A father receives a postcard from his son who is away at college. It simply reads
SEND
MORE
MONEY
The father is slightly upset that this is all his son
wrote but noticed something interesting. If each
letter is replaced with a single and unique digit, it
would make a true addition statement. The father
replies that he would send money if his son could
figure out what digit each letter would represent.

S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, Y = 2

Step-by-step explanation:

The given letters are;

SEND

MORE

MONEY

If we are to add the first two words to get the third word, then we have;

SEND + MORE = MONEY

Where, the letters are unique digits

The maximum value of M = 1, because, the two words are in thousands and their sum is in tens of thousands, they can make up to only a 10

Therefore, S = 9

O = 0

D + E = 10 + Y

1 + N + R = 10 + E

1 + E  = N

∴ 1 + N + R = 10 + E gives;

1 + 1 + E + R = 10 + E

R = 10 + E - (1 + 1 + E) = 8

R = 8

We have;

9 XXX + 108X = 10XXX

From 1 + N + R = 10 + E, we have;

1 + N + 8 = 10 + E

END + RE = NEY

E(1 + E)D + 8E = (1 + E)EY

(1 + E)EY - E(1 + E)D = 8E

10 + Y - D = E

By trial and error, we have;

If Y = 2 and D = 3, we have E = 9 which is not unique

Y = 4 and D = 3, we have E = 11 which is a double digit

Y = 2 and D = 7, we have E = 5

∴ N = 6 which is unique

Trying the combination gives;

S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, Y = 2

SEND + MORE = MONEY → 9567 + 1085 = 10652 which is correct.