letter puzzle: SEND + MORE = MONEY

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My niece just sent me this problem and it is difficult for me to understand. Please show you work if you are able to help me because I must tell my niece how I got to this answer and show her how to do it. The question is-

The story goes that a young man away at college needed some extra cash. He sent his mother this plea. He wanted her to send the amont indicated by the following sum: SEND + MORE = MONEY Each letter stands for a different digit, 0 through 9. No two letters stand for the same digit. How much money did the young man want.
Thank you so much for your help.
 

Denis

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stapel

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In Need of Math Help said:
SEND + MORE = MONEY
Just use logical guess-n-check. (There is no "formula".)

If you're adding two four-digit numbers and getting a five-digit number, then there must have been a "carry". So what must "M" equal?

If S + M gave a "carry", what values could S possibly be?

And so forth. Work through the various options until you find one that works.

Eliz.
 

TchrWill

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In Need of Math Help said:
My niece just sent me this problem and it is difficult for me to understand. Please show you work if you are able to help me because I must tell my niece how I got to this answer and show her how to do it. The question is-

The story goes that a young man away at college needed some extra cash. He sent his mother this plea. He wanted her to send the amont indicated by the following sum: SEND + MORE = MONEY Each letter stands for a different digit, 0 through 9. No two letters stand for the same digit. How much money did the young man want.
Thank you so much for your help

Method 1

1--M is obviously 1 as the sum of S and N, with, or without, a carryover (c.o.) from E + O cannot possibly equal 20 or more.
2--As for S, S + 1 = 10 + O or S - O = 9 or S + 1 + c.o. = 10 + O or S - O = 9 - c.o..
3--SInce the c.o. can also be no more than 1 from E + O, S - O equals either 8 or 9.
4--S + M can result only in 10 or 11, but 1 is already used, thus, O must be 0 and S = 8 or 9.
5--If S = 8, E must then be 9 making N = 0 which cannot be as O = 0 thus making S = 9.
So where are we?
.......9END
....+ 10RE
-----------------
.....10NEY
6--SInce 9 + 1 = 10, E + 0 = N has no c.o.
7--Since E + 0 = N, there must be a c.o. from N + R making E + 1 = N.
8--To get the c.o. for E + 0, N + R must be greater than 9 or N + R = E + 10 for no c.o. from D + E or N + R = E
+ 9 if there is a c.o.
9--Substiruting N = E + 1 into both expressions for N + R, we have E + 1 + R = E + 10 and E + 1 + R = E + 9.
10--Thus, R = 8 or 9.
11--Since S already = 9, R must be 8 and E + D = 12 or more.
12--The only possibilities for E, D, and N are 5, 6, or 7. Since N = E + 1 and E + D = 12 or more, E = 5, N = 6, D = 7, and Y = 2.

Method 2

1--M must equal 1 since MONEY is the sum of two 4-digit numbers and must be less than 20,000.
2--S must equal 9 and O must equal 0 as S + 1 = 1(O).
3--E + 1 = N because E + 0 = N can't have E = N meaning we have a c.o. from the previous column.
4--R must be 8 since N + R = E requires us to carry a 10 and since E + 1 = N this implies that R = 9. Since S = 9,
R must be 8 and there is a 1 c.o. from the previous column.
5--E must be 5 and N must be 6 because E + 1 = N and D + E = Y forces us to carry a 10. The only numbers left are 2, 3, 4, 5, 6, and 7. Only E = 5, N = 6, D = 7, and Y = 2 is the only solution that satisfies both expressions.
 

Tevinmccartney

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Help

There can be many probabilities like TchrWill explained in this question so, there cannot be a fixed amount for this question. But you can get more information from FinancePolice.com may be.
 
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HallsofIvy

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There can be many probabilities like TchrWill explained in this question so, there cannot be a fixed amount for this question.
??? TchrWill just explained the problem and gave the correct "fixed amount"!
 

Denis

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