Four Fours
The goal of four fours is to find the simplest mathematical expression for every whole number from 0 to some maximum, using only common mathematical symbols and the digit four (no other digits permitted).
Most versions of four fours require that each expression have exactly four fours, but some variations require that each expression have the minimum number of fours.
There are many variations of four fours; their primary difference is which mathematical symbols are allowed. Essentially all variations permit addition ("+"), subtraction ("−"), multiplication ("×"), division ("÷"), and parentheses, as well as, concatenation (e.g., "44" permitted).
Most versions allow the factorial ("!"), exponentiation (e.g. "444"), the decimal digit (".") and the square root operation, although sometimes square root is specifically excluded on the grounds that there is an implied "2" associated with the root.
While not exclusive to the specific expressions provided, four fours solutions are provided below for the numbers zero through 10:
It may be noted in two of the solutions listed above that "0.4" is written as ".4" since only the digit "4" may be used.