Mr and Mrs Tan's only daughter

Observe in the rightmost column that N+A=A. There is no carry over so we can safely conclude from here that N=0. We have $\overline{DARRE0}$ + $\overline{DORRA}$ = $\overline{BRE0DA}$ .

Looking at the third column from the right, we have R+R=N. Since N=0, R must be greater than 0 so we assume R+R=10. There may or may not be carry over from the second right column. If there is, we have 1+R+R=10 which means 2R=9 which is impossible as R must be an integer. Hence there is no carry over which means 2R=10 and R=5. We have $\overline{DA55E0}$ + $\overline{DO55A}$ = $\overline{B5E0DA}$ .

Looking at the second right column which has no carry over, E+5=D. Note that D (same value as E+5) is at most 8 which means E is at most 3. Note that the maximum possible value of D is 8 and not 9 as from the leftmost column, B=D+1 (otherwise B=D) so we already have B at most 9. We have (E, D) = (1, 6), (2, 7), (3, 8). Also, there is carry over from the third right column so looking at the third left column, 1+5+O=6+O= E mod 10. Observe that since E is at most 4, we must have 6+O = 10+E or O=4+E. This carry over will affect the second left column such that 1+A+D=15 so that A+D=14. Note that we use 15 and not 5 as there is a carry over affecting the leftmost column (B=D+1).

If E=1 and D=6, then O=5 resulting in a duplicate (R=5) so (E, D) = (1, 6) is out. If E=2 and D=7, then O=6 but A is also 7. (E, D) = (2, 7) is out too. This leaves us with (E, D) = (3, 8). Therefore, B=9, O=7 and A=6. We have our answer, $\overline{BRENDA}=953086$ .

This was not that hard with permutations from itertools python:

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for d,a,r,e,n,o,b in permutations('0123456789',7):
  if '0' in (d,b):
    continue
  if int(d+a+r+r+e+n)+int(d+o+r+r+a)==int(b+r+e+n+d+a):
    print(b+r+e+n+d+a)

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Solution:
953086