Mystery Number 7
Logic puzzles require you to think. You will have to be logical in your reasoning.
There is a tendigit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?
1) Either A = B / 3 or A = G + 3.
2) Either B = I  4 or B = E + 4.
3) Either C = J + 2 or C = F * 3.
4) Either D = G * 4 or D = E / 3.
5) Either E = J  1 or E = D / 4.
6) Either F = B * 2 or F = A  4.
7) Either G = F + 1 or G = I  3.
8) Either H = A / 2 or H = C * 3.
9) Either I = H + 3 or I = D / 2.
10) Either J = H  2 or J = C * 2.
Answer
5038612947
A = 5, B = 0, C = 3, D = 8, E = 6, F = 1, G = 2, H = 9, I = 4, J = 7
1) A = G + 3 = 2 + 3 = 5.
2) B = I  4 = 4  4 = 0.
3) C = F * 3 = 1 * 3 = 3.
4) D = G * 4 = 2 * 4 = 8.
5) E = J  1 = 7  1 = 6.
6) F = A  4 = 5  4 = 1.
7) G = F + 1 = 1 + 1 = 2.
8) H = C * 3 = 3 * 3 = 9.
9) I = D / 2 = 8 / 2 = 4.
10) J = H  2 = 9  2 = 7.
A) Check each letter for any value that it can not be on the left side of an equation. For example, A can not be 0, as B would also have to be 0 or G would have to be negative. On the first pass through the letters, the following can be determined: A not 0, C not 0, C not 1, D not 0, D not 5, D not 6, D not 7, D not 9, E not 9, F not 7, F not 9, G not 8 (because F not 7), H not 0, H not 5, H not 7, H not 8, I not 0, I not 3 (because H not 0 and D not 6), I not 8 (because H not 5), J not 3 (because H not 5), J not 5 (because H not 7), and J not 9.
B) Make a second pass through the letters. The following can be determined: C not 5, C not 7, D not 3, E not 4, E not 8, and G not 0.
C) Make a third pass. The following can be determined: B not 8.
D) For D, only four numbers are still valid: 1, 2, 4, and 8. Plug each of these numbers into D and check the resulting flow of equations. If D = 1, then the resulting flow will lead to J having to be both 4 and 0. If D = 2, then the resulting flow will lead to 2 also being assigned to G. If D = 4, then the resulting flow will lead to 4 also being assigned to either A or I. If D = 8, then G = 2, F = 1, and A = 5.
E) For E, four numbers are still valid: 0, 3, 6, and 7. Plug each number into E and check the resulting flow. If E = 0, then the flow will lead to J being assigned 1, which has already been assigned to F. If E = 3, then the flow will lead to C being assigned 2, which has already been assigned to G. If E = 7, then the flow will lead to J being assigned 8, which has already been assigned to D. If E = 6, then J = 7, H = 9, and C = 3.
F) The only remaining value for I is 4, which leaves 0 being assigned to B.
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Comments
jhosek
Nov 24, 2010
 I got it. A little tricky but solvable. 
quesadillaman12
Jan 09, 2011
 My brain hurts. 
affanak
May 10, 2011
 Equation 1. A= B/3
From your solution:
B=0, which would imply that A=0 too.
0/3=3 
affanak
May 10, 2011
 Take back my comment (cant delete it) 
galanix
Feb 03, 2012
 Good puzzle. I followed a strategy similar to the one you displayed in the answer but slightly different. After a few passes instead of testing the different values of D I just tested which letter could be 0. At that point I had B,E,F, and J which could possibly be 0. I tried B as zero first and it worked. 
galanix
Feb 03, 2012
 Simplified version of the answer:
A = G + 3 = 5
B = I  4 = 0
C = F * 3 = 3
D = G * 4 = 8
E = J  1 = 6
F = A  4 = 1
G = F + 1 = 2
H = C * 3 = 9
I = D / 2 = 4
J = H  2 = 7 
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