Respuesta :
Answer:
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.
