Question: Substitute digits for the letters to make the following addition problem true.
O N E
N I N E
T W E N T Y
+ F I F T Y
-------------------
E I G H T Y
Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter Y, no other letter can be 3 and all other Y in the puzzle must be 3.
Answer:
G=0, H=1, Y=2, T=3, E=4, I=5, W=6, F=7, N=8, O=9
It is obvious that E = T + 1
Also, 2E + 2Y = Y i.e. 2E + Y must be either 10 or 20 and Y must be an even number. Thus, possible values of (E, Y) pair are (4, 2) (9, 2) (3, 4) (8, 4) (2, 6) (7, 6) (1, 8) (6, 8)
Now, taking each pair individually, only one pair makes the addition true.
O N E 9 8 4
N I N E 8 5 8 4
T W E N T Y 3 6 4 8 3 2
+ F I F T Y + 7 5 7 3 2
------------------- -------------------
E I G H T Y 4 5 0 1 3 2