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 9-complements 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?

It is not very easy to find (A*B)+(C*D). However, it is easy to find (A*C)+(B*D). Since A=B and D=999-C, (A*C)+(B*D)=(A*C)+(A*(999-C))=A*999. To find A*999, just solve (A*1000)-A.

Posted by Math Man on 2016-07-07 08:34:02