Four Fours and Beyond


What does the expression above equal?

The Four Fours problem is well known by most Mathematics teachers. Each time I have tried it with year 7 to year 9 classes it has proven to be a great success. You can download my Four_Fours_Grid.xls worksheet by clicking on the Scribd icon at right.

There are many references to this problem on the internet:

1.  Wikipedia gives rules and variations as well as solutions for 1 to 20

2.  Four Fours Problem compiled by Paul Bourke gives solutions up to 9370240

3.  The Definitive Four Fours Answer Key by David A. Wheeler is available as a pdf document

210px-Arithmetic_symbols_svgAlso of note is the adaption of the problem to other single digit numbers (eg. Four Fives) and to particular years (eg. I first used this in 1984). If you check out the following link you will notice that the answers 1 to 100 are possible for four 3’s, four 4’s, four 5’s, four 9’s, but probably not for the other single digits. Similarly the years 2000 – 2009 are not suitable for this puzzle, but using a student’s year of birth can overcome this. 

4.  The Year Puzzle  © Copyright 1998 by Heiner Marxen

3-4-5-6-7-number-puzzleBill Lombard explains some other variations of this problem, such as the 3-4-5-6-7 digit puzzle and The Triple Nine Wallclock.

If you are new to Mathematics teaching, I highly recommend this activity to you. If you are an experienced Maths teacher, why not try one of the variations mentioned above. In any case, post a comment about how the activity went!


About webmaths

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
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