Solve this set of simultaneous alphametic equations, where HUIT and NEUF are respectively positive integers in base 8 and base 9 notation. Each of the letters in bold represents a different digit, and none of the numbers contains any leading zero.
(HUIT)8 = (NEUF)9 - 1, and:
sod(HUIT) = sod(NEUF) - 1
Extra Challenge: A non computer program aided solution.
*** sod(x) denotes the numeric value of the sum of the digits of x.