This trick does not appear to take into account that century years not divisible by 400 are not leap years. If every fourth year were a leap year, then there would be 365*100 + 100 days in a 400-year period. That number, 14,700, is clearly divisible by 7, so the doomsday for every four-hundredth year would be the same. But three of those '00 years are not leap years, so you have to subtract three days, which messes things up. Have I missed something?