# Magic Sum Puzzle

Pupils analyse a numerical puzzle, solve some examples and then deduce that a further example is impossible.

# Practical details

Suitability
National Curriculum levels 5 to 7
Time
30 minutes to 1 hour
Resources
Pencil, paper and sheet of blank grids for rough work

# Key Processes involved

Representing
Choose an appropriate logical way to solve a puzzle
Analysing
Make a conjecture (an example is or is not impossible) and then seek to justify it; work logically towards a solution, recognising the impact of the constraints involved
Interpreting and evaluating
Form convincing arguments, and formulate proofs
Communicating and reflecting
Communicate reasoning and findings effectively

# Teacher guidance

You could begin by showing slide 1. Cross 2 off the list and write it in, at the top of the puzzle. Then make the following points:

• I want to find a way to place the seven numbers in the boxes

so that each straight line adds up to the same total.

• This is called the magic sum.
• I am only allowed to use each number 1 to 7 once in the puzzle.

Now, complete the puzzle as shown, silently,

without telling pupils how you did it.

• Does this work? What is the magic sum? How can you tell?

Slide 2 provides an alternative starting point. The content and range in this task are low, requiring only the use of properties of integers (e.g. even or odd) to make generalisations. There is also an opportunity to construct, express in symbolic form, and use simple formulae when formulating the proof.