perplexus.info :: Numbers : Simple number trick

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).

What's your secret?

Submitted by Jer

Rating: 2.5000 (2 votes)

Solution: (Hide)

There is an error in the problem. The given expression is not easy to compute in ones head. It should have been (A*C)+(B*D)
Example:
A = 379
B = 379
C = 653
D = 346
The board would look something like
379 653 379 346
To which you could add symbols to make
(379*653)+(379*346)
Which is easily computable as 378621
The trick is that since C+D=999 and A=B all you need to compute is 999*A = 1000A - A.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Answer	Math Man	2016-07-07 08:34:02
re: Likely answer	Jer	2016-06-30 09:08:26
Likely answer	Steve Herman	2016-06-30 08:22:49
re: comment	Jer	2016-06-29 10:45:33
comment	Charlie	2016-06-29 10:13:15

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (16)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info