -- that's all. It is a 3 part-routine, so when asked "Once more?" the spectator should click "Yes" to see it completely. Have fun!

Note
The software is not compatible with Windows Vista. Freeware –- no warranty, no liability, no support.

Werner Miller