Question

Multiply
\[24\times 53\] (or any two 2-digit numbers) using 3 multiplications instead of the usual 4

Answer 1

no takers on this one?

Answer 2

No Takers, Only Under Takers!!

Answer 3

i think this is a computer algorithm problem. cuts down on multiplications

Answer 4

I can do it using only two multiplications:
20 x 53
plus
4 times 53

oh - ok - misunderstood the question...

Answer 5

yeah that is still 4 right?

Answer 6

use ethiopian multiplication!

Answer 7

ok, what might that be?

Answer 8

rosettacode.org/wiki/Ethiopian_multiplication

Answer 9

http://rosettacode.org/wiki/Ethiopian_multiplication

Answer 10

wow! not exactly what i had in mind though...

Answer 11

method i had was somewhat shorter

Answer 12

here is a list of algorithms for doing multiplication: http://en.wikipedia.org/wiki/Multiplication_algorithm

Answer 13

funny i looked here and didn't see it

Answer 14

One of these is particularly interesting: http://en.wikipedia.org/wiki/Karatsuba_algorithm

Answer 15

hint is
\[(a+b)(c+d)=ac+ad+bc+bd\] and you need the numbers
\[ac, bd, ad+bc\]

Answer 16

yeah that is it! for example
\[53\times 24\]
\[5\times 2=10,3\times 4=12,(5+3)(2+4)=8\times 6=48, 48-10-12=26\]
1 2
26
10
__________--
1 2 7 2

Answer 17

yes - until you brought this up I was wasn't even aware of efficient multiplication methods. thanks for opening the door to new knowledge. :-)

Answer 18

i never knew the name, and only remember it from a discrete algorithms class. in fact it is all i recall from that class

Answer 19

karatsuba! i will try to remember that name

Answer 20

how can we ever forget a name like that! :-)

Answer 21

especially with a bookmark!

Answer 22

lol!

Answer 23

I have just invented a way for me to remember this:

rabbits hop around and multiply very fast.
so what is their favourite meal? "carrot soup" of course! (hence katatsuba)