# Lab46 Wiki

### Site Tools

journal:spring2020:jgleas15:week9

# Differences

This shows you the differences between two versions of the page.

 journal:spring2020:jgleas15:week9 [2020/03/19 23:16]jgleas15 journal:spring2020:jgleas15:week9 [2020/03/25 21:35] (current)jgleas15 Both sides previous revision Previous revision 2020/03/25 21:35 jgleas15 2020/03/19 23:16 jgleas15 2020/03/19 23:13 jgleas15 2020/03/19 22:38 jgleas15 2020/03/19 17:59 jgleas15 2020/03/19 07:31 external edit 2020/03/25 21:35 jgleas15 2020/03/19 23:16 jgleas15 2020/03/19 23:13 jgleas15 2020/03/19 22:38 jgleas15 2020/03/19 17:59 jgleas15 2020/03/19 07:31 external edit 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 + 