A. Have someone write down a 3 digit number.
B. You write down the same number.
C. Have them write down another 3 digit number. (Don't let them write 999.)
D. You write down the number whose digits are 9complements to theirs. i.e. If their first digit is 7 your first digit is 2. Try not to let them notice this.
Astound them by quickly computing (A*B)+(C*D).
What's your secret?
If I'm reading this right, D depends only on C. A and its identical mate B are independent of C and D.
It seems to me there's no way around calculating the square of a 3digit number in your head. This is a topic in Arthur T. Benjamin's course Secrets of Mental Math (lecture 11: Advanced Multiplication), in "the Great Courses" series, but that's an entire learned practice, and daunting in itself.
I don't see a way around this unless, say, the choice of D is some way affected by A.

Posted by Charlie
on 20160629 10:13:15 