Cryptarithmetic problems?

Question

each letter stands for a one -digit number. When decoded,the first line added to the second line will yield the third line. What are the numbers?+

LETS
+WAVE
= LATER

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Answer 1

1567
+ 9085
= 10652

*EDIT*
cssmith below used the 9 for two letters, S and W. If you could repeat digits, then any solution would work.

Steps:
1) The max sum of 2 4-digit nos is 19998
So L = 1

2) If L = 1, W = 8 or 9

3) Now the max sum = 1999 + 9999 = 11998
or 1999 + 8999 = 10998
So A = 0 or 1, but since 1 is taken, A = 0

4) Now if W = 8, the max sum = 1999 + 8099 = 10098
This makes T = 0, but 0 is already taken
So W = 9

5) Now we have
1ETS +
90VE =
10TER
Clearly T = E + 1, with 1 being the carry over from T+V
T+V = 10 + E
or T+V+1 = 10 + E
Substituting T = E+1
V = 8 or 9
But since 9 is taken, V = 8

6) This means there is a carry over of 1 from S + E
ie S+E > 10
Looking at the remaining numbers, 7 and 5 is the only combination that gives a new value for R ( = 2)
And since T > E
S = 7, E = 5, T = 6

This is the only solution involving distinct digits for each letter.

Answer 2

Cryptarithmetic Problems

Answer 3

1552 + 9005 = 10557

Answer 4

1349
+9083
----------
10432