## Substitute digits for the letters to make the following relation true. S T I L L + W I T H I N -------------------- L I M I T S Note that the leftmost letter cant 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?

The value of L must be one more than W i.e. L=W+1 and there must be one carry from S+I=I. Also, the value of S must be 9 as S+I=I with one carry from T+T=M, which means that the value of T must be greater than 4.
From I+H=I, the value of H must be 0 as the value of S is 9.

Now, applying all those constraints and using trial-n-error, we get two possible answers.

9 7 1 6 6 9 8 5 3 3

+ 5 1 7 0 1 3 + 2 5 8 0 5 6
--------------- ---------------
6 1 4 1 7 9 3 5 6 5 8 9

258056
+98533
---------
356589

is wrong as the value of both N and M is 6 here.

I have tried all the combinations and there seems to be only one solution i.e. the first one
517013
+ 97166
----------
614179

The other constraints that i have found while solving the question are :

L cant be 1
N cant be 8
H = 0
T can have only values 6/7/8
and corresponding M is 2/4/6