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 Simple number trick (Posted on 2016-06-29)
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).

 See The Solution Submitted by Jer Rating: 2.5000 (2 votes)

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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 3-digit 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 2016-06-29 10:13:15

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