Rules
There are many variations of four fours; their primary difference is which mathematical symbols are allowed. Essentially all variations at least allow addition ("+"), subtraction ("−"), multiplication ("×"), division ("÷"), and parentheses, as well as concatenation (e.g., "44" is allowed). Most also allow the factorial ("!"), exponentiation (e.g. "444"), the decimal point (".") and the square root ("√") operation, although sometimes square root is specifically excluded on the grounds that there is an implied "2" for the second root. Other operations allowed by some variations include subfactorial, ("!" before the number: !4 equals 9), overline (an infinitely repeated digit), an arbitrary root power, the gamma function (Γ, where Γ(x) = (x − 1)!), and percent ("%"). Thus 4/4% = 100 and Γ(4)=6. A common use of the overline in this problem is for this value:
Typically the "log" operators are not allowed, since there is a way to trivially create any number using them. Paul Bourke credits Ben Rudiak-Gould with this description of how natural logarithms (ln) can be used to represent any positive integer n as:
Additional variants (usually no longer called "four fours") replace the set of digits ("4, 4, 4, 4") with some other set of digits, say of the birthyear of someone. For example, a variant using "1975" would require each expression to use one 1, one 9, one 7, and one 5.
Read more about this topic: Four Fours
Famous quotes containing the word rules:
“The duce of any other rule have I to govern myself by in this affair—and if I had one ... I would twist it and tear it to pieces, and throw it into the fire when I had done—Am I warm? I am, and the cause demands it—a pretty story! is a man to follow rules—or rules to follow him?”
—Laurence Sterne (1713–1768)
“A man often thinks he rules himself, when all the while he is ruled and managed; and while his understanding directs one design, his affections imperceptibly draw him into another.”
—François, Duc De La Rochefoucauld (1613–1680)
“You’d leave your own mother here, if the rules called for it.”
—Michael Wilson (1914–1978)