Question

Trying to formalize my answer to http://i.imgur.com/Or6h9.jpg

Answer 1

File not found

Answer 2

So \( M = 10^{61}\cdot2k + 10^{60}\cdot 2k +\cdots+10^{0}\cdot 2k\) and \(N = 10^{60}\cdot k + 10^{59}\cdots 10^0\cdot k\) where \(k=3\).

Answer 3

http://i.imgur.com/Or6h9.jpg

Answer 4

this is easy...... wherever you see 9, just ignore it, like 94-->sum=4
637--->6+3=9---->sum = 7
here, sum of digits for N will be 0, so sum of digits for N*M =0

Answer 5

So how would I get the digit sum? I got \(558\) because I noticed that the digit sum is always \(9\times [\text{number of 6's}]\) for all \(\underbrace{666\cdots666}_{n \text{ number of 6's}} \times \underbrace{333\cdots333}_{n-1 \text{ number of 3's}}\)

Answer 6

0 or 9, both are equivalent.

Answer 7

It's actually \(558\) @hartnn

Answer 8

9 can be ignored.....thats the catch.

Answer 9

digit sum is always single digit.

Answer 10

2219778 = 36
^Like this

Answer 11

Yes. ^

Answer 12

oh, sorry, there are 61 3's , so we ignore 60 3's as their sum is 0 and what remains is one 3
so, sum of digits og N =3

Answer 13

36 is still 3+6=9

Answer 14

No, we just need 36 :)

Answer 15

hmm... then use some different method...

Answer 16

But we need the digit sum of \(M\times N\)...

Answer 17

My method was a little brute-forcey. I need a formal method =/

Answer 18

sum of digits follow distributive property

Answer 19

@ParthKohli Mine is even worse..
Digit sum of MxN= 2(n-2)+7(n-2)+1+9+8 :|

Answer 20

How did you get that? ._.

Answer 21

lol

Answer 22

By observation :|

Answer 23

3x66 = 198
33x666=21978
333x6666=2219778
3333x66666=222197778

Sigh... Too bad :(

Answer 24

But that's not the digit sum :p the digit sum would be number of 6's times 9.\[198\mapsto 18 \ \ \rm and \ \ 9 \times \underbrace{2}_{number ~of~6's} =18\]Try this for others

Answer 25

Hmm... I meant to say from the above results, I got this:
digit sum of MxN = 2(n-2) + 7(n-2) +1+9+8, n= no. of 6
I know it's not good.

Answer 26

Oh yes :D you're completely right!

Answer 27

But I wanna formalize the answer =(

Answer 28

@satellite73 Would you mind giving a hand here?

Answer 29

Yo @satellite73