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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Analytical Solution (too much information) | Comment 2 of 4 |
`Starting with Clue 8, the cases are`
`HAC12?24?36?38?3?16?29?3`
`Applying Clue 1, we can Rule out 36?.Applying Clue 3, we can Rule out 3?1Leaving us with`
`HAC12?24?38?6?29?3`
`Considering clue 1 next gives us:HACBG12?6?24??148??56?2??9?3??`
`Clue 2 rules out 12?6?Clue 7 rules out 48??5Leaving us withHACBG24??16?2??9?3??`
`Applying Clue 3 next gives usHACBGJF24??1??6?2??0?9?3??1?9?3???1`
`Clue 10 rules out6?2??0?9?3??1?Leaving us with HACBGJF24??1??9?3???1`
`Applying Clue 10 gives usHACBGJF24??10?24??1??9?3??719?3??61`
`Applying Clue 6 gives us the value of A for the last two casesHACBGJF24??10?24??1??953??71953??61`
`Applying Clue 1 gives us the value of G for the last two casesHACBGJF24??10?24??1??953?271953?261`
`Applying Clue 9 gives us possible I & D valuesHACBGJFID24??10?5?24??1??5?953?27148953?26148`
`Clue 5 rules out24??10?5?953?26148and establishes that E must be J-1`
`Applying Clue 5 gives possible E and J valuesHACBGJFIDE24??17?5?624??18?5?724??19?5?8953?271486`
`Clue 2 eliminates24??17?5?624??19?5?8Leaving us withHACBGJFIDE24??18?5?7953?271486`
`Clue 7 determines F in one caseHACBGJFIDE24??1805?7953?271486`
`Clue 3 then rules out24??1805?7Leaving just HACBGJFIDE953?271486`
`Clue 2 (or process of elimination) determines BHACBGJFIDE9530271486`
`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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