MathDB

A complete number is a

9

digit number that contains each of the digits

1

9

exactly once. The difference number of a number

N

is the number you get by taking the differences of consecutive digits in

N

and then stringing these digits together. For instance, the difference number of

25143

is equal to

3431

. The complete number

124356879

has the additional property that its difference number,

12121212

, consists of digits alternating between

1

and

2

. Determine all

a

with

3 \le a \le 9

for which there exists a complete number

N

with the additional property that the digits of its difference number alternate between

1

and

a

1