## satellite73 5 years ago Multiply $24\times 53$ (or any two 2-digit numbers) using 3 multiplications instead of the usual 4

1. anonymous

no takers on this one?

2. saifoo.khan

No Takers, Only Under Takers!!

3. anonymous

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

4. asnaseer

I can do it using only two multiplications: 20 x 53 plus 4 times 53 oh - ok - misunderstood the question...

5. anonymous

yeah that is still 4 right?

6. anonymous

use ethiopian multiplication!

7. anonymous

ok, what might that be?

8. anonymous

rosettacode.org/wiki/Ethiopian_multiplication

9. anonymous
10. anonymous

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

11. anonymous

method i had was somewhat shorter

12. asnaseer

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

13. anonymous

funny i looked here and didn't see it

14. asnaseer

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

15. anonymous

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

16. anonymous

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

17. asnaseer

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

18. anonymous

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

19. anonymous

karatsuba! i will try to remember that name

20. asnaseer

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

21. anonymous

especially with a bookmark!

22. asnaseer

lol!

23. asnaseer

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)