letter puzzle: SEND + MORE = MONEY

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Sep 19, 2006
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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.
 
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.
 
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.
 
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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