Before they discontinued it, Dr Dobbs "Dr Ecco's Omniheurst Corner" was great because they had these kinds of problems -- but they were too big to be brute forced!

Brute force here is at worst 10^5. But since digit3 depends on digit1, and digit5 depends on digit4 there are only three 'loose' digits, or 10^3 possibilities.

You could brute-froce the 1000 combinations on paper ;)

-jack

ps, you can find old Ecco columns by typing 'ecco' in the search box on ddj.