I think this one works:

The other white element (other than the big one) is the next element that will be the larger one.

This leaves

row 1 , column 2

row 2, column 1

and implies the next big element is a square.

Then the black elements are sequentially the last big element.

Therefore row 2 column 1 and implies a black triangle.

## quick check

figure 1 :

Large object : square

small non-square : triangle

Black object : N/A

figure 2 :

Large object : triangle

small non-triangle : pentagon

Black object : square

figure 3 :

Large object : pentagon

small non-pentagon : triangle

Black object : triangle

figure 4 :

Large object : triangle

small non-triangle : square

Black object : pentagon

Therefore

figure 5 :

Large object : square

small non-square : ?

Black object : triangle

A bit tedious to write and process like this so.

figure X:

large object: *K*

small non-*K* object : **M**

Black object: V

next :

figure X+1:

large object: **M**

small non-**M** object : (you get given this)

Black object: *K*

Out of curiosity, is there a reason you are learning sequences like these?

Also if you want to do these yourself you should look at the properties as a rule of thumb.

For example, here, abstractly you have the properties :

Large object, Shape, count of object of shape, edges, black/not black, position, small object.

You are bound to get questions relevant to these.

Almost indirectly, property arithmetic.

As for why you should look at properties, that is because

If you have an object lets call it L

L:

property V

property P

property N

and object

L+1:

property K

property P

property N

property Q

L itself can be represented by it’s properties, e.g shape,color,texture and what not.

So the fact that it is L or L+1 can fade out entirely for sequences.

Instead that itself can be a property, e.g sequence number.

Why should you do that at all? Simply because this is all the data you are working with.

The solution is definitely using one or some of these bits of data in conjunction. So when you are missing data you are not seeing the properties entirely or not combining them effectively. This is almost a deductive process, so you can definitely ensure you see all properties and exhaustively combine them, but there may be too many if you focus on say ‘being 1 degree off or not’. Therefore it makes sense to do this in a more overview sort of state(layers). In this case looking at position shouldn’t be done first because the position is not very much evenly split. What is immediately appearing to highlight is the: shape,size,black/not. On a subsequent layer maybe the edges or quantities, it is a bit debatable here. However, the rotation would seem a bit less relevant instantly.

As can be seen from my example answer, some of these actually use the previous elements properties to compute some of the next values.

This is actually somewhat important, from a single sample the pattern is something you should only see if it is self-contained in that sample.

If you want a pattern that spans the entire sequence, you need to look at the entire sequence.

Most patterns tend to be literally sequential, if you have A,B,C,D the pattern can be seen by looking at

A and B

B and C

C and D.

Important is that you do indeed look at this pattern. This can also be done somewhat deductively.

For example

In the sequence A,B,C,D

You can hypothesize that the pattern is either self contained in each element

so A on it’s own is sufficient.

Alternatively that the pattern is contained in the sequence from the last element

A and B

B and C

C and D.

The also less likely

That the pattern is a full pattern across all 4 elements

A and B and C and D.

That the pattern is alternative

A and C, B and D.

Since a pattern must be evident, the last 2 cases are unlikely and can be considered afterwards.

Similarly, If you know the pattern is

in

A and B

B and C

C and D.

you actually can extract the pattern also by ‘cross-comparing’ it in the form

A and B to B and C

A and B to C and D

B and C to C and D

etc.

As logically as you can formulate information, your brain is still the one doing the activity. For the brain often there are more efficient processes that are not particularly efficient mechanically.

If you have a minute or 30 seconds to do a question like this, then it makes sense to not explicitly think the way I have demonstrated and instead do this as a collective. For example, looking at these elements will take 5 seconds maximum to notice the basic 2 layers of properties. Within 6 seconds you should be at a point where you can compare or have compared 2 elements. If on the other-hand you did everything explicitly that might be 30-60 seconds without practice.

I haven’t really trained for this sort of thing, but the reason I understand an approach to do these sort of things is due to the abstract structure.

Regarding brain efficiency, this is also common in mathematics. For example the inverse of a 3x3 matrix. If you look at a verbal explanation of this, it can span 2-3 full paragraphs. Yet with the visual explanation, you see maybe 3-5 small images

As with the above and understand how to do it.

When you have concrete objects in a question that uses these objects or their properties, it is significantly easier to solve these problems when you are aware that you have access to all the data that could be used.

When you can effectively isolate properties you can also learn to pay attention to them more directly at a time, which can lead to seeing the answer when you perhaps aren’t really thinking.