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?

1667=10002/6. so 1667*abc where abc=a*100+b*10+c
gives us the number (abcABCD)/6 where ABCD are the four digits of the number equal to 2*abc. if you can divide by 6 in 10 seconds (after multiplying the given number by 2 and placing it next to the given number in a 4 digit format, of course), you have your answer, starting from the left to the right (possibly what the problem-poser means by the words "most significant number").
for e.g. 1667*101=101[0202]/6 ....where 0202=2*101
=1010202/6
= 168367!
and 1667*999=999[1998]/6....where 1998=2*999
=9991998/6
=1665333!
-mohan.

Posted by mohan on 2003-10-06 01:32:25