|
In mathematics a polydivisible number is a number with digits ''abcde...'' that has the following properties : # Its first digit ''a'' is not 0. # The number formed by its first two digits ''ab'' is a multiple of 2. # The number formed by its first three digits ''abc'' is a multiple of 3. # The number formed by its first four digits ''abcd'' is a multiple of 4. # etc. For example, 345654 is a six-digit polydivisible number, but 123456 is not, because 1234 is not a multiple of 4. Polydivisible numbers can be defined in any base - however, the numbers in this article are all in base 10, so permitted digits are 0 to 9. The smallest base 10 polydivisible numbers with 1,2,3,4... etc. digits are 1, 10, 102, 1020, 10200, 102000, 1020005, 10200056, 102000564, 1020005640, ... The largest base 10 polydivisible numbers with 1,2,3,4... etc. digits are 9, 98, 987, 9876, 98765, 987654, 9876545, 98765456, 987654564, 9876545640, ... ==Background== Polydivisible numbers are a generalisation of the following well-known problem in recreational mathematics : : ''Arrange the digits 1 to 9 in order so that the first two digits form a multiple of 2, the first three digits form a multiple of 3, the first four digits form a multiple of 4 etc. and finally the entire number is a multiple of 9.'' The solution to the problem is a nine-digit polydivisible number with the additional condition that it contains the digits 1 to 9 exactly once each. There are 2,492 nine-digit polydivisible numbers, but the only one that satisfies the additional condition is :381654729 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「Polydivisible number」の詳細全文を読む スポンサード リンク
|