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Author Topic: Letter equations  (Read 4013 times)
Exploited
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« on: October 08, 2007, 11:20:27 am »

Can you solve this:

  DONALD
+GERALD
= -------
  ROBERT

Tell me what is the number "ROBERT" if D=5 (that mans that you must replace D with the number 5 and so on convert all letters to digits)
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« Reply #1 on: October 24, 2007, 09:26:18 am »

Not much interest in that, but here is the soltution:

6th row:
D=5 => 5ONAL5
           GERAL5
          --------
           ROBERT

5+5 = 10 => T = 0
=>       5ONAL5
           GERAL5
          --------
           ROBER0

5th row: L+L (2*L) is even and we have +1 added from 5+5 => R is ODD, because R = 2*L+1 and also R>5.

2nd row: O+E=O, and O cannot be 0, because T is 0 => E=9 AND we have addition +1 from N+R
=>       5ONAL5
           G9RAL5
          --------
           ROB9R0

4th row: E=9=A+A (even) <- impossible => E=9=A+A+1=L+L=> L>5 (in 5th row)
1st row: 5+G+1=R => R>6...AND R is ODD (look back). We know that 9 is taken => the only solution left is R=7 => G=1:
=>       5ONAL5
           197AL5
          --------
           7OB970

5th row: We have 1+L+L AND L>5 (look back) => we must have 1+2*L = 17 (we have 7 in the 5th row) => L=8
=>       5ONA85
           197A85
          --------
           7OB970

4th row: A+A+1 = 9 => A=4

=>       5ON485
           197485
          --------
           7OB970

For O, B and N we have three digits left - 2, 3 and 6. We must have N+7>10 (we must have addition in the second row) => N=6
=>       5O6485
           197485
          --------
           7OB970

3rd row: 10+B=6+7 => B=3
=>       5O6485
           197485
          --------
           7O3970

2nd row: Finally the only option for O is 2
=>       526485
           197485
          --------
           723970

T=0
G=1
O=2
B=3
A=4
D=5
N=6
R=7
L=8
E=9
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