Magic Sum Puzzle


Magic Sum Puzzle

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

Practical details

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

Key Processes involved

Choose an appropriate logical way to solve a puzzle
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.