* * * Hard Math Problem * * *?

Question

Each letter in the problem is a digit. Find each letter's number.

S e n d

+ M o r e

_________________

M o n e y

Answer 1

There are 2 solutions that I worked out, possibly more

  9567

+1085

---------

10652

7429

+0814

-----------

08243

Answer 2

Can some of the letters have the same value?

because I get  "e" = "y"  from the units location.  

I wrote a little program to solve this and got the following list starting with the trivial solution that all digits are equal to zero:

S E N D M O R Y

0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 2 0 0 0 0 0

0 0 3 0 0 0 0 0

0 0 4 0 0 0 0 0

0 0 5 0 0 0 0 0

0 0 6 0 0 0 0 0

0 0 7 0 0 0 0 0

0 0 8 0 0 0 0 0

0 0 9 0 0 0 0 0

8 0 0 9 8 9 1 1

8 0 1 9 8 9 1 1

8 0 2 9 8 9 1 1

8 0 3 9 8 9 1 1

8 0 4 9 8 9 1 1

8 0 5 9 8 9 1 1

8 0 6 9 8 9 1 1

8 0 7 9 8 9 1 1

8 0 8 9 8 9 1 1

8 0 9 9 8 9 1 1

8 0 0 8 8 9 2 2

8 0 1 8 8 9 2 2

8 0 2 8 8 9 2 2

8 0 3 8 8 9 2 2

8 0 4 8 8 9 2 2

8 0 5 8 8 9 2 2

8 0 6 8 8 9 2 2

8 0 7 8 8 9 2 2

8 0 8 8 8 9 2 2

8 0 9 8 8 9 2 2

8 0 0 7 8 9 3 3

8 0 1 7 8 9 3 3

8 0 2 7 8 9 3 3

8 0 3 7 8 9 3 3

8 0 4 7 8 9 3 3

8 0 5 7 8 9 3 3

8 0 6 7 8 9 3 3

8 0 7 7 8 9 3 3

8 0 8 7 8 9 3 3

8 0 9 7 8 9 3 3

8 0 0 6 8 9 4 4

8 0 1 6 8 9 4 4

8 0 2 6 8 9 4 4

8 0 3 6 8 9 4 4

8 0 4 6 8 9 4 4

8 0 5 6 8 9 4 4

8 0 6 6 8 9 4 4

8 0 7 6 8 9 4 4

8 0 8 6 8 9 4 4

8 0 9 6 8 9 4 4

8 0 0 5 8 9 5 5

8 0 1 5 8 9 5 5

8 0 2 5 8 9 5 5

8 0 3 5 8 9 5 5

8 0 4 5 8 9 5 5

8 0 5 5 8 9 5 5

8 0 6 5 8 9 5 5

8 0 7 5 8 9 5 5

8 0 8 5 8 9 5 5

8 0 9 5 8 9 5 5

8 0 0 4 8 9 6 6

8 0 1 4 8 9 6 6

8 0 2 4 8 9 6 6

8 0 3 4 8 9 6 6

8 0 4 4 8 9 6 6

8 0 5 4 8 9 6 6

8 0 6 4 8 9 6 6

8 0 7 4 8 9 6 6

8 0 8 4 8 9 6 6

8 0 9 4 8 9 6 6

8 0 0 3 8 9 7 7

8 0 1 3 8 9 7 7

8 0 2 3 8 9 7 7

8 0 3 3 8 9 7 7

8 0 4 3 8 9 7 7

8 0 5 3 8 9 7 7

8 0 6 3 8 9 7 7

8 0 7 3 8 9 7 7

8 0 8 3 8 9 7 7

8 0 9 3 8 9 7 7

8 0 0 2 8 9 8 8

8 0 1 2 8 9 8 8

8 0 2 2 8 9 8 8

8 0 3 2 8 9 8 8

8 0 4 2 8 9 8 8

8 0 5 2 8 9 8 8

8 0 6 2 8 9 8 8

8 0 7 2 8 9 8 8

8 0 8 2 8 9 8 8

8 0 9 2 8 9 8 8

8 0 0 1 8 9 9 9

8 0 1 1 8 9 9 9

8 0 2 1 8 9 9 9

8 0 3 1 8 9 9 9

8 0 4 1 8 9 9 9

8 0 5 1 8 9 9 9

8 0 6 1 8 9 9 9

8 0 7 1 8 9 9 9

8 0 8 1 8 9 9 9

8 0 9 1 8 9 9 9

8 1 0 1 9 0 0 0

8 1 1 1 9 0 0 0

8 1 2 1 9 0 0 0

8 1 3 1 9 0 0 0

8 1 4 1 9 0 0 0

8 1 5 1 9 0 0 0

8 1 6 1 9 0 0 0

8 1 7 1 9 0 0 0

8 1 8 1 9 0 0 0

8 1 9 1 9 0 0 0

8 1 0 0 9 0 1 1

8 1 1 0 9 0 1 1

8 1 2 0 9 0 1 1

8 1 3 0 9 0 1 1

8 1 4 0 9 0 1 1

8 1 5 0 9 0 1 1

8 1 6 0 9 0 1 1

8 1 7 0 9 0 1 1

8 1 8 0 9 0 1 1

8 1 9 0 9 0 1 1

7 1 0 9 7 9 2 2

7 1 1 9 7 9 2 2

7 1 2 9 7 9 2 2

7 1 3 9 7 9 2 2

7 1 4 9 7 9 2 2

7 1 5 9 7 9 2 2

7 1 6 9 7 9 2 2

7 1 7 9 7 9 2 2

7 1 8 9 7 9 2 2

7 1 9 9 7 9 2 2

7 1 0 8 7 9 3 3

7 1 1 8 7 9 3 3

7 1 2 8 7 9 3 3

7 1 3 8 7 9 3 3

7 1 4 8 7 9 3 3

7 1 5 8 7 9 3 3

7 1 6 8 7 9 3 3

7 1 7 8 7 9 3 3

7 1 8 8 7 9 3 3

7 1 9 8 7 9 3 3

7 1 0 7 7 9 4 4

7 1 1 7 7 9 4 4

7 1 2 7 7 9 4 4

7 1 3 7 7 9 4 4

7 1 4 7 7 9 4 4

7 1 5 7 7 9 4 4

7 1 6 7 7 9 4 4

7 1 7 7 7 9 4 4

7 1 8 7 7 9 4 4

7 1 9 7 7 9 4 4

7 1 0 6 7 9 5 5

7 1 1 6 7 9 5 5

7 1 2 6 7 9 5 5

7 1 3 6 7 9 5 5

7 1 4 6 7 9 5 5

7 1 5 6 7 9 5 5

7 1 6 6 7 9 5 5

7 1 7 6 7 9 5 5

7 1 8 6 7 9 5 5

7 1 9 6 7 9 5 5

7 1 0 5 7 9 6 6

7 1 1 5 7 9 6 6

7 1 2 5 7 9 6 6

7 1 3 5 7 9 6 6

7 1 4 5 7 9 6 6

7 1 5 5 7 9 6 6

7 1 6 5 7 9 6 6

7 1 7 5 7 9 6 6

7 1 8 5 7 9 6 6

7 1 9 5 7 9 6 6

7 1 0 4 7 9 7 7

7 1 1 4 7 9 7 7

7 1 2 4 7 9 7 7

7 1 3 4 7 9 7 7

7 1 4 4 7 9 7 7

7 1 5 4 7 9 7 7

7 1 6 4 7 9 7 7

7 1 7 4 7 9 7 7

7 1 8 4 7 9 7 7

7 1 9 4 7 9 7 7

7 1 0 3 7 9 8 8

7 1 1 3 7 9 8 8

7 1 2 3 7 9 8 8

7 1 3 3 7 9 8 8

7 1 4 3 7 9 8 8

7 1 5 3 7 9 8 8

7 1 6 3 7 9 8 8

7 1 7 3 7 9 8 8

7 1 8 3 7 9 8 8

7 1 9 3 7 9 8 8

7 1 0 2 7 9 9 9

7 1 1 2 7 9 9 9

7 1 2 2 7 9 9 9

7 1 3 2 7 9 9 9

7 1 4 2 7 9 9 9

7 1 5 2 7 9 9 9

7 1 6 2 7 9 9 9

7 1 7 2 7 9 9 9

7 1 8 2 7 9 9 9

7 1 9 2 7 9 9 9

7 2 0 2 8 0 0 0

7 2 1 2 8 0 0 0

7 2 2 2 8 0 0 0

7 2 3 2 8 0 0 0

7 2 4 2 8 0 0 0

7 2 5 2 8 0 0 0

7 2 6 2 8 0 0 0

7 2 7 2 8 0 0 0

7 2 8 2 8 0 0 0

7 2 9 2 8 0 0 0

7 2 0 1 8 0 1 1

7 2 1 1 8 0 1 1

7 2 2 1 8 0 1 1

7 2 3 1 8 0 1 1

7 2 4 1 8 0 1 1

7 2 5 1 8 0 1 1

7 2 6 1 8 0 1 1

7 2 7 1 8 0 1 1

7 2 8 1 8 0 1 1

7 2 9 1 8 0 1 1

7 2 0 0 8 0 2 2

7 2 1 0 8 0 2 2

7 2 2 0 8 0 2 2

7 2 3 0 8 0 2 2

7 2 4 0 8 0 2 2

7 2 5 0 8 0 2 2

7 2 6 0 8 0 2 2

7 2 7 0 8 0 2 2

7 2 8 0 8 0 2 2

7 2 9 0 8 0 2 2

6 2 0 9 6 9 3 3

6 2 1 9 6 9 3 3

6 2 2 9 6 9 3 3

6 2 3 9 6 9 3 3

6 2 4 9 6 9 3 3

6 2 5 9 6 9 3 3

6 2 6 9 6 9 3 3

6 2 7 9 6 9 3 3

6 2 8 9 6 9 3 3

6 2 9 9 6 9 3 3

6 2 0 8 6 9 4 4

6 2 1 8 6 9 4 4

6 2 2 8 6 9 4 4

6 2 3 8 6 9 4 4

6 2 4 8 6 9 4 4

6 2 5 8 6 9 4 4

6 2 6 8 6 9 4 4

6 2 7 8 6 9 4 4

6 2 8 8 6 9 4 4

6 2 9 8 6 9 4 4

6 2 0 7 6 9 5 5

6 2 1 7 6 9 5 5

6 2 2 7 6 9 5 5

6 2 3 7 6 9 5 5

6 2 4 7 6 9 5 5

6 2 5 7 6 9 5 5

6 2 6 7 6 9 5 5

6 2 7 7 6 9 5 5

6 2 8 7 6 9 5 5

6 2 9 7 6 9 5 5

6 2 0 6 6 9 6 6

6 2 1 6 6 9 6 6

6 2 2 6 6 9 6 6

6 2 3 6 6 9 6 6

6 2 4 6 6 9 6 6

6 2 5 6 6 9 6 6

6 2 6 6 6 9 6 6

6 2 7 6 6 9 6 6

6 2 8 6 6 9 6 6

6 2 9 6 6 9 6 6

6 2 0 5 6 9 7 7

6 2 1 5 6 9 7 7

6 2 2 5 6 9 7 7

6 2 3 5 6 9 7 7

6 2 4 5 6 9 7 7

6 2 5 5 6 9 7 7

6 2 6 5 6 9 7 7

6 2 7 5 6 9 7 7

6 2 8 5 6 9 7 7

6 2 9 5 6 9 7 7

6 2 0 4 6 9 8 8

6 2 1 4 6 9 8 8

6 2 2 4 6 9 8 8

6 2 3 4 6 9 8 8

6 2 4 4 6 9 8 8

6 2 5 4 6 9 8 8

6 2 6 4 6 9 8 8

6 2 7 4 6 9 8 8

6 2 8 4 6 9 8 8

6 2 9 4 6 9 8 8

6 2 0 3 6 9 9 9

6 2 1 3 6 9 9 9

6 2 2 3 6 9 9 9

6 2 3 3 6 9 9 9

6 2 4 3 6 9 9 9

6 2 5 3 6 9 9 9

6 2 6 3 6 9 9 9

6 2 7 3 6 9 9 9

6 2 8 3 6 9 9 9

6 2 9 3 6 9 9 9

6 3 0 3 7 0 0 0

6 3 1 3 7 0 0 0

6 3 2 3 7 0 0 0

6 3 3 3 7 0 0 0

6 3 4 3 7 0 0 0

6 3 5 3 7 0 0 0

6 3 6 3 7 0 0 0

6 3 7 3 7 0 0 0

6 3 8 3 7 0 0 0

6 3 9 3 7 0 0 0

6 3 0 2 7 0 1 1

6 3 1 2 7 0 1 1

6 3 2 2 7 0 1 1

6 3 3 2 7 0 1 1

6 3 4 2 7 0 1 1

6 3 5 2 7 0 1 1

6 3 6 2 7 0 1 1

6 3 7 2 7 0 1 1

6 3 8 2 7 0 1 1

6 3 9 2 7 0 1 1

6 3 0 1 7 0 2 2

6 3 1 1 7 0 2 2

6 3 2 1 7 0 2 2

6 3 3 1 7 0 2 2

6 3 4 1 7 0 2 2

6 3 5 1 7 0 2 2

6 3 6 1 7 0 2 2

6 3 7 1 7 0 2 2

6 3 8 1 7 0 2 2

6 3 9 1 7 0 2 2

6 3 0 0 7 0 3 3

6 3 1 0 7 0 3 3

6 3 2 0 7 0 3 3

6 3 3 0 7 0 3 3

6 3 4 0 7 0 3 3

6 3 5 0 7 0 3 3

6 3 6 0 7 0 3 3

6 3 7 0 7 0 3 3

6 3 8 0 7 0 3 3

6 3 9 0 7 0 3 3

5 3 0 9 5 9 4 4

5 3 1 9 5 9 4 4

5 3 2 9 5 9 4 4

5 3 3 9 5 9 4 4

5 3 4 9 5 9 4 4

5 3 5 9 5 9 4 4

5 3 6 9 5 9 4 4

5 3 7 9 5 9 4 4

5 3 8 9 5 9 4 4

5 3 9 9 5 9 4 4

5 3 0 8 5 9 5 5

5 3 1 8 5 9 5 5

5 3 2 8 5 9 5 5

5 3 3 8 5 9 5 5

5 3 4 8 5 9 5 5

5 3 5 8 5 9 5 5

5 3 6 8 5 9 5 5

5 3 7 8 5 9 5 5

5 3 8 8 5 9 5 5

5 3 9 8 5 9 5 5

5 3 0 7 5 9 6 6

5 3 1 7 5 9 6 6

5 3 2 7 5 9 6 6

5 3 3 7 5 9 6 6

5 3 4 7 5 9 6 6

5 3 5 7 5 9 6 6

5 3 6 7 5 9 6 6

5 3 7 7 5 9 6 6

5 3 8 7 5 9 6 6

5 3 9 7 5 9 6 6

5 3 0 6 5 9 7 7

5 3 1 6 5 9 7 7

5 3 2 6 5 9 7 7

5 3 3 6 5 9 7 7

5 3 4 6 5 9 7 7

5 3 5 6 5 9 7 7

5 3 6 6 5 9 7 7

5 3 7 6 5 9 7 7

5 3 8 6 5 9 7 7

5 3 9 6 5 9 7 7

5 3 0 5 5 9 8 8

5 3 1 5 5 9 8 8

5 3 2 5 5 9 8 8

5 3 3 5 5 9 8 8

5 3 4 5 5 9 8 8

5 3 5 5 5 9 8 8

5 3 6 5 5 9 8 8

5 3 7 5 5 9 8 8

5 3 8 5 5 9 8 8

5 3 9 5 5 9 8 8

5 3 0 4 5 9 9 9

5 3 1 4 5 9 9 9

5 3 2 4 5 9 9 9

5 3 3 4 5 9 9 9

5 3 4 4 5 9 9 9

5 3 5 4 5 9 9 9

5 3 6 4 5 9 9 9

5 3 7 4 5 9 9 9

5 3 8 4 5 9 9 9

5 3 9 4 5 9 9 9

5 4 0 4 6 0 0 0

5 4 1 4 6 0 0 0

5 4 2 4 6 0 0 0

5 4 3 4 6 0 0 0

5 4 4 4 6 0 0 0

5 4 5 4 6 0 0 0

5 4 6 4 6 0 0 0

5 4 7 4 6 0 0 0

5 4 8 4 6 0 0 0

5 4 9 4 6 0 0 0

5 4 0 3 6 0 1 1

5 4 1 3 6 0 1 1

5 4 2 3 6 0 1 1

5 4 3 3 6 0 1 1

5 4 4 3 6 0 1 1

5 4 5 3 6 0 1 1

5 4 6 3 6 0 1 1

5 4 7 3 6 0 1 1

5 4 8 3 6 0 1 1

5 4 9 3 6 0 1 1

5 4 0 2 6 0 2 2

5 4 1 2 6 0 2 2

5 4 2 2 6 0 2 2

5 4 3 2 6 0 2 2

5 4 4 2 6 0 2 2

5 4 5 2 6 0 2 2

5 4 6 2 6 0 2 2

5 4 7 2 6 0 2 2

5 4 8 2 6 0 2 2

5 4 9 2 6 0 2 2

5 4 0 1 6 0 3 3

5 4 1 1 6 0 3 3

5 4 2 1 6 0 3 3

5 4 3 1 6 0 3 3

5 4 4 1 6 0 3 3

5 4 5 1 6 0 3 3

5 4 6 1 6 0 3 3

5 4 7 1 6 0 3 3

5 4 8 1 6 0 3 3

5 4 9 1 6 0 3 3

5 4 0 0 6 0 4 4

5 4 1 0 6 0 4 4

5 4 2 0 6 0 4 4

5 4 3 0 6 0 4 4

5 4 4 0 6 0 4 4

5 4 5 0 6 0 4 4

5 4 6 0 6 0 4 4

5 4 7 0 6 0 4 4

5 4 8 0 6 0 4 4

5 4 9 0 6 0 4 4

4 4 0 9 4 9 5 5

4 4 1 9 4 9 5 5

4 4 2 9 4 9 5 5

4 4 3 9 4 9 5 5

4 4 4 9 4 9 5 5

4 4 5 9 4 9 5 5

4 4 6 9 4 9 5 5

4 4 7 9 4 9 5 5

4 4 8 9 4 9 5 5

4 4 9 9 4 9 5 5

4 4 0 8 4 9 6 6

4 4 1 8 4 9 6 6

4 4 2 8 4 9 6 6

4 4 3 8 4 9 6 6

4 4 4 8 4 9 6 6

4 4 5 8 4 9 6 6

4 4 6 8 4 9 6 6

4 4 7 8 4 9 6 6

4 4 8 8 4 9 6 6

4 4 9 8 4 9 6 6

4 4 0 7 4 9 7 7

4 4 1 7 4 9 7 7

4 4 2 7 4 9 7 7

4 4 3 7 4 9 7 7

4 4 4 7 4 9 7 7

4 4 5 7 4 9 7 7

4 4 6 7 4 9 7 7

4 4 7 7 4 9 7 7

4 4 8 7 4 9 7 7

4 4 9 7 4 9 7 7

4 4 0 6 4 9 8 8

4 4 1 6 4 9 8 8

4 4 2 6 4 9 8 8

4 4 3 6 4 9 8 8

4 4 4 6 4 9 8 8

4 4 5 6 4 9 8 8

4 4 6 6 4 9 8 8

4 4 7 6 4 9 8 8

4 4 8 6 4 9 8 8

4 4 9 6 4 9 8 8

4 4 0 5 4 9 9 9

4 4 1 5 4 9 9 9

4 4 2 5 4 9 9 9

4 4 3 5 4 9 9 9

4 4 4 5 4 9 9 9

4 4 5 5 4 9 9 9

4 4 6 5 4 9 9 9

4 4 7 5 4 9 9 9

4 4 8 5 4 9 9 9

4 4 9 5 4 9 9 9

4 5 0 5 5 0 0 0

4 5 1 5 5 0 0 0

4 5 2 5 5 0 0 0

4 5 3 5 5 0 0 0

4 5 4 5 5 0 0 0

4 5 5 5 5 0 0 0

4 5 6 5 5 0 0 0

4 5 7 5 5 0 0 0

4 5 8 5 5 0 0 0

4 5 9 5 5 0 0 0

4 5 0 4 5 0 1 1

4 5 1 4 5 0 1 1

4 5 2 4 5 0 1 1

4 5 3 4 5 0 1 1

4 5 4 4 5 0 1 1

4 5 5 4 5 0 1 1

4 5 6 4 5 0 1 1

4 5 7 4 5 0 1 1

4 5 8 4 5 0 1 1

4 5 9 4 5 0 1 1

4 5 0 3 5 0 2 2

4 5 1 3 5 0 2 2

4 5 2 3 5 0 2 2

4 5 3 3 5 0 2 2

4 5 4 3 5 0 2 2

4 5 5 3 5 0 2 2

4 5 6 3 5 0 2 2

4 5 7 3 5 0 2 2

4 5 8 3 5 0 2 2

4 5 9 3 5 0 2 2

4 5 0 2 5 0 3 3

4 5 1 2 5 0 3 3

4 5 2 2 5 0 3 3

4 5 3 2 5 0 3 3

4 5 4 2 5 0 3 3

4 5 5 2 5 0 3 3

4 5 6 2 5 0 3 3

4 5 7 2 5 0 3 3

4 5 8 2 5 0 3 3

4 5 9 2 5 0 3 3

4 5 0 1 5 0 4 4

4 5 1 1 5 0 4 4

4 5 2 1 5 0 4 4

4 5 3 1 5 0 4 4

4 5 4 1 5 0 4 4

4 5 5 1 5 0 4 4

4 5 6 1 5 0 4 4

4 5 7 1 5 0 4 4

4 5 8 1 5 0 4 4

4 5 9 1 5 0 4 4

4 5 0 0 5 0 5 5

4 5 1 0 5 0 5 5

4 5 2 0 5 0 5 5

4 5 3 0 5 0 5 5

4 5 4 0 5 0 5 5

4 5 5 0 5 0 5 5

4 5 6 0 5 0 5 5

4 5 7 0 5 0 5 5

4 5 8 0 5 0 5 5

4 5 9 0 5 0 5 5

3 5 0 9 3 9 6 6

3 5 1 9 3 9 6 6

3 5 2 9 3 9 6 6

3 5 3 9 3 9 6 6

3 5 4 9 3 9 6 6

3 5 5 9 3 9 6 6

3 5 6 9 3 9 6 6

3 5 7 9 3 9 6 6

3 5 8 9 3 9 6 6

3 5 9 9 3 9 6 6

3 5 0 8 3 9 7 7

3 5 1 8 3 9 7

Answer 3

from some common sense, you know that "M" has to be "1" beacuse there are no two numbers in the thousands that you can add which will make the answer with a 2 in the "ten thousand" place.

then you know that since you have"M" as 1, then "S" will have to be "9" inorder for the number to advance to the next higher digit.....

so keep going with that logic....using trial and errors for the rest of the 3 digits....

since they can't repeat, you only have a couple to try...

but so far, we already know>  M=1, o=0, and S=9.....  go from there

good luck