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 Integer Illation (Posted on 2014-06-10)
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.

 No Solution Yet Submitted by K Sengupta Rating: 5.0000 (1 votes)

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 A different analytical solution | Comment 3 of 4 |

From clues 3 and 10:

If J = H-2 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 2014-06-11 10:09:57

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