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Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?

How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Good Work If You Can Get It

Age 11 to 14 Challenge Level:


Why do this problem?

This problem encourages students to think of different ways in which it can be solved. This can be done using trial and improvement, but preferably, and more efficiently, by creating some linear equations. The very fact that the six men have names beginning with the letters A to F should make an algebraic solution stand out!



Possible approach


You could introduce the problem to the class, and give them a little bit of time to work in pairs to suggest ways it could be tackled. Then come together again to share possible strategies and discuss any difficulties that might arise.


Once students have had a chance to develop clear strategies for working on the problem allow them some time in pairs to develop and discuss their answers.



Allow some time for feed back at the end and to explore and discuss both learners' methods and their answers.



Key questions


Have you thought of making a table to show how long each man worked?
Have you thought of making some algebraic equations from the information given?
Is your strategy the quickest way to work out the answer?


Possible extension

Learners could follow-up with this harder problem, How Many Miles to Go?



Possible support

Suggest making a table and tackle the problem using trial and improvement.