Question

Suppose
N
is an
n
-digit positive integer such that
(a) all the
n
-digits are distinct; and
(b) the sum of any three consecutive digits is divisible by 5.
Prove that
n
is at most 6. Further, show that starting with any digit one can find a six-digit
number with these properties.

Answer 1

Try figuring out the number of ways three consecutive digits could add up to something divisible by 5, and combine that with the condition that all digits are distinct. for the first part.

Answer 2

Thankyou Madam