Logical Reasoning Test

Hey Duders,

I've just finished an aptitude test for a job, the third part of which was a "logical reasoning" psychometric test which involved a series of jumbled grid patterns. I had to try and attempt to complete 12 in 12 minutes, but they did advise most do not finish them all. I've included below an image of the 11th, the hardest of the lot and took me 6 of the allotted 12 alone to complete.

The Rules

Each grid has 9 numbers and/or letters included inside, and either a grey or green dot connected on the outside. The colour dot denotes that those grids follow the same pattern. So in this instance, three of the grids denoted green follow one pattern, while the three grey ones follow another, a different one. The four grids listed below the line must be coloured either grey or green and any could fit into either pattern. The user is tasked to figure out what the pattern linking each grid group is, then applying this to the ones below and figuring out whether they are green, or grey.

It may interest many of you duders just for fun, as to which is which. Anyone fancy giving it a go?

The numbers in green add up to 10 or less, and the numbers in gray add up 11 or more. So left to right it's gray-green-green-gray.

Did I get it right? That's the fastest theory I could spit out so I haven't mulled over it much.

Technically that is correct, @tobbrobb but it is a little too obtuse. From the outset, the test stated there was only one possible, concrete answer and mine were different.

I arrived at the same answer as @tobbrobb. Although I have to say, I take issue with the entire format of the test. Do you mind saying what kind of job you were applying for? Maybe it's different for certain jobs, but I generally hate it when HR gives these kinds of examinations because they often times have absolutely nothing to do with the actual job beyond showing you can do Stupid Human Tricks(TM). If I were in charge the person I would be most likely to hire would be the one with the chutzpah to provide the answer of "This entire test is stupid."

Also, the idea that there is one correct solution is laughable given that it states right on the test that it is one of inductive logic. By definition inductive reasoning is based on probability, which means that you cannot arrive at a solution that you know to be correct - you can only provide the most statistically likely answer given the provided information. If they are looking for a solution that must be true in all circumstances they should be labeling the thing as a deductive reasoning test.

For example, you could just as easily say that a pattern in the images is that the green images all contain only 3 numbers, while the grey images contain 3 or 4 numbers, making the correct solution Grey-Grey/Green-Grey/Green-Grey.

as @lawgamer said, these 'which is the odd one out' / 'what do these have in common' puzzles are always dodgy. They're often an exercise in reading the mind of the person that wrote it.

Anyway, I guess the answer is one group contains letters that correspond to a number on its grid. i.e. Grey, Green, Green, Green.

That's the problem with this "inductive logic," test: he and I both found the same pattern that held true to our answer, yet that specific pattern is not correct. How can a test ask you to spot the pattern if there are multiple patterns to be spotted? There can not be only one concrete answer in this case.

What do you mean by this? If you're saying one group contains at least one letter that corresponds to at least one number (grey), while the other does not (green), then green 2 has "D" that corresponds with 4. If not, then I'm curious as to your pattern.

First, I'd use the phrase "inductive reasoning" or "inductive inference", rather than "inductive logic" or "logical reasoning", logic being commonly understood to concern deduction.

wrt the "how can there be a single correct answer in an inductive reasoning test" hangup, Occam's razor could be the tie-breaker: generally the "simplest" rule matching the samples is the rule most likely to differ the least from the rule which generated the samples. What "simplest" means is pretty foggy unless you pin down a concrete way of representing rules, though.

fwiw, I came up with the same rule as @tobbrobb.

It's always a guess whether the simplest answer is right and the surrounding stuff is done to throw you off, or if you're just missing a bigger pattern that basically tells you the rules to filling in an entire thing like this.

@fnrslvr: Here, this is the simplest answer:

The first group contains these three specific grids. Anything other than those three grids belongs in the other group.

@beachthunder: From an information-theoretic standpoint your answer isn't all that simple. You're basically stating that the rule is

[t(1, 1) = P and t(2, 1) = 2 and t(2, 2) = J and t(3, 1) = L and t(3, 2) = 5 and t(3, 3) = U and t(4, 1) = 3 and t(4, 2) = Z and t(5, 1) = H] or [t(1, 1) = Z and t(2, 1) = J and t(2, 2) = D and t(3, 1) = 4 and t(3, 2) = S and t(3, 3) = 4 and t(4, 1) = T and t(4, 2) = C and t(5, 1) = 1] or [t(1, 1) = S and t(2, 1) = 1 and t(2, 2) = H and t(3, 1) = K and t(3, 2) = K and t(3, 3) = 7 and t(4, 1) = C and t(4, 2) = E and t(5, 1) = 2]

whereas the first answer given in this thread, depending on the representation you allow, can be encoded as

sum_{(i, j) in dom(t), t(i, j) a number} t(i, j) > 10

Mind, depending on what kind of language we allow for representing these rules (think computer programs or logical languages), the spoilered rule here might get to be pretty long. But three green tables and three grey tables is an uncomfortably small amount of data to carry out induction on as well.

Inductive inference (and the job of the natural sciences, for that matter) can be seen as the task of finding the most compressed description of the separations among your data that you can find. In this case, we want the shortest description of the green tables that excludes the grey tables, or vice versa.

@lawgamer: All I can divulge is the position is an Intelligence Analyst for the UK Civil Service. From that, I'd guess that it may be a slight trick and inferring there is merely one answer (when there, in fact, can be many) and the very short time limit is pushing candidates to analyse and judge the sequence merely as quick as possible.

Personally, I'd claim nearly all inductive/psychometric tests are designed not to judge how smart a person is, but in this case, to judge how they eventually came across their answer.

@beachthunder: This was also the answer I formulated initially, but then found the simplest answer you posted yourself, and as such decided to see what other duders would think just out of interest. I'm glad it has sparked such interest.

I like the "Occam's Razor" theory from @fnrslvr in regard to these exercises personally as there could be so many solutions depending upon how the candidate's mind works, they aren't necessarily deduction but designed to make the candidate think fast, and analyse under pressure.

@clintdriftwood wait, what are you saying you came up with as the answer? I came to the same one as @tobbrobb using sum of the numbers

EDIT: good luck with the job!

@tobbrobb: I came to the same conclusion as you after checking a few other things that came to my mind but didn't pan out.

Just the one I came too during the test, it was listed as correct. But if wager many different ones could.be the same. There have already been three suggested on this thread alone.

Cheers duder, appreciate it.

I'd have let myself out.

Green-green-green-gray
My process wasn't at all simple, though, and it took me more than 11 minutes.

I make sure people have the correct ID.