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Topic: Letter equations (Read 4007 times)
Exploited
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Letter equations
«
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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Philip Petrov - C/C++, PHP, MySQL and others
Exploited
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Re: Letter equations
«
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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Philip Petrov - C/C++, PHP, MySQL and others
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