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journal:spring2020:jgleas15:week9

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journal:spring2020:jgleas15:week9 [2020/03/19 23:16]
jgleas15
journal:spring2020:jgleas15:week9 [2020/03/25 21:35] (current)
jgleas15
Line 59: Line 59:
                ====                ====
                1628                1628
 +
 +
 +
 +My puzzle for this week was
 +
 +
 +
 +
 +                 WD
 +            _______
 +      JCDD | WBBDRR
 +            - JCDD
 +              ====
 +              RDGGR
 +             ​-RWKWB
 +              =====
 +               RWKR
 +               
 +               
 +Right away we can see that JCDD x W = JCDD so that means W = 1
 +
 +Next we can look at B - J = R where we know that B is borrowing so B << J and B << R Now that we know this we can look at R - B = R where no borrowing is taking place so B = 0
 +
 +Next we can look at D - W = R where there is no borrowing taking place so R < D Now we can look at D - D = G and R - D = G since R < D then R is borrowing so D must also be borrowing making the equation (D + 8) - D = G so G = 8
 +
 +Next we can look at G - K = W where since we know no borrowing is taking place it is 8 - K = 1 so K = 7
 +
 +Knowing all of this we can look at B - J = R and B - C = D factoring in the borrowing taking place it is (B + 8) - J = R and (B + 8) - C = D so the values available since D > R are J = 3,6 , R = 2,5 and D = 3,6 , C = 2,5 this leaves P = 4
 +
 +To find the remaining values we must look at JCDD x D = RWKWB the 2 possible base 9 equations this could be are 3266 x 6 = 51710 or 6533 x 3 = 21710 if we convert it to base 10 the only values that work is if J = 6, C = 5, R = 2 and D = 3
 +
 +so we have 
 +
 +0 = B
 +
 +1 = W
 +
 +2 = R
 +
 +3 = D
 +
 +4 = P
 +
 +5 = C
 +
 +6 = J
 +
 +7 = K
 +
 +8 = G
 +
 +to verify the values we plug the numbers in and the numbers check out
 +
 +
 +
 +                 13
 +            _______
 +      6533 | 100322
 +            - 6533
 +              ====
 +              23882
 +             ​-21710
 +              =====
 +               2172
 +               
  
  
journal/spring2020/jgleas15/week9.txt · Last modified: 2020/03/25 21:35 by jgleas15