An eleven digit duodecimal positive integer N is constituted by each of the nonzero digits from 1 to B exactly once, such that N satisfies all the following conditions.
- The sum of the digits 1 and 2 and all the digits between them is equal to the duodecimal number 12.
- The sum of the digits 2 and 3 and all the digits between them is equal to the duodecimal number 23.
- The sum of the digits 3 and 4 and all the digits between them is equal to the duodecimal number 34.
- The sum of the digits 4 and 5 and all the digits between them is equal to the duodecimal number 45.
- The sum of the digits 5 and 6 and all the digits between them is equal to the duodecimal number 56.
If the first digit of N is more than the last digit, determine all possible value(s) that N can assume.
Note: Think of this puzzle as an extension of
An ID Number Problem.