1

Part of 2018 Dutch Mathematical Olympiad

Problems(1)

10-digit shuffle numbers, divisible by 11, 12 (at any order of the digits)

Source: Dutch NMO 2018 p1

We call a positive integer a shuffle number if the following hold: (1) All digits are nonzero. (2) The number is divisible by

11

. (3) The number is divisible by

12

. If you put the digits in any other order, you again have a number that is divisible by

12

10

-digit shuffle numbers are there?

number theoryDigitsdivisible