DONALD + GERALD = ROBERT

All letters represent distinct numbers 0-9.

1. Given D=5
2. D + D = T Therefore T = 0
3. D+G <=R by given word
4. R <= 9 by definition
5. 5+G <=R by 1 and 3
6. G <=4 by 4 and 5
7. R > 5 by 1 and 3 and 6
8. R is odd because L + L + 1 = R or 1R by word and 1
9. R is 7 or 9 by 7 and 8
10. L = 3 or 4 or 8 or 9 by 9 and 2L+1 = R or 1R
11. N+R > 10 because O+E=O otherwise and E <> 0 (10,000 column)
12. O + E + = O by 11 and 10,000 column the only way this is true is if E = 9
13. R = 7 by 9 and 12
14. A+A = E or 1E or 2A +1 = E or 1E by 100's
15. 2A = 9 or 19 or 2A + 1 = 9 or 19 by 12 and 14.
16. 2A+1 = 9 or 19 by 15 and defn of odd
17. 2A = 8 or 18; A = 4 or 9 can't be 9 by 12 os A = 4
18. 2L+1 = 7 or 17 by 8 and 13.
19. 2L+1 = 17 because 16 had to have a remainder
20. 2L = 16 by 19 therefore L = 8
21. N + R = B (no remainder for sure because A = 4) by 1000's
22. N + 7 = B
23. N>=4 because otherwise O + E = O can not resolve
24. N = 6 by 23 and the fact that it is the only number left >=4
25. B = 3 by 22 and 24.
26. only numbers remaining are 1 and 2
27. 5 + G + 1= 7 by 100,000's and 12 and the fact that O+E=O has to cause a carry becaue E = 9 and O <> 0
28. G = 1 by 27
29. O = 2 because it is the last number left

Lets see if it makes sense.

526,485 + 197,485 = 723,970

Kind of long and drawn out... I just started going and seen where I would end up.