he
solver
of this puzzle will see the
first part of the student's message...
...as hiding the key for decoding the
numbers. He or she might then proceed as follows:
Assumptions:
 Each letter corresponds to a
distinct decimal digit.
 The leftmost digit of each number
is not zero.
If two four digit numbers are added
together to produce a five digit number, the left most
digit of the sum must be 1. Thus, by inspection, M = 1.
The sum S + 1 must be at least 10. There
are two ways for that condition to be met...
 S = 9 or...
 S = 8 AND the additions to
the right produce a carry into the leftmost
position.
To be systematic about the matter, let us
name that leftmost carry digit A and, while we're at
it, we should give names to other possible carries as
indicated.
If A = 0, then S = 9, since M = 1,
then O = 0.
If A = 1 and S = 9, then O = 1 = M. BLAGH!
If A = 1 and S = 8, then O = 0, which
is OK.
So we know that whatever the value of A, O
= 0.
We still don't know if S = 8 or 9.
If B = 0, then N = E. BLAGH!
If B = 1, then N = E + 1, which is OK,
so we know that B = 1.
If A = 1, then E + 1 = 10 and N = 0
= O. BLAGH!
So we know that A = 0, which means S
= 9.
If C = 0, E = N + R  10 (that 10 is
the effect of B = 1).
Since N = E + 1, then E = E + 1 + R 
10, and R = 9 = S. BLAGH!
If C = 1, E = N + R + 1  10, then R =
8, which is OK.
The available digits for D, E, N, Y are
2, 3, 4, 5, 6, 7.
Since N = E + 1, then 2 < N < 8
and 1 < E < 7.
Now, Y = D + E  10 (that 10 is the
effect of C = 1).
 If E = 2, then D = 9 or D = 8.
Either way, BLAGH!
 If E = 3, then D = 7 and Y = 0. BLAGH!
 If E = 4, then D = 6 and Y = 1. BLAGH!
 If E = 5 and D = 5 BLAGH! or
D = 6, then Y = 1 BLAGH!
 If E = 5 and D = 7, then Y = 2,
which is OK.
SEND
+MORE
MONEY

9567
+1085
10652 
...and the keys are...
0
O

1
M

2
Y

5
E

6
N

7
D

8
R

9
S

olvers
are
all set to decode the two messages and discover the
implications.
The Student's Message
20,
1006 10751.
857
751069 0875857 107586 780659!
7001
95519 9006.
60952
7081 7007.

The Mother's Reply
065
9085 70608 9559 15992 8001, 206758.
60 1085
10652 087589 85675857.
90882,
101.

