[Guest]

A tridecimal (base 13) positive integer N consists of a string of sevens, that is, N = 77777.....7777 (base 13) such that N is evenly divisible by the base 13 number 124. Let N₀ be the minimum value of N satisfying the given conditions and N₀/124(base 13) is equal to Q.

Determine the tridecimal digital root of Q.

*** For an extra challenge, solve this problem without using a computer program.

Note: Tridecimal digital root is similar to digital root, with the exception that the digit operations are performed on the digits of a tridecimal number rather than the digits of a base ten number.

Edited May 16, 2010 by K Sengupta

[superprismatic]

This was a fun problem. I hope I didn't make any

mistakes!

The smallest N produces the following 97 tridecimal

digit number Q:

6594C25BC09AB616242B02269C7720A8BCBA48A3A9A0578B1B

3747C33C5B1030739B968366755CA138286081A56AA80C5

The sum of its digits in tridecimal form is 384,

the tridecimal sum of this is 12, and, finally,

the tridecimal sum of this is 3. So, the

tridecimal digital root of Q is 3.