Four Fours is a mathematical challenge that can be explored to many levels. If you are new to this puzzle, you should take on the First Challenge below. If you like Four Fours, or have suggestions, please use the feedback form.
The First Challenge is to find answers for the whole numbers 0 to 19, using the Basic Rules (below).
If you're really stuck, Solutions have been submitted by the Web community.
A number is chosen, for example, '1'. Using only four '4's, i.e. 4, 4, 4, and 4, with any number of operators and parentheses, you must arrive at the chosen solution. For example,
0 = (4+4) – (4+4)
1 = (4/4) / (4/4)
OK, that's 0 and 1 done, what about the rest? All numbers are now open for suggestions. As the web community submits solutions, gaps in the sequence will become apparrent – the challenge is to fill these gaps!
Basic operators to start you off:
If you're really stuck, Solutions have been submitted by the Web community. These solutions do not stop at 99, and other puzzlers have used the Third Challenge to achieve solutions to 40,000 and beyond, using different rules.
The detailed rules below will become more important as you progress to larger numbers.
See Education for ideas on how to turn any of these challenges into an educational resource.