Challenge Level

Here is a grid of four "boxes":

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

This gives four two-digit numbers:

$52$ | (reading along the $1$st row) |

$19$ | (reading along the $2$nd 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. *