# 2019 Puzzle

Be creative and find how many ways you can put together 2,0,1 & 9 to make different numbers.

2019 is the year and this brings a new challenge. This activity is the 2019 puzzle. Using ALL the digits in the year 2019 once and only once (you may not use any other numbers except 2, 0, 1, and 9) write down as many different mathematical expressions that give results for the numbers 1 to 100. You should learn many different tricks along the way to help you and you may even surprise yourself how creative you can be to find solutions to ‘difficult’ numbers.

Resources

The manipulative below may help as a stimulus to start this activity.

A Student grid can be printed off

Teachers may wish to display this Classroom Poster and get classes to collate their results.

#### Rules

Use ALL the digits in the year 2019 (you may not use any other numbers except 2, 0, 1, and 9) to write mathematical expressions that give results for the numbers 1 to 100.

You may use the arithmetic operations + , - , x , / , square root and ! (see below).

Indices or exponents may only be made from the digits 2, 0, 1, and 9, for example \(2^{\sqrt{9}+1+0}=16\) is allowed; it has used all the digits.

Multi-digit numbers and decimal points can be used such as 20, 102, .02 but you CANNOT make 30 by combining (2+1)0.

Recurring decimals can be used using the overhead dots or bar e.g. \(2\div0.\overline{1}\)

Trigonometric functions can be used if you know how to use them, e.g.\(sin^{-1}(\frac{1}{2})=30°\)

**Factorials are allowed**

n! = nx(n - 1)x(n - 2)x...x2x1

For example

- (10-9+2)! = 3! = 3x2x1 = 6
- 0! = 1

#### Tips for students

- The four digits 2, 0, 1 & 9 can be used ONCE and once only.
- 0! is a very useful result that will help you a good deal. Use it wisely!
- Make good use of brackets. Your solutions should only have one equal sign in them.
- Remember the order of operations: 2+1x9+0=11 , but (2+1)x9+0=27
- Don’t set your mind necessarily on finding the solution to one particular number. Play with the digits and different operations and see what you can make.
- Try to work in clusters of numbers. If you find the solution to one number maybe you could find the solution to a number one more or one less than the number by a simple manipulation.

Description

Here follows an outline of how the task could be run.

- The class could be introduced to an expression and asked to work out the solution. An example is given in the manipulative above.
- It is important to share some solutions early on to clarify the rules and iron out some misconceptions.
- Check students work so that misunderstandings can be corrected.
- A competitive element could be added to the task.
- Students could be asked to choose a solution that they are most proud of and share it with the class. They can learn from each others' clever tricks!
- Students love entering their correct solutions on a classroom poster. They could take it in turns to enter one at a time with their name written beside it for posterity!
- It is often a good idea to set students targets on the number of solutions you think they might be able to get.
- This puzzle can run for weeks and months especially if incentives are set to find solutions to the more elusive numbers.
- Students can do this puzzle year after year. What a great way to bring the New Year in!