MathDB

The distance between towns

A

and

B

999

km. At every kilometer of the road that connects

A

and

B

a sign shows the distances to

A

and

B

as follows:

\fbox{0-999}

\fbox{1-998}

\fbox{2-997}

. . .

\fbox{998-1}

\fbox{999-0}

How many signs are there, with both distances written with the help of only two distinct digits?

350