Well, let's start at the left-hand side.
a) The carryover from adding three numbers is 0, 1 or 2.
Thus, D is clearly 1 or 2.
b) Looking at the last column, we observe that E cannot be 0
c) Looking at the first two columns, we see that
2L + D + carryover = 10D + E
Rearranging, L = (9D + E - Carryover)/2
Possibly values are
D E carryover L
-- -- --------- --
2 1 1 9
2 2 2 9 -- no good D and E are the same
1 1 2 4 -- no good D and E are the same
1 1 0 5 -- no good D and E are the same
1 2 1 5
1 3 2 5
1 3 0 6
1 4 1 6
1 5 2 6
1 5 0 7
1 6 1 7
1 7 2 7 -- no good E and L are the same
1 7 0 8
1 8 1 8 -- no good E and L are the same
1 9 2 8
1 9 0 9 -- no good E and L are the same
d) Looking at the last column, we see that O = L - 2E (mod 10)
Possible values are
D E L O
-- -- -- --
2 1 9 7
1 2 5 1 -- no good O and D are the same
1 3 5 9
1 3 6 0
1 4 6 8
1 5 6 6 -- no good O and L are the same
1 5 7 7 -- no good O and L are the same
1 6 7 8
1 7 8 9
1 9 8 7
e) Do the sum mod 9, we determine that
L + 2O +2E + 2V = 0 (mod 9),
ie,
L + 2O +2E + 2V = 0
Possible values are
D E L O V
-- -- -- -- --
2 1 9 7 1 -- no good V and E are the same
1 3 5 9 8
1 3 6 0 3 -- no good V and E are the same
1 4 6 8 3
1 6 7 8 5
1 7 8 9 7 -- no good V and E are the same
1 9 8 7 7 -- no good V and L are the same
f) Looking at the last two columns, we see that
I = 3V + carryover from 2E + O (all mod 10)
Possible values are:
D E L O V I
-- -- -- -- -- --
1 3 5 9 8 5 -- no good I and L are the same
1 4 6 8 3 0
1 6 7 8 5 7 -- no good I and L are the same
So the only solution is
D E L O V I
-- -- -- -- -- --
1 4 6 8 3 0
6034
1438
6834
----
14306