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I encountered a pattern recognition problem as described in the following picture.

What's the odd one out in the following patterns?

My choice would be B. My rationale is based on the logic of grouping and elimination.

First, I grouped the patterns into three groups, namely, the group of one dot (Group A), the group of two dots (Group B) and the group of four dots (Group C).

Secondly, I observed that Group A and Group C are valid, so they're eliminated from the "Odd Group".

Thirdly, in Group B, there are two subgroups: one subgroup (Group B1) (Grids 1 & 3) contain two dots, one of which is solid. The other subgroup (Group B2) (Grids 5, 7 and 9) contain two dots, both of which are empty. Since the patterns (Grids 1 & 3) in Group B1 seems to have similarity to patterns (Grids 2 & 4) in Group C, they're eliminated. That means Answer A is eliminated. Now in Group B1 (Grids 5, 7 and 9), the patterns in Grid 7 and 9 are pointing to the similar direction while Grid 5 is pointing to a different direction. That's why I singled out Gird 5 as the odd one out. Hence, the answer B. How about other ways of considering this logical problem?

Thank you very much for your participation and help.

I'd like to say I agree with the opinion by KingW3 that the answer to this question is open to different views. There might not be a definite answer. But I also believe that if there are different answers based on different opinions, those opinions should have a basis that is rational from a certain perspective, e.g., mathematical, logical. So, I welcome different interpretations to this same problem to how people will think of the odd one out among the nine. Thanks again for whatever perspective you contribute.

Michael May
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  • Why not $A$ is the odd one out because $B$ and $C$ are the same? There is no proof that you can give to assure your answer is correct so this question cannot be answered with a mathematical approach. – Peter Foreman Aug 06 '19 at 10:42
  • Thanks for your comment. Actually, I'm not sure my answer is valid. So, I'd like to invite you and other people to discuss this matter to see whether there will be a rational answer to this problem. – Michael May Aug 06 '19 at 10:46
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    Why would any rational answer be better than another? One could rationally argue any solution is correct as there is no 'correct' way to pattern match data. – Peter Foreman Aug 06 '19 at 10:47
  • Thanks again. It may be true that there might not be any real rational answer to this question. But I'd like to invite more people to this discussion to see more alternative views. It can be a good chance to see a wide range of different thoughts on the same problem. – Michael May Aug 06 '19 at 11:16
  • I'd say $6$ is the odd one out. – kingW3 Aug 06 '19 at 11:52
  • My answer was the same as @kingW3 .. cell 6 is the only one with an odd number of items in it. – GEdgar Aug 06 '19 at 12:01

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