Week 3 Problem F

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Week 3 Problem F

Post  Archis on Tue Nov 11, 2008 11:09 pm

Theo made an elaborate code to remember the 10-digit combination to his bicycle lock. This is the code he came up with: A-K-B-J-C-H-D-G-E-F. In his code, each letter stands for a different digit (0-9). To find the combination, use the clues below to figure out what digit is represented by each letter. When two letters are written together without an operation symbol, they represent a tens digit and a ones digit.
D + D + D = F
B / H = K
H + H = B
D x H = CK
G + B + E = F + A + C
A x H = KE
J + A = CC
J / D = K
F x D = KG
D / J = H/B
What is the 10-digit combination to Theo's bicycle lock?

A quick note to problem solvers: I do not write these problems and will post the answers once given to me.
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Re: Week 3 Problem F

Post  AK_Kadaveru on Sat Jan 09, 2010 11:16 pm

Archis wrote:
D + D + D = F
B / H = K
H + H = B
D x H = CK
G + B + E = F + A + C
A x H = KE
J + A = CC
J / D = K
F x D = KG
D / J = H/B

My answer
Spoiler:
5286143709

Explanation:
Spoiler:
since J+A=CC, C has to be one. F has to be 6, or 9 because D+D+D=F. and D can't be one because C is 1. Then D has to be 2, or 3. FxD=KG so KG is either 12 or 27. KG cant be 12 because C is already one so K is 2 and G is 7. Then F is 9 and D is 3. Since J/D=K, J/3=2 so J is 6. DxH is CK so 3xH=12 so H is 4. H+H is B so B is 8. J+A=CC so 6+A=11 so A is 5. AxH=KE so 5x4=2E so E is 0. The Final answer is A-K-B-J-C-H-D-G-E-F or 5286143709

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