# Solve "SEND+MORE=MONEY" Puzzle

• aricho
In summary, Letters to Numbers?The letters in this problem represent different digits, and the sum of the digits must not be greater than 9999. The sum of the digits in "send" must be less than or equal to 9999+9999=19998. If "m" is different from zero, then "m" must be 1.

#### 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

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

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.

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

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

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?

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,

arildno, yes, got it now.

Whats next?

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!

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?

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,

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..

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

yer, kinda...

What do you mean by "kinda"?

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

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

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:
.....1?

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)

yer....got that

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

## What is the "SEND+MORE=MONEY" puzzle?

The "SEND+MORE=MONEY" puzzle is a mathematical problem that involves assigning digits to letters to create a valid equation. Each letter represents a unique digit, and when solved correctly, the equation should result in a sum of money.

## What is the solution to the "SEND+MORE=MONEY" puzzle?

The solution to the "SEND+MORE=MONEY" puzzle is 9567+1085=10652. In this solution, each letter represents a different digit, with S=9, E=5, N=6, D=7, M=1, O=0, R=8, and Y=2.

## How can the "SEND+MORE=MONEY" puzzle be solved?

The "SEND+MORE=MONEY" puzzle can be solved using algebraic techniques. By assigning variables to each letter and setting up equations based on the puzzle's constraints, the puzzle can be solved systematically until a valid solution is found.

## Are there any other solutions to the "SEND+MORE=MONEY" puzzle?

No, there is only one valid solution to the "SEND+MORE=MONEY" puzzle. This solution is unique because each letter represents a different digit, and no two digits can be the same in the final solution.

## What is the significance of the "SEND+MORE=MONEY" puzzle?

The "SEND+MORE=MONEY" puzzle is significant because it demonstrates the power of mathematical problem-solving and the importance of logical thinking. It is also a classic example used to teach algebraic concepts and critical thinking skills.