**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