Title: Letter equations Post by: Exploited 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) Title: Re: Letter equations Post by: Exploited 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 |