 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Three Digit Number 3 (Posted on 2020-08-05) 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.

 No Solution Yet Submitted by Larry No Rating Comments: ( Back to comment list | You must be logged in to post comments.) With bases loaded... (partial spoiler) Comment 4 of 4 | An n-digit number is assumed to be zero-leading and base-10, yet if not limited to base-10 there are other possible solutions.

The smallest base where there is a solution is base-7: 135, which like the base-10 solution has all odd digits.
The smallest base where there is a solution for all even digits is base-31: 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 23-digits 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 2020-09-17 09:11:31 Please log in:

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