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?

First, in 'normal' multiplication you work out the result right to left - finishing with "the most significant" (the biggest). I think the poster is simply saying they quote the answer in full (left to right). The 'impressive' part, I assume, is that the whole answer appears to have been worked out by some method other than the 'standard' method. Anyway that's my interpretation.
Also I assume nnn is any 3 digit number (not just 111,222,333...)

This method still requires mental skill, but with practise should become fairly straightforward (under 10 sec)

1. Divide nnn by 3 to give xxx (include leading 0 if nnn<300)
2. Remember the remainder (0,1/3, 2/3)
3. If the remainder is 1/3 work out xxx+667
4. If the remainder is 2/3 work out xxx+334
5. These are you last 3 digits
6. Now divide xxx (and any remainder) by 2
7. The first 3 digits are the first 3 digits of the result (if nnn<600). If nnn =600 or greater use the first 4 digits

Example 634 * 1667
1. 634/3 = 211 (and a third)
2. 211 + 667 = 878 (the last 3 digits of the result)
3. (211 1/3)/2 = 105.6666666
4. Result 1056 878

Posted by Lee on 2003-10-05 14:09:50