- Choose a whole number.
- If your number is chosen by someone else that number is out.
- Lowest number wins.

Love that. Have all your students in all your classes submit a piece of paper at the end of class one day. Tally the results, award class winners, award overall winners, show distributions, and talk strategy the next day.

**BTW**: This MathOverflow thread offers some extended reading.

## 18 Comments

## Craig

December 13, 2011 - 6:08 pm -Patrick Vennebush has been talking about this game on his blog for a little while. He even collected some results an posted them.

## Simon

December 13, 2011 - 11:23 pm -This is called a reverse auction. There’s a whole heap of sites out there that use it to fool the gullible (I remember reading somewhere that many of them use bots to help keep the various auctions busy…)

## Matt E

December 14, 2011 - 5:30 am -What might be more interesting is to officially hold off “talking strategy” for awhile, and conduct this once a day for maybe a week or two, offering no comment yourself at all. I can see the discussions about strategy happening more organically–and vociferously!

## Matt E

December 14, 2011 - 5:32 am -Also interesting to think about what would happen if the only information they received about the outcome was the winning number, and not the distribution… Great stuff!

## Jason Dyer

December 14, 2011 - 8:59 am -An early issue of GAMES Magazine (1980? 1981? I have the back issue lurking somewhere) did the same thing as a contest with “earliest word in the Merriam-Webster dictionary”.

## Nico

December 14, 2011 - 9:01 am -Some things I can add.

1) There were 364 entrants. Mode=1, Median=23, and Mean=1.2million-ish. These 3 numbers were interesting to analyze within the math class.

2) I’ve done this before on a smaller scale and reproducing the experiment becomes more manageable (obv) with a class of 30. The distribution is less interesting. Strategy talk still works.

3) Primes seemed to be popular. The 3 most popular numbers (outside of 1) were 7, 13 and 19.

4) 10 was the winner.

@Craig, thanks for sharing. Nice work Patrick. Sorry I missed it.

@Simon, I have to credit seeing this idea first on rubiks.com where they played the game monthly for prizes. Entrants reached 1000 if memory serves. Years ago.

@Matt. Lots of interesting variations, I agree. Strategy talk becomes intense, almost personal. Love it.

We physically put the ballots on the ground to see the distribution. Bright pink ballots on a long mural. It took some time but the math team was up for it. I prefer Patrick’s digital solution but nothing wrong with getting the physical results.

Thanks for sharing Dan.

## John Berray

December 14, 2011 - 10:11 am -Two classes done. Kids love it! Love it!

2 won and 0 won (gutsy).

Tomorrow I’ll do it combined.

## Alex

December 14, 2011 - 11:33 am -Please tell me someone tried a negative number. That would make me so happy.

## Nico

December 14, 2011 - 11:41 am -@Alex. I got 2 negative numbers when I played with over 300 students. The numbers were -50 000 and -7 999.

## James C.

December 14, 2011 - 4:26 pm -Game Theory offers so much opportunity for reasoning exercises like this one.

Here’s another simple one. Have a bidding war with the students. The highest number gets the amount of dollars they bid, the second highest bid has to pay it. The trick of this exercise (some flare needed by the teacher) is to get the first bid thrown out.

And another, the classic: Everyone guess a number. Whoever guesses closest to 2/3 of the class average wins.

## Bowen Kerins

December 14, 2011 - 8:09 pm -This is also an auction style: a “low unique bid” auction…

http://en.wikipedia.org/wiki/Unique_bid_auction

There are several websites that do these types of auctions and make their results available.

Related (?) is the raffle scheme from a Martin Gardner article. He said anyone could send him a postcard giving the number of raffle tickets they wanted; the winner is drawn randomly. The prize was $1,000,000, divided by the total number of raffle tickets. He rounded the prize up to the nearest penny and paid the winner 1c.

I tried this in my own classes with $100 divided by the total number of tickets, and I think the most I ever paid out was about 50 cents. It’s an extreme example of Prisoner’s Dilemma, where one jerk gets to ruin it for everyone…

## Neal

December 15, 2011 - 4:24 am -Another game idea (paraphrased below), which just got suggested on a club chat list from my college:

Pick a number between 0 and 100. All numbers will be totalled, and the average computed. The winner is the person with the number closest to 2/3 of the average.

## Jim

December 15, 2011 - 11:29 am -Done it in all classes today… gave out loads of chocolate, kids love it! A great time filler! Thanks!

Started to do it with lowest square number, prime number, traingule number, etc etc – to get some more maths in there.

On a similar vain, I also like splitting the class in half. Each half takes it in turn to add a number (1 to 10) into the cummulative total. Team which lands of 100 wins.

Lots of extension work to go from there too… why do you always win, etc etc!

## Kaleb

December 15, 2011 - 9:31 pm -I wonder how it would change the results if the winner got his answer in dollars.

I thought I’d do this in class, not with the money, and so I made this funny intro video. If you’re interested…

http://www.youtube.com/watch?v=vinfm8Jz-LI&feature=youtube_gdata_player

Kaleb

## Ernie

December 17, 2011 - 7:38 am -fyi, they do this every day at tanga.com to give away some kind of prize, it’s called their bottom feeder contest (near the bottom of the homepage). when they post results they show the 20 lowest unique #’s and they also show how many people picked the ones that you picked.

## David

December 19, 2011 - 11:50 am -Hi everyone,

I did this in my class on Friday and believe it or not, the number 1 was the winner. My whole class was in disbelief and even the student who won couldn’t believe that he got away with that. He said “I just had a feeling nobody else would put 1…” :)

Thanks, it was fun.

## Simon

December 21, 2011 - 5:57 am -Did this with four classes yesterday. Really interesting to see how students responded to each round.

Thanks Jim for the types of numbers idea ( I.e lowest prime).

One of the ‘classes’ was me with two students.

Was great watching them realise they could fix the game by picking 1 and 2. Took a good 6 rounds however.

Some of my keen 11 year olds wanted to stay back at lunch and keep playing! That’s an endorsement.

## Haylee

December 29, 2011 - 10:33 am -This looks like so much fun! We may have to try this for some fun when we get back from winter break!