PART ONE
The next few posts in this thread are going to be how to approach a Raven's progressive matrix test, a test to measure IQ. As I mentioned
in another post, I believe that with most of these tests you can work out the solution if you are able to identify the underlying rules.
I've had to divide the entire write-up into separate parts because the forum does not allow more than 8 attachments per post, so I wasn't able to squeeze all the examples into a single post.
It won't necessarily make you a genius overnight but hopefully after reading this you may have a better idea of how to approach a Raven's test and get a higher IQ score than you would have ordinarily gotten.
If you have no idea what a Raven's test is, go to
http://www.iqtest.dk/main.swf and have a look.
For an alternative method to solve Raven's tests, you can go to
http://www.jperla.com/blog/post/how-to-ace-an-iq-test, which also has all the answers for the test at the link above.
(What you can also do is just
buy the Raven's test books and memorise the answers, if you have $1000 US lying around to buy all the different versions.)
There are 2 reasons why you'd want to do well on a Raven's test:
1) Your potential employer may decide to make you write it as a pre-employment test
2) You may want to get into Mensa or a similar high IQ society for networking purposes. For example, if you are moving from city to city, Mensa can arrange a welcoming at your destination so that at least you know someone in your new city. (WARNING: not all Mensa branches use the Raven test.)
Here's a tip: Always claim to be suffering from the flu when writing a Raven's test. Sickness has been shown to drop your score by a few points on these tests and your examiners may decide to add a few points rather than retesting you when you are 'well.'
So how does a Raven's test look like? Basically it's a 3 x 3 sequence of blocks:
|_|_|_|
|_|_|_|
|_|_|_|
And in these blocks are patterns and shapes and things, and the lower right block is left blank. Based on your assessment of the shapes and patterns, you have to guess what the image will be in the lower right block, based on logical rules you deduce by checking out the other blocks.
To make discussion easier, I'm going to assign a letter to each block, like so:
|A|B|C|
|D|E|F|
|G|H|I|
To deduce the missing pattern (block I) you will have to figure out the underlying logic of the pictures. Generally, a specific logic rule runs in the rows or columns.
So a specific rule may apply to ABC and then DEF (the rows), you then apply the same rule to figure out sequence GHI.
Or the rule may apply to columns, so a rule will exist in ADG and BEH, which you then have to extrapolate to CFI.
The easier puzzles will usually have rules that apply both to columns and rows, so you can choose to look at either to solve the puzzle. Harder puzzles however will either use only rows or only columns, and it will be up to you to quickly decide which one has applicable rules of logic.
On some harder puzzles, crossway rules will apply. CEG will follow a rule that you have to then extrapolate to AEI.
So how do you discover the underlying logic in the puzzle? Actually, Raven's tests use only a few puzzle elements and if you approach the test methodically by checking for each potential puzzle element, you should be able to solve the problem without too much thought going into it.
These are the questions you need to ask to identify the puzzle elements:
1) What are the large shapes involved?
2) What are the small shapes involved?
3) What are the symbols involved?
4) What are the lines doing?
5) What are the colours doing?
6) What are the dots doing?
7) In 3x3 within 3x3 problems: Check if the answers lies in the fact that the columns in each 3 x 3 successive matrix shift one column to the right, and in doing so, the shapes change each time according to a logical rule?
8) Can you stack the boxes on each other?
9) Is there a numerical sequence?
Now let's go through each of these questions in detail one by one. I will use various examples that I culled from the net, but especially the online version at:
http://www.iqtest.dk/main.swf While this online version is not actually from the Raven test book, it will give you enough of an idea when faced with the real thing, since many of the online puzzles at that website are just remixed Raven's tests anyway.
What are the large shapes involved?
In general, the third row must always contain the same large shapes as rows 1 and 2, in the same proportion. For easier tests, this usually applies to columns also. For harder tests, it may only apply to rows or only to columns.
Let's start off with a very basic puzzle. Look at this example:
This one is easy. ABC and DEF both have 3 circles. Therefore GHI must also have 3 circles. Therefore I must be a circle in order to complete the sequence.
Note that ADG and BEH also have 3 circles each. Therefore CFI must also have 3 circles, so I needs to be a circle.
Look at the next one. For now,
please ignore the lines, and just look at the circles:
Ignoring the lines, we still know that in I there has to be a circle, for the same reason as the previous example: if the first two rows have 3 circles, then I has to be a circle to follow the rule.
Next example. Ignore the lines and the small circle. Just look at the large shapes (the triangles):
Both ABC and DEF have two triangles pointing up and one down. Note that the same rule applies for ADG and BEH. In order for GHI and CFI to match the other two, then I must be a triangle pointing down in order not to break the pattern.
The last example. Ignore the lines and focus just on the shapes for now:
You'll see that the top two rows and left two columns both contain one square, one triangle and one diamond each. Therefore I must be a square in order not to break the sequence.
My approach to these Raven's test is to always first look at the big shapes (ignoring other elements) and first work out what big shape needs to go into I.
Once the large shape is identified (or if there are no large shapes to work with), the next question to ask is:
What are the small shapes involved?
Much as for large shapes: in general, the third row must always contain the same small shapes as rows 1 and 2, in the same proportion. For easier tests, this usually applies to columns also. For harder tests, it may only apply to rows or only to columns.
Have a look at this example:
We have a sequence of large shapes with smaller shapes within them. The first rule as taught about is to ask 'What are the large shapes involved?' and to figure which large shape will be in I (in this example it will be the square). The next question is 'What are the small shapes involved?' Looking at ABC and DEF, we get a small dark square and a small dark circle in each row. The columns ADG and BEH follow the same pattern. So in order to continue the sequence, GHI and CFI should both only have one small dark circle and one small dark square. However, these conditions are already satisfied, so actually no small shape is required in I. So the final shape in I is simply a large square with nothing in it.
Let's go back to the triangle example from above (we can ignore the lines for now):
We already know that in I we should have an upside down large triangle. But should it have a circle in it? Looking at the rows, we see each row has only one circle; furthermore each column also has only one circle. Putting a circle in I would violate this rule of only one circle so there are no small shapes in I, so no small shape is required in I.
As you can see, for large shapes and small shapes the rules tend to be quiet logical.
Now we start moving on to trickier territory:
What are the symbols involved?
Various symbols may be present, like multipliers, plusses, minuses, division symbols, etc.
Their behaviour can be odd, sometimes they act as ‘rules’, altering the behaviour of things around them
Here's an easy enough example to start off with:
First we can work out that the large shape is a square. Note that the rows and columns are operating with different rules for large shapes. The rows are operating on a 'one-of-each' principle while the columns are 'three-of-a-kind' for large shapes. There are no small shapes, so we can skip that question. The symbols consist of a diamond, a star, and a plus-sign, and follow the inverse rule to the large shapes : the rows are three-of-a-kind, and the columns are one-of-each. In I we get a square with a plus-sign inside of it.
Now let's go on to a puzzle where the symbols start developing weird rules of their own:
There are shapes here, but they at first seem to be doing their own thing. But actually they are being transformed by the symbols. Symbols often have rules which you have to dissect. Consider ADG. The large square suddenly becomes a smaller square. It appears that a plus-sign causes a shape to decrease in size - in other words, ADG can be read as 'Large square in A is diminished in size by the symbol in D, causing a small square to result in G.'
BEH does not have a plus-sign though, it has a diagonal line. Rather than having an effect on size, it appears to have an effect on orientation, causing objects to revolve by 45 degrees. So BEH can be read as 'S-shaped line in B is forced to revolve by diagonal line in E, resulting in an s-shape that has been nudged 45 degrees in H'. Consider also DEF as 'Plus sign in D is forced to revolve by diagonal line in E, resulting in a plus sign that has been nudged 45 degrees in F'.
Look at ABC, the s-line appears to transform shapes without changing shapes or orientation i.e 'The square in A becomes transformed by the s-shape line in B, resulting in a clover shape in C.'
So let's solve for I now. Based on the observations above, we know that: 1) the plus sign causes the top shape to diminish into a smaller bottom
shape 2) the s-shaped lines cause the shape on the left to transform into something different on the right hand side. 3) diagonal lines change orientation
Following the rules and looking at CFI, the large clover needs to be come diminished into a smaller clover in I; likewise looking at GHI, the small square needs to be transformed into a small clover in I; however both the plus sign in F is skew, and now has diagonal lines, so we can assume the small clover changes in orientation. This gives our answer as a small clover with a slight orientation change i.e. answer 'e'
Once you've sorted out the large shapes, small shapes and symbols, the next question to ask is:
"What are the lines doing?"
TO BE CONTINUED.
Circumstances permitting, I'll try to post Part 2 and Part 3 within the next few days.