This is a competition to choose the smallest number that no one else has chosen.

The number you choose must be a positive whole number (not zero).

## Instructions

Each person is given a small piece of paper on which they write down their name and a number. The number must be a positive integer. (A whole number, not zero). The winner is the person who has written down the smallest number that no one else has written down. Each person should keep their number secret.

When everyone has finished writing the teacher collects each of the pieces of paper in a hat (or similar) then, using the table below the teacher records the names and numbers one by one. Each name is typed next to the number they have chosen. If more than one person has chosen a number, that number is "out of the game". Click on the number button on the left side of the table to disqualify a number.

The winner is the person who has chosen the lowest number that no one else has chosen

NumberName(s)
>25

Play the game a few times so that strategies can be developed!

## Example

Here is an example of a game played with a class of 25 children. Notice how the number is disqualified as soon as more than one person has chosen it.

NumberName(s)
1Sophia Aiden Emma
2Jackson Olivia Ethan Isabella Liam
3Ava Mason
4Lily
5Noah Zoe Lucas
6Chloe Jacob
7Jayden
8
10
11
12Jack
13Logan
14
15
16Ella
17
18
19
20Ryan
21
22
23Caleb
24
25
>25Connor(30) Oliver(42)

In this case the winner is Lily as she has chosen the smallest number that no one else has chosen.

## Thoughts

What number would you choose if you were playing this game?

Are there any winning strategies?

What is the probability of each of the numbers being the winning number?

## The Big Money Give Away!

As a variation on the Smallest Number game this is certain to captivate the interest of everyone one in the class. It's a risk, but unless your class are really clever (and psychic) it shouldn't cost you too much. Transum takes no responsibility if this goes horribly wrong!

Begin by describing the 'prize fund' on offer. This could be £10 or \$10 or some other desirable amount of money. Say that from now on no one is allowed to talk or communicate with anyone else in the class in any way.

Each person has a piece of paper on which they write down their chosen number. Explain that the prize will be awarded to the person who has chosen the largest number in the class but the actual value of the prize will be the 'prize fund' divided by that number.

For example if the numbers chosen by the pupils in the class are 3, 100, 1000, 4, 20, 50, 10 , 0.1 and 55. The pupil who chose 1000 (the largest number) is the winner but the prize is £10 ÷ 1000 = 1p.

If you decide to be a risk taker and try this game please let us know how it went!