# Apple + Lemon = Banana ;where Each Letter Represents One Digit From 0 To 9?

Clue 1
Assume A and L are the biggest number within 0 - 9 digit
Let A = 9 or 8 and L = 8 or 9
So A + L = 17
Therefore B must be 1

Clue 2
The only reason A + L = A, because L = 9

A + L + 1 = A
therefore P + E > 10

Clue 3
E + N < 10 otherwise L + O = O instead of = N

Clue 4
E > N
Let say E is 2 and N is 4
What number should P is for P(?) + E(2) = N(4)
P should be 12, right? Since each alphabet represents as a digit therefore P should not be 12 so E > N

Proof:
Let say E is 6 and N is 2
P(?) + E(6) = N(2), P can be either 6 or 5 ( If P + M > 10 )

In conclusion
A = {5, 6, 7, 8}, Why?

Proof:
E + N = A , remind E > N

0 is impossible because E(0) + N(0) = A(0)

1 is impossible too because E(1) + N(0) = A(1) and main reason is digit 1 is for B

2 is impossible too because E(2) + N(0) = A(2)

A cannot be 3, 4 and 9 too.

So A = {5, 6, 7 ,8}, E + N = A , remind E > N
if A = 5 means E + N can be either 0 + 5, 5 + 0, 4 + 1, 1 + 4, 2 + 3 or 3 + 2.
E(5) + N(0) = A(5) impossible!
4 + 1 impossible too because digit1 is for B
so left 3 + 2

E(3) + N(2) = A(5)
L(9) + O(?) = N(2) so ? = 3 therefore 3 is repeated in E and O so 3 + 2 is wrong.

Try and error for the following

A = {5, 6, 7 ,8}
A = E + N
5 = 3 +2
6 = 4 + 2
7 = 5 + 2
7 = 4 + 3
8 = 5 + 3
8 = 6 + 2

then you will get the answer!

APPLE + LEMON = BANANA
67794 + 94832 = 162626

By Kc
thanked the writer.