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 |
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+ | My puzzle for this week was | ||

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+ | WD | ||

+ | _______ | ||

+ | JCDD | WBBDRR | ||

+ | - JCDD | ||

+ | ==== | ||

+ | RDGGR | ||

+ | -RWKWB | ||

+ | ===== | ||

+ | RWKR | ||

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+ | Right away we can see that JCDD x W = JCDD so that means W = 1 | ||

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+ | 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 | ||

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+ | 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 | ||

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+ | 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 | ||

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+ | 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 | ||

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+ | 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 | ||

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+ | so we have | ||

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+ | 0 = B | ||

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+ | 1 = W | ||

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+ | 2 = R | ||

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+ | 3 = D | ||

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+ | 4 = P | ||

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+ | 5 = C | ||

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+ | 6 = J | ||

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+ | 7 = K | ||

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+ | 8 = G | ||

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+ | to verify the values we plug the numbers in and the numbers check out | ||

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+ | 13 | ||

+ | _______ | ||

+ | 6533 | 100322 | ||

+ | - 6533 | ||

+ | ==== | ||

+ | 23882 | ||

+ | -21710 | ||

+ | ===== | ||

+ | 2172 | ||

+ | |||

journal/spring2020/jgleas15/week9.txt · Last modified: 2020/03/25 21:35 by jgleas15

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