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:
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—Leontine Young (20th century)
“There are two great rules in life, the one general and the other particular. The first is that every one can in the end get what he wants if he only tries. This is the general rule. The particular rule is that every individual is more or less of an exception to the general rule.”
—Samuel Butler (1835–1902)
“Most of the rules and precepts of the world take this course of pushing us out of ourselves and driving us into the market place, for the benefit of public society.”
—Michel de Montaigne (1533–1592)