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.

Starting with Clue 8, the cases are

HAC

12?

24?

36?

38?

3?1

6?2

9?3

Applying Clue 1, we can Rule out 36?.

Applying Clue 3, we can Rule out 3?1

Leaving us with

HAC

12?

24?

38?

6?2

9?3

Considering clue 1 next gives us:

HACBG

12?6?

24??1

48??5

6?2??

9?3??

Clue 2 rules out 12?6?

Clue 7 rules out 48??5

Leaving us with

HACBG

24??1

6?2??

9?3??

Applying Clue 3 next gives us

HACBGJF

24??1??

6?2??0?

9?3??1?

9?3???1

Clue 10 rules out

6?2??0?

9?3??1?

Leaving us with

HACBGJF

24??1??

9?3???1

Applying Clue 10 gives us

HACBGJF

24??10?

24??1??

9?3??71

9?3??61

Applying Clue 6 gives us the value of A for the last two cases

HACBGJF

24??10?

24??1??

953??71

953??61

Applying Clue 1 gives us the value of G for the last two cases

HACBGJF

24??10?

24??1??

953?271

953?261

Applying Clue 9 gives us possible I & D values

HACBGJFID

24??10?5?

24??1??5?

953?27148

953?26148

Clue 5 rules out

24??10?5?

953?26148

and establishes that E must be J-1

Applying Clue 5 gives possible E and J values

HACBGJFIDE

24??17?5?6

24??18?5?7

24??19?5?8

953?271486

Clue 2 eliminates

24??17?5?6

24??19?5?8

Leaving us with

HACBGJFIDE

24??18?5?7

953?271486

Clue 7 determines F in one case

HACBGJFIDE

24??1805?7

953?271486

Clue 3 then rules out

24??1805?7

Leaving just

HACBGJFIDE

953?271486

Clue 2 (or process of elimination) determines B

HACBGJFIDE

9530271486

Final Answer:

ABCDEFGHIJ =

5038612947

I notice that I never used clue 4, and that I never used the "exclusivity" of the OR.

However, this solution is consistent with both