Question: Substitute digits for the letters to make the following addition problem true.
I
A G R E E
+ I T S
-------------------
T O U G H
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 S, no other letter can be 3 and all other S in the puzzle must be 3.
Answer:
I=7, A=2, G=9, R=4, E=5, T=3, S=6, O=0, G=9, H=8
It is obvious that T=A+1. Also, G=9, O=0 and R+I>10. Hence, T>1
There must be a carry from the units. Hence E+T=8. So (E, T) can be (6, 2), (5, 3), (3, 5), (2, 6) or (1, 7).
Now, use trial-n-error and solve it.
I 7
A G R E E 2 9 4 5 5
+ I T S + 7 3 6
------------------- -------------------
T O U G H 3 0 1 9 8