Notice that as you go down the column the tens digits of the answers are counting up and the ones digits are counting down. Also, the sums of the digits in the answers always equal nine, i.e. 7x9=63, 6+3=9. So to get the answer you take one away from seven (7-1=6) to get the tens digit and then the ones digit is whatever you need to add to make nine (6+3=9) so the answer is 63.
I just saw this recently in Dr. Silverman's article and thought it was so cool! I had never "seen" it before. I had one of those silly lightbulb moments that I should have had in elementary school but didn't happen until my 30's, lol.
