翻訳と辞書 Words near each other ・ Four Field Kono ・ Four Fires ・ Four First Nights ・ Four Fish ・ Four Flicks ・ Four Flies on Grey Velvet ・ Four flush ・ Four Foot Shack ・ Four for the Show ・ Four for Tomorrow ・ Four for Trane ・ Four for Venice ・ Four Forks ・ Four Forks, Virginia ・ Four Four Bravo ・ Four fours ・ Four Freedoms ・ Four Freedoms (disambiguation) ・ Four Freedoms (Norman Rockwell) ・ Four Freedoms (novel) ・ Four Freedoms Award ・ Four Freedoms Monument ・ Four Freedoms Plaza ・ Four Freshmen and 5 Trombones ・ Four Freshmen and Five Saxes ・ Four Friends ・ Four Friends (1981 film) ・ Four Friends (2010 film) ・ Four Frightened People ・ Four from Planet 5 Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Four fours ： ウィキペディア英語版 Four fours Four fours is a mathematical puzzle. 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 digit is allowed). 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. ==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. Other operations allowed by some variations include the reciprocal function ("1/x"), subfactorial ("!" before the number: !4 equals 9), overline (an infinitely repeated digit), an arbitrary root, 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: :$.\backslash overline\; =\; .4444...\; =\; 4/9$ 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: :$n\; =\; -\backslash sqrt4\backslash frac\_\backslash right)"\; TITLE="\backslash left(\backslash ln\backslash underbrace\_\backslash right)">/\; \backslash ln4\backslash right\; )\}\{\backslash ln\{4\}\}$ 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. You can try playing a basic version of this game online in this implementation (Online Four Fours Game 0 to 9 ) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Four fours」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.