MathDB

Determine the number of ten-digit positive integers with the following properties:

\bullet

Each of the digits

0, 1, 2, . . . , 8

and

9

is contained exactly once.

\bullet

Each digit, except

9

, has a neighbouring digit that is larger than it. (Note. For example, in the number

1230

, the digits

1

and

3

are the neighbouring digits of

2

while

2

and

0

are the neighbouring digits of

3

. The digits

1

and

0

have only one neighbouring digit.)
(Karl Czakler)

Problem Statement