What comes next in this sequence?

January 2, 2009 2:07 AM

IQ tests among others usually have questions that contain a sequence of shapes or numbers with the question asking what the next shape or number in the sequence will be.

Something like this or this. I don't think I've ever answered one of these questions correctly. I stare at the thing and know that I'm supposed to find some sort of pattern but I don't even know how to start. What are these questions testing and am I some sort of weirdo because I don't understand any of it?

posted by @homer to education (12 comments total)

It's basically testing the ability abstract rules from instances of the rules' application.

And, I wouldn't say you're a weirdo. I consider myself quite bright, very good at analytical reasoning, very good at abstraction (I'm a programmer), I've tested high 140's on the last two professionally-administered IQ tests I've taken, and I do just terribly at these things. I do a little better with arithmetic/geometric sequences, but not much. Mostly, I think, because they don't attract my attention... I mostly look at them and think, "There's probably a pattern here, but finding it doesn't help me, and it's tedious." That thought then blocks any chance I might have to answer the question.

Every one of my IQ testers has looked at me funny when I told them I had no idea and they should go on, like "Dude, you found all the differences between those pictures, and you can't figure out it's a yellow circle inside a blue square? Duh."

Which is one of the many reasons I think IQ tests are bogus.
posted by Netzapper at 2:34 AM on January 2 [1 favorite has favorites]

I can't link to current papers, thoughts or research on the subject, but "intelligence" tests have always been rather fraught, and my understanding is that they really do not test any sort of innate intelligence or potential. Test scores generally vary wildly, and you can also learn how to take any sort of test better.

These pattern recognition tests you have problems with were probably developed to be "universal" so that culture and language, etc., would not interfere with the assessment, which is one of the biggest criticisms of intelligence tests. Of course these types of questions aren't "universal," but they are learnable.

In the first link, for example, you have two basic options: color and shape. If you look at each row and column, you see that the outer color does not repeat. So the missing space is likely intended to have an out color that is red. If the outer layer was colored blue or yellow, that color would have been repeated in its row and column, which would break the pattern.

When you look at the shapes, you see that there are three options, and again, they do not repeat. The last row and column have squares and circles already, meaning the missing space likely contains two triangles.

The middle colors also do not repeat, and there are only three options, so the middle color in the last shape is the one that is missing from the middle in that column and row: blue.

Now that you have been walked through it, you can work out what the center color is on your own, right? And I bet that if you take the same process (identify what the variables are, and work out whether any are linked, and if so, to what) to the second link you posted, you can work out that question on your own.

If you try it and you can, you can thank me for increasing your "intelligence" by five points. If not, don't sweat it. You're not weird. The tests are awkward and limited.
posted by Nonce at 2:35 AM on January 2

The way I solve these is to try and break them down into parts. They're looking for visual pattern recognition, and the ability to break a problem down I think.

Take the first one, for example. There's two patterns; the colours, and the shapes. I looked for the shapes first, and saw that the shapes appear to follow the diagonal, top left to bottom right. I conclude the bottom right spot will be a triangle.

Next, the colours, using both the two circles and the two squares as the source, given they both follow the same pattern on the diagonal. In both cases, going top left to bottom right diagonally, the colour sequence goes 'inwards' with the innermost colour going to the outside.

Looking at the triangle diagonal line, and following the same colour pattern, I conclude the missing square is a triangle with red, blue and yellow colours going inwards.
posted by ArkhanJG at 2:39 AM on January 2

Hah, and after posting, you can see there are two entirely different ways of seeing and solving the first problem, and both come to the same answer.
posted by ArkhanJG at 2:42 AM on January 2 [1 favorite has favorites]

I've always looked at these things as a "what's missing?" rather than "what's next?" That is to say, examine each row or column and see what's missing from each one, rather than looking at the squares as a sequence.

So in your first example:

In each row and column there is a triangle, a square, and a circle - which is missing from the last row / column? Looks like the triangle.

In each row and column there is a yellow background, a red background, and a blue background. If the last square has a red background that follows the rule.

Likewise for the 2 colours of the shape - each row and column has a blue outer, red outer, and yellow outer; and blue inner, red inner, and yellow inner. From the last row / column is missing a blue outer, yellow inner.

So the last square has a red background, and is a blue outer triangle with a yellow inner triangle.
posted by Dali Atomicus at 2:43 AM on January 2

The form of these puzzles was supposed to be universally easy/hard to solve, but then someone went and invented Sudoku, and suddenly I have a huge advantage because I can see the underlying pattern instantly, and the mental machinery to manipulate that system is highly practised.

So now it's merely a test of whether you've played Sudoku before or not. I suspect the next iteration of IQ tests will change the form of that puzzle.
posted by -harlequin- at 4:54 AM on January 2

I'm really good at these usually and I would approach the two problems you linked to exactly like how Dali Atomicus explained. To me, it's a question of what's missing.

If the question was a number or letter pattern, eg. which comes next in the series, I would approach the question by first looking at the relationship between the items in the pattern and then try to figure it out from there. Sometimes they will give you a series based on a commonly known pattern, like the Fibonacci Sequence, or the numbers are all primes, or factorials, and being familiar with how they look will make you better at those.

-harelquin- also brings up a good point. The logic of a lot of common types of standardized IQ test questions like this can be practiced.

If you want to do better at those pattern recognition questions, you could probably go to Barnes and Noble and pick up a book of them and do a few of them a day, starting with the easy ones, and working up to the hard ones, and you would most likely improve.

My daughter started doing pattern completion math problems in kindergarten last year, and this year they're doing slightly harder patterns. They started with something very easy like two different colored blocks alternating (red, green, red, green, etc.) and would have to color the next one in the series. Now they have more complex patterns to complete and are starting some simple ones with numbers in them.

If you're completely hopeless at them and you want to get better, maybe check the kids' section for workbooks with really simple puzzles. That probably sounds a bit silly, but you can definitely improve your ability at recognizing patterns.
posted by howrobotsaremade at 7:18 AM on January 2

Incoming derail...

I can't link to current papers, thoughts or research on the subject, but "intelligence" tests have always been rather fraught, and my understanding is that they really do not test any sort of innate intelligence or potential. Test scores generally vary wildly, and you can also learn how to take any sort of test better.

Your understanding is wrong. Test scores are generally very stable between tests and within tests--.90 or higher--even with years between tests, barring brain or neurological damage. Measuring "innate" intelligence is not really the intention--the key goal of IQ tests are to measure aptitude for real world learning. A person who works very hard at learning something can match the performance of a slacker with a higher IQ. Think of IQ as a measure of ease with which one can learn relative to others, not a be-all-end-all tests of raw computation and cognition.

As for doing much worse in one area and thus IQ tests being bunk, that's not a flaw of the tests. It means that the area you are performing poorly in is more difficult for you relative to other areas. Matrix completion tests rely on a number of skills, so even if you're an excellent computer programmer, maybe your spatial reasoning is relatively weak. There's nothing wrong with that. My digit span scores were/are always much lower than anything else on my tests, and anyone who knows me will tell me my short term memory is a little fritzy when it comes to phone numbers. Doesn't mean I'm screwed over at math (I'm good at math!), but phone numbers evaporate from my mind and a pencil and sheet of paper are vital to me.

And yes, these skills are learnable. That's the point! Let's say you spend a few weeks playing Sudoku before your next IQ tests, and perform better at abstract reasoning than before. You know how I mentioned a dedicated worker could match the performance of a slacker with a higher IQ? Well, by teaching yourself those skills, you have raised your IQ. What you've taught yourself to do won't abandon you, and it will actually be easier for you to learn new skills in that area, which is what IQ tests are intended to measure. Ever see someone progress from the easy to expert Sudoku books? They're getting better at that skill, and better performance SHOULD be reflected in objective tests.
posted by Benjy at 9:07 AM on January 2

it's weird... these two puzzles actually have the exact same over-all pattern, but the second one is much harder than the first. I grasped the first one intuitively as soon as I saw it, but it took noticing the diagonal pattern in the second one (which is the same as the first) to see the second one's overall pattern. In the first one, the colour progression is very clear, but in the second one the triangles' relationship to the circles is more difficult to work out. But once I noticed the diagonal pattern, I noticed that the colour of the the triangles is not linked to the circles (each patterned circle has its specific colours of triangles), but the placement of the triangles has to be different from each circle. (Describing this is twisty)

Overall, the strategy for approaching these puzzles is to try to break the pictures into elements (shape, colour, placement) and then find some pattern to the smaller element, which can in turn be linked to other elemental patterns.

I'm also with Netzapper. I think whether or not one does well on these has a lot to do with whether they grab your attention, and not so much to do with some abstract concept of intelligence.
posted by carmen at 10:10 AM on January 2

Thanks everyone. I just might be able to get these things figured out!
posted by @homer at 10:39 AM on January 2

These problems are pretty damn near identical.
What are the chances of that, huh?

Anyway if you picked these because they both had you stumped...
:) not everything is left to right, straight up and down.

Sometimes you'll find all the things you need to know will lie diagonally.
posted by mu~ha~ha~ha~har at 12:01 PM on January 2

this:
Your understanding is wrong. Test scores are generally very stable between tests and within tests--.90 or higher--even with years between tests, barring brain or neurological damage.
and this:
And yes, these skills are learnable. That's the point! Let's say you spend a few weeks playing Sudoku before your next IQ tests, and perform better at abstract reasoning than before. You know how I mentioned a dedicated worker could match the performance of a slacker with a higher IQ? Well, by teaching yourself those skills, you have raised your IQ. What you've taught yourself to do won't abandon you, and it will actually be easier for you to learn new skills in that area, which is what IQ tests are intended to measure.

Seem like they are saying very different things. And the first statement, for whatever parameters it is a correct statement, indicated the tests are precise--that does not mean they are accurate, or that they in fact are actually measuring what they think they're measuring with any sort of a) certainty and b) cultural neutrality.
posted by Nonce at 1:18 PM on January 2