MathDB

We say that a positive integer N is nice if it satisfies the following conditions:

\bullet

All of its digits are

1

2

\bullet

All numbers formed by

3

consecutive digits of

N

are distinct. For example,

121222

is nice, because the

4

numbers formed by

3

consecutive digits of

121222

, which are

121,212,122

and

222

, are distinct. However,

12121

is not nice. What is the largest quantity possible number of numbers that a nice number can have? What is the greatest nice number there is?

Problem Statement