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This one is very simple: How many formulas can you devise, using
only addition, subtraction, mulitplication and division, that are made up of
only **four** digits of the number **four **that will produce as many
numbers in the integer sequence 0, 1, 2, 3, 4, etc. as possible. (You can also
use parentheses/brackets and let's also add SQUARE ROOTS too.) Here are some
easy examples:

**0 = (4-4)+(4-4)
**and the easiest
one for the integer 1 is:

44

1 = ----

44

You must use a different
formula for the integer **1** now. You should be able
to find *at least* one formula for **1 through 10** before using a square
root at all; so try that first.

Using square roots, you
should be able to find formulas for every integer up through **20**
(*except for***19**). For the integer
19, you are also allowed to use a **decimal point** in front of any of the
four fours [**.4**] (that's **4/10** or 2/5, so
something like: 4**/**.4 = 10 might give you an idea). An alternate method
for arriving at a formula of ** four fours** for

**4!
= 1 x 2 x 3 x 4 = 24**.

*The Starman.*