Math Question on TED Talks, Number Theory

Arthur Benjamin asks volunteers to multiply 8649 by randomly selecting 3-digit numbers. In each of these cases they obtain a 7-digit number (but I think 6-digit is possible). He asks the participants to tell him 6 of the 7 digits in any random order and he can immediately tell them the missing digit. I can't figure out how he does this trick. Can anyone here help me?

http://www.ted.com/talks/arthur_benjamin_does_mathemagic.html

As 8649 is divisible by 9, the product of 8649 and any 3-digit number is divisible by 9. A property of all multiples of 9 is that their digits sum to a multiple of 9. So given any six digits of a seven digit number that is a multiple of 9, the remaining digit is whichever will sum with the other six to produce a multiple of 9. For any set of six digits, there is only one possible value for the seventh digit.