N is a ten digit positive integer having the form ABCDEFGHIJ, where each of the letters represent a different digit from 0 to 9.
Find the value of N, given that:
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.
*** The
or definition is exclusive for each of the ten parts.
From clues 3 and 10:
If J = H2 then C != J+2
If J = C*2 then C != J+2
Therefore, C = F*3.
From clue 6:
If F = B*2 then:
F = 2
B = 1
I = 5
H = 2
This is a contradiction. Therefore, F = A  4.
From clue 8:
If H = A/2 then:
A = 6
F = 2
C = 6
This is a contradiction. Therefore, H = C*3.
We have H = 9F so F = 1, C = 3, and H = 9, and A = 5.
From clues 4 and 5:
If D = G*4 then E != D/4
If D = E/3 then E != D/4
Therefore, E = J  1.
At this point the only letters that can be 0 are B (if I = 4), E (if J = 1) or G (if I = 3). But we know J != 1 and I != 3, therefore B = 0 and I = 4.
It then follows directly from the clues that G = 2, D = 8, J = 7, and E = 6.
Solution: 5038612947

Posted by tomarken
on 20140611 10:09:57 