Find a three digit number that fits the following criteria:
1)The digits are all different.
2)The product of the digits times the largest of the 3 digits equals the original 3 digit number.
3)The digits are either all odd or all even.
An ndigit number is assumed to be zeroleading and base10, yet if not limited to base10 there are other possible solutions.
The smallest base where there is a solution is base7: 135, which like the base10 solution has all odd digits.
The smallest base where there is a solution for all even digits is base31: C2M.
The smallest base where there are two or more solutions is base 35 and having two solutions: 2CA and M4E, both with digits of even parity.
The smallest base where there are multiple solutions of differing parity is base 43: 4AE (even) PF5 (odd).
The smallest base where there are three or more solutions is base 77 having three solutions, each having odd parity: 1aB, 1q5, and 3e7.
Note: A base85 system of digits has been proposed as of April 1, 1996 with the standard set of digits 0~9, A~Z, followed by the extended a~z, and extended by the 23digits of ASCII characters: ! # $ % & ( ) * +  ; < = > ? @ ^ _ ` {  } ~
The smallest base where one of the 23 special characters is part of the solution is base 93: 42& [even parity].
The proposed base85 system is insufficient as a single character per digit display of all of base 93's digits, but there is no other solution for this base  or any base less than 100  requiring any further extension.
Edited on September 17, 2020, 9:51 am

Posted by Dej Mar
on 20200917 09:11:31 