I can multiply any three-digit number by 1667 in my head, usually in less than 10 seconds.

Also, to make it even more impressive, I come up with the digits of the result in proper order (not in reverse!)

How can I do this?

That's where I started.
1667 =10002/6
It's the 2 that makes it awkward I think.
nnn * 10002/6 = nnn * [10000/6 + 2/6]

nnn * 2/6 is where I divide by 3 (step1)
Dividing this result by 2 gives me the digits involved in 10000/6 element.
The awkward part is when nnn is not divisible by 3 (and therefore not 6). You can't just stick the numbers together. (hence my messy "if the remainder = 1/3...." stage)
I tried this on about six or seven examples and by the end was getting much quicker!(but not 10 seconds)

Posted by Lee on 2003-10-05 14:54:06