How to Decode SEND+MORE=MONEY?

[aricho]

Letters to Numbers?

Hey, I have no idea how to do this...

Replace all the letters with the respective digits in such a way that the calculation is correct

SEND+MORE=MONEY

the answer is 9567+1085=10652, but i don't know how to get there.

Thanks for your help

 

[arildno]

All right, let us say S, E, N, D, M,R,O, Y stands for different digits s,e,n,d, m,r,o,y between 0 and 9.
Hence, SEND=s*1000+e*100+n*10+d*1
Do you agree to this?

 

[aricho]

sorry, lost

 

[arildno]

sorry, lost

Why are you lost now?
Try to formulate what EXACTLY you are struggling with understanding; that's difficult, I know, but the only way to actually start achieving understanding.

 

[aricho]

SEND=s*1000+e*100+n*10+d*1

i would have thougt it would have been s*1000+e*100+n*10+d

 

[arildno]

And your thought is perfectly correct and valid!

But, since any number multiplied with 1 equals itself, d=d*1, right?
So that means we agree on our expression after all..


The reason why I put in the *1 notation, is that it is conventional (and systematic) to do so, not because your idea is wrong (which it isn't)!

OK?

 

[VietDao29]

This problem have so many solutions to it... I'll give you another one:
9342 + 1093 = 10435. Is that also correct?
Looking thoroughly at that, you will notice: m = 1, o = 0, r = 8 (or 9). The other number can be wisely chosen to fit the SEND + MORE = MONEY.
Viet Dao,

 

[aricho]

arildno, yes, got it now.

Whats next?

 

[arildno]

This problem have so many solutions to it... I'll give you another one:
9342 + 1093 = 10435. Is that also correct?
Looking thoroughly at that, you will notice: m = 1, o = 0, r = 8 (or 9). The other number can be wisely chosen to fit the SEND + MORE = MONEY.
Viet Dao,

WOW, YOU ARE VERY SMART!
IT IS SO GREAT THAT YOU MAKE O.P. A LOT MORE CONFUSED THAN HE ALREADY WAS!

 

[arildno]

arildno, yes, got it now.

Whats next?

Okay, now you can make a similar decomposition into sum expressions of MORE and MONEY as well, right? (Do that!)

Verify therefore that SEND MORE=MONEY can be written as:
(s+m)*1000+(e+o)*100+(n+r)*10+(d+e)*1=m*10000+o*1000+n*100+e*10+y*1

Ok?

 

[VietDao29]

IT IS SO GREAT THAT YOU MAKE O.P. A LOT MORE CONFUSED THAN HE ALREADY WAS!

Whoops, I thought I will have a chance to explain more when he continues asking questions. I hate reading long, long posts... therefore I just shorten everything.
Viet Dao,

 

[arildno]

Whoops, I thought I will have a chance to explain more when he continues asking questions. I hate reading long, long posts... therefore I just shorten everything.
Viet Dao,

He's all yours now, if you like.
I'm logging off..

 

[VietDao29]

Just stay there,... I don't like, anyway. Maybe I can learn a different way from you.
Viet Dao,

 

[aricho]

yer, kinda...

 

[arildno]

What do you mean by "kinda"?

Did you get what I was doing , but don't understand why I've done it like that?

 

[aricho]

sorry, i just wrote it down, agree-got it

 

[arildno]

All right:
1. Now, you agree that whatever digits the letters represent, each of the numbers SEND and MORE must be less than or equal to 9999, right?

2. But that must mean that their sum must be less than or equal to 9999+9999=19998, agreed?

3. Now, look at the MONEY-side of your equation:
The first term there is m*10000
Thus, if you combine this with the insight you've gained in the above argument, what digit must "m" be if we assume that "m" is different from zero?

If you have problems with this post, please pinpoint what you didn't understand too well.

 

[aricho]

.....1?

 

[arildno]

Okay, 9 is the biggest digit we've got, right?
So, the number 9999 must be bigger than any other number with 4 digits, whatever digit a given letter might represent.
Get it?

(I made a writing error in 1., I've fixed it now)

 

[aricho]

yer....got that

 

[HallsofIvy]

Since 9+ 9= 18, even if we borrowed 1 from the previous column, the largest the left most column sum can be is 19 so m must be 1. Knowing that the m in "more" must be a 1. That means that the s in "send" has to be either 8 or 9 (because even borrowing 1 from the previous column, if s= 7 we would have 7+1+1= 9 and there is no 1 to carry). So far we have

8end 9end
1ore or 1ore
1oney 1oney