2

Part of 2020 Regional Competition For Advanced Students

Problems(1)

7-digits numbers with digits 1, 3, 4, 6, 7, 8,9 each once

Source: 2020 Austrian Regional Competition For Advanced Students p2

M

consists of all

7

-digit positive integer numbers that contain (in decimal notation) each of the digits

1, 3, 4, 6, 7, 8

9

exactly once. (a) Find the smallest positive difference

d

of two numbers from

M

. (b) How many pairs

(x, y)

x

y

from M are there for which

x - y = d

?
(Gerhard Kirchner)

Digitsnumber theory