Package 3-5: All the digits

In this task your child will think about place value and the way that written strategies for multiplication work.

Week 4 - Package 5 - Year 5 and 6 Mathematics - All the digits

From NRICH maths.

Things you need

Have these things available so your child can complete this task.


  • Blank paper for working out

Before you start

Write out the equation below using boxes for unknown numbers. This task requires students to think about place value and the way that written strategies for multiplication work. Although the problem can be done by trial and improvement, it is solved more efficiently if worked through systematically. This will take some patience.

What your child needs to know and do

This activity requires the ability to use multiplication facts.

What to do next

Solve the problem! Here are your clues (and challenges):

  • Put the numbers 0 to 9 once only into the squares so that the equation is correct.

  • The 4-digit number contains three consecutive numbers, which are not in order.

  • The third digit is the sum of two of the consecutive numbers.

  • The first, third and fifth figures of the five-digit number are three consecutive numbers not in order. The second and fourth digits are also consecutive numbers.

4 empty square on top row. Times by 3. Answer row shows 5 empty squares.

Options for your child

Activity too hard?

Use a multiplication grid or calculator to help with calculations.

Activity too easy?

Challenge your child to prove to you that there is only one solution. How many solutions would there be if the clues about consecutive numbers did not hold?

Extension/additional activity

Consecutive numbers are numbers which follow one after the other. For example, 6, 7, 8, 9.

  • Choose 4 consecutive numbers and write them in a row.

  • Add a multiplication or division symbol between the numbers. E.g. 6 x 7 ÷ 8 x 9 =?

  • Practise using different sets of consecutive numbers.

  • Use a calculator to check your answers.

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