# Letters to Numbers?

#### 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 dont know how to get there.

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#### arildno

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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?

sorry, lost

#### arildno

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aricho said:
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

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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

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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

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VietDao29 said:
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

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aricho said:
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

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arildno said:
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

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VietDao29 said:
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

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

yer, kinda....

#### arildno

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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

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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.

Last edited:

#### aricho

.....................1?

#### arildno

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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

"Letters to Numbers?"

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