## Archive for January 9, 2011

### Presentation at Central Connecticut State University

Yesterday morning, I presented a math and technology workshop at Central Connecticut State University. The attendees were teachers who are testing a new Algebra I curriculum. As part of the workshop, the attendees participated in my favorite online activity, and they attempted my favorite problem.

To ensure that I provided appropriate activities, I reviewed a draft of the new curriculum ahead of time. The vocabulary list for the first unit contained the word *hendecagon*. Guessing that most attendees were unfamiliar with the term, I provided a diagram:

Seriously, a *hendecagon* is an 11‑sided polygon. The Susan B. Anthony dollar coin is probably the most common example of a hendecagon in everyday life. (As it turns out, there is no connection between the number 11 and Susan B. Anthony, but the reverse side of the coin contains an image adapted from the Apollo 11 mission insignia.)

(For the record, I’d be interested in creating more silly images like the one of the hendecagon above. Are there other math terms that lend themselves to similarly silly drawings? If you think of one, post a comment.)

At the end of the workshop, I gave away several copies of *Math Jokes 4 Mathy Folks*. To determine who would get the copies, we played my favorite game:

- On a piece of paper, write down a positive integer.
- Share your number with a neighbor (for verification later, if necessary).
- The winner is the person who wrote down
*the smallest integer not written by anyone else*.

The rule for determining a winner often confuses folks, so let me give an example. Let’s say 20 people chose the following numbers:

4, 1, 7, 11, 4, 6, 5, 2, 1, 3, 2, 1, 8, 1, 4, 7, 9, 2, 3, 18

- The smallest integer in the list is 1, but it was written by four people. Hence, none of them would win.
- The next smallest integer is 2, but it was written by three people, so none of them would win, either.
- The number 3 was chosen by two people, and the number 4 was chosen by three people — no winners.
- Which brings us to the number 5. The person who chose 5 is the winner, because she wrote the smallest integer not written by anyone else.
- Although the folks who wrote 6, 8, 9, 11, and 18 wrote numbers that weren’t written by anyone else, they did not choose the smallest numbers not written by anyone else.

As with many things, this game may not sound very fun with a text explanation. But play it a few times. Or better yet — play it the next time you go to dinner with a large group of friends, and the losers have to buy dinner for the winner.

I learned this game from my friend Richard Rusczyk, who referred to it as “Harold’s Game,” because he learned it from our friend Harold Reiter. Despite the name Richard has given the game, I do not believe that Harold is the creator.