10-digit shuffle numbers, divisible by 11, 12 (at any order of the digits)
Source: Dutch NMO 2018 p1
September 7, 2019
number theoryDigitsdivisible
Problem Statement
We call a positive integer a shuffle number if the following hold:
(1) All digits are nonzero.
(2) The number is divisible by .
(3) The number is divisible by . If you put the digits in any other order, you again have a number that is divisible by .
How many -digit shuffle numbers are there?