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Integer Illation (Posted on 2014-06-10) Difficulty: 3 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Analytical Solution (too much information) | Comment 2 of 4 |
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
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