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At Least Three Difference (Posted on 2010-08-04) Difficulty: 3 of 5
Place the numbers 1-9 in the boxes so that the difference of each pair of numbers joined by a line is at least three. The number 8 has already been placed.

No Solution Yet Submitted by Brian Smith    
Rating: 5.0000 (1 votes)

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Some Thoughts re(2): solution by reasoning-show me yours | Comment 7 of 13 |
(In reply to re: solution by reasoning by ed bottemiller)


It took me very short time to solve the puzzle while it was on the review board. The reasons I did not rush to post it as soon
as I  saw it published were :

a)I do not like to provide just answers with no explanation .
b) In this case, as in many others, solving was much easier and faster than summing up  the process of finding a qualifying answer.

In a nutshell,- while reading the post I grasped the division of 9 digits into a rich set R(1,2,8,9) and poor set P(3,4,5,6,7).

Member of R have 5 eligible numbers as neighbors,the rest only 4.

Calling the squares asv follows: ABC -upper row;  DEF -mid and GHI low and counting the branches outgoing from each of them - I get H as calling  for a member of the R set, i.e. 1,2, or 9 -8 being placed in A by problem's initial condition. 
Assigning 1 to H, D  could be either 4 or 5.

etc etc

I continue in this way, keeping track of used (spent) links.

This process cannot be called analytical, but is not an "exaustive "
search (checking each of 8! possible permutations) but rather a selective and ordered sequence of trying at each stage to advance with the most likely candidate.

 Once reaching a solution - no need, other than curiosity, to prove uniqueness or look after additional solution.

I  believe that you did not use a blind comprehensive search and since you have forced me to spend 33 minutes to write doen what took 6-7 minutes to solve - i would like you to reciprocate with a short description of your method.

As they say: I've shown you mine , now show me yours.


  Posted by Ady TZIDON on 2010-08-04 23:02:10
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