Reach 100

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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Reach 100 printable sheet

Here is a grid of four boxes:

 

  
  

You must choose four different digits from 1 - 9 and put one in each box. For example:

 

52
19

This gives four two-digit numbers:

52 (reading along the first row)

19 (reading along the first row)

51 (reading down the left-hand column)

29 (reading down the right-hand column)

 

In this case their sum is 151.

Try a few examples of your own.

Is there a quick way to tell if the total is going to be even or odd?

Your challenge is to find four different digits that give four two-digit numbers which add to a total of 100.

 

How many ways can you find of doing it?

You may be interested in the other problems in our Mastering Mathematics: Developing Generalising and Proof Feature.

This problem is adapted from Make 200 from 'Mathematical Challenges for Able Pupils Key Stages 1 and 2', published by DfES.