You may also like

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Have You Got It?

Can you explain the strategy for winning this game with any target?

Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Making a Difference

Age 11 to 14 Challenge Level:

There are a number of ways the digits $2, 5, 7, 8$ can be placed in a subtraction sum like the one below:

57 - 28 = 29 as a column subtraction

In this example, the answer is 29.

Can you rearrange the four digits to find all the (positive) answers it is possible to make?


Here are two follow-up questions you might like to consider:


  • Can you work out which four digits you need to start with to be able to get all the possible answers $7, 9, 11, 13, 18, 22, 29$ and $31$?
  • Can you show that, if we're only allowed to use consecutive digits (e.g. $5, 6, 7, 8$), $31$ is the largest possible answer and $7$ is the smallest?


With thanks to Don Steward, whose ideas formed the basis of this problem.