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

Posted by Steve Herman on 2014-06-10 23:57:50