'Be creative and find how many ways you can put together 2,0,1 & 3 to make different numbers.'

2013 is the year and this brings a new challenge.  This activity is the 2013 puzzle. Using ALL the digits in the year 2013 once and only once (you may not use any other numbers except 2, 0, 1, and 3) 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

A  Student Grid can be printed off.

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

An Interactive whiteboard manipulatives file can be used to start this activity: Smartboard , ActivInspire

#### Rules

• Use ALL the digits in the year 2013 (you may not use any other numbers except 2, 0, 1, and 3) to write mathematical expressions that give results for the numbers 1 to 100.

• You may use the arithmetic operations  (see below).

• Indices or exponents may only be made from the digits 2, 0, 1, and 3, for example  is allowed, but it has used the 2, 1 and 3.

• 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.

• The functions  may be used if you know how to!

Note on factorials

Here's how factorials may be used:

• n! = nx(n - 1)x(n - 2)x...x2x1, for example 3! = 3x2x1 = 6
• 0! = 1
• (3!)! = (3x2x1)! = 6! = 720

#### Tips for students

• The four digits 2, 0, 1 & 3 can be used ONCE and once only.
• 0! is a very useful result that will help you a good deal.  Use it wisely!
• Remember the order of operations: 2+1x3+0=5 , but (2+1)x3+0=9
• 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 interactive whiteboard manipulatives file.
• 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.
• 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!