### The four fours problem

Posted:

**Wed May 02, 2007 12:32 am UTC**A fun problem a former history professor gave to me an a friend to keep us occupied during class

Using only four 4's in whatever combination, using as many operators as you desire, create a representation for each of the first 100 whole numbers. A couple examples to get you started:

0: 4 + 4 - 4 - 4 OR 44 - 44

1: 44/44 OR 4/4 + 4 - 4

The rules are only as strict or as lax as you make them. There are plenty of websites on the problem if you're so inclined to chea^H^H^H^Hresearch the problem, although it's a lot more fulfilling if you do it yourself. Things start to get very hairy around 31 or 73.

Enjoy!

EDIT:Some clarification of the rules as I understand them:

Using only four 4's in whatever combination, using as many operators as you desire, create a representation for each of the first 100 whole numbers. A couple examples to get you started:

0: 4 + 4 - 4 - 4 OR 44 - 44

1: 44/44 OR 4/4 + 4 - 4

The rules are only as strict or as lax as you make them. There are plenty of websites on the problem if you're so inclined to chea^H^H^H^Hresearch the problem, although it's a lot more fulfilling if you do it yourself. Things start to get very hairy around 31 or 73.

Enjoy!

EDIT:Some clarification of the rules as I understand them:

- You must use exactly four 4's
- You cannot use numbers other than 4. This means
- The multiplicitative inverse is no good (unless there's a way you can do it without 4^-1 or 1/4 that I'm not aware of)
- Sqr(4) is ambiguous. 4^2 is obviously no good, so I'm hesitant to say that Sqr(4) is an acceptable workaround. Any answer that can be done without it (i.e. pretty much all of them I think) would be preferable
- Sqrt(4) is ok. In ordinary mathematical notation, the root operator defaults to 2 the same way log(x) implies log_10(x). No need to get terribly pedantic here
- Constants are no good, as they are neither a function nor a four. This is also to avoid simply adding euler's identity an arbitrary number of times