<html> <p><img src="http://www.jobat.be/uploadedImages/pictures/IQ-homer.jpg" width="250" height="243"/></p> <p>IQ tests can be daunting. They mostly measure your skills in pattern recognition, logical inference, classification and 3D visualisation skills in terms of folding and rotation skills. </p> <h2>Background</h2> <p>Whereas pattern recognition, inference and classification skills are essential elements of our analytical intelligence (even if you’re unaware of it), 3D visualisation skills are a very typical type of skills, which do not fit in the intelligence algorithm as I have described it. It involves the right hemisphere of the brain, which is usually capable of presenting virtual images in your “mind’s eye”. Unfortunately, there are people who suffer from a condition called aphantasia, which makes it impossible to rotate or fold objects in the mind’s eye, because they lack a mind’s eye. Because 3D folding and rotation skills require an extreme comprehensive and almost impossible approach to represent in words, I will leave them out of this series.</p> <p>In this series however, I wish to show you some tips and tricks to tackle typical pattern recognition, logical inference and classification problems which you can encounter in an IQ test. I took some of the examples from http://www.intelligencetest.com. This site however does not systematically explain why a given answer is right, let alone that it provides you with tools to tackle the problems therein. Today's topic will be numbers sequences.</p> <h2>Mathematical Patterns: Number sequence prediction.</h2> <p>IQ tests are fond of number sequences. They give you a few numbers and then ask you to give the missing number. In the sequence 25,24,22,19,15, you might see that in every step you subtract 1 more than in the previous step. Thus there is a progressive decrease of -1,-2,-3,-4 -5. Other number sequences do progressive additions or combinations of additions or subtractions with multiplications or divisions. Any combination of operations is possible. But there is a great trick to tackle all these number sequences, without having to figure out what kind of operations are involved.</p> <p>There are different types of number sequences: polynomial numbers such as triangular numbers, square numbers and cubic numbers, but there are also non-polynomial numbers e.g. Fibonacci type numbers.</p> <h3>Polynomial number sequences</h3> <p> The trick is to look at the differences between the numbers. Sometimes these differences themselves are still a complex pattern and then you must look at the differences between the differences. You do this recursively until you arrive at a constant difference between numbers or at a repetition of the pattern above. You create a kind of inverted pyramid (see figure 1).</p> <p>For instance a third degree polynomial sequence might appear extremely difficult. Let's put it to the test:</p> <p>In the sequence 1,4,10,20,35 what is the next number?</p> <p><img src="http://i67.tinypic.com/t00oyg.jpg"/></p> <p> Figure 1 inverted pyramid for number sequence prediction</p> <p>Now we want to determine the next number. we do this by starting at the lowest level and adding the value of the “differences of differences of differences” ( a 1 in this case, in figure 2 the third 1 in the lowest row) to the last value in the row of the “differences of differences” (this is the 6 in the penultimate row resulting from the 5 plus the 1 from “the differences of differences of differences”). This new value of the “differences of differences” (the 6) is added to the last value in the row of the “differences of numbers”: giving 15+6=21. This new value of the “differences of numbers” (i.e. 21) is added to the last value in the row of the “number sequence” (i.e. 35) to give: 35+21=56.</p> <p>Or visually as indicated by the dashed lines:</p> <p><img src="http://i64.tinypic.com/2vtny3a.jpg"/></p> <h3> Non-polynomial sequences:</h3> <p>There are however also non-polynomial sequences where this does not work this way. For instance the sequence 3,5,8,13,21 yields us a “difference of numbers” pattern of 2,3,5,8,13. After the first number we see a repetition of the original number sequence. Whenever this occurs, you know that it is a sequence which adds combinations of previous numbers. In this case the next number is the sum of the preceding to numbers. So the next number in the sequence is 13+21=34.</p> <p>It becomes more difficult if you do not see an inverted pyramid as above or a Fibonacci like sequence. </p> <p><br></p> <p>But it can be trickier:</p> <p>You can have multiplication or divisions of preceding numbers, and then you do not see a pattern when you use the inverted pyramid technique. For instance the sequence 2,3,6,18,108 multiplies the two preceding numbers, so the next number would be 18*108=1944.</p> <p>Sometimes you have numbers of alternating sequences e.g. 1,2,4,3,10,5,20,8,35, In this example an alternation of the above-mentioned two examples 1,4,10,20,35 and 2,3,5,8. So the next number is the next of the second of these two sequences, which is 5+8=13.</p> <p>The sequence 19,5,17,21,5,14,3,5 has as next number 19 again. Why? Because it is a numerical encoding of the word “sequences”, in which each letter of the alphabet used in the word corresponds with its position in the alphabet.</p> <p>Or take the pattern 4,8,7,5,.. Although it doesn’t make sense at first glance in fact it is the doubling algorithm 4,8,16,32 etc. with an additional <strong>Indig</strong>-rule. An Indig is the sum of the ciphers that make up a number: If the outcome is again a number you continue by adding ciphers until you end up with only a cipher. So the Indig of 16 is 7 and the Indig of 32 is 5. Since the next number in the doubling algorithm is 2*32=64 and the Indig of 64 is 1, the next number in the above mentioned sequence is 1.</p> <p>Don't worry to much about the tricky sequences. The tricky ones usually are <strong>not</strong> asked in IQ tests unless it’s purposefully a heavy one. I am not convinced that they really measure intelligence for people who have never seen such peculiar sequences before in their life. Once you have seen a couple of them, then decoding a sequence can actually become a fun puzzle. It also teaches you smart ways to put information in secret codes. Where do you think all the encryption keys and random number generators come from? They use algorithms employing complex strange codings.</p> <p>So far for today. In a next post I will go into column and row number patterns.</p> <p>If you liked this post please upvote or resteem. by Technovedanta a.ka. Antonin Tuynman</p> <p>Homer Simpson image from http://www.jobat.be/nl/artikels/5-simpele-trucs-om-je-iq-te-verhogen/</p> </html>
| author | technovedanta |
|---|---|
| permlink | how-to-improve-your-score-on-an-iq-test |
| category | iq |
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Cool little post again! I used to "train", actually just had a blast solving the puzzles given to me by MENSA and hit scores that made me wonder whether or not I should actually follow their suggestion and apply to be a permanent member. You are sharing good tricks in there, thanks. Namaste :)
| author | eric-boucher |
|---|---|
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Thanks Eric. I did not know Mensa. Just had a look at their brainteasers. Glad you like solving puzzles. Unfortunately usually I do not have enough time for this type of entertainment. What little time I have left after taking care of my job, my wife and 4 children, meditation, music playing and blogging I spent on writing books. Perhaps something for during a holiday :) Namaste.
| author | technovedanta |
|---|---|
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All of the above does qualify i my mind as major brainteasers! Namaste :)
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|---|---|
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interesting math :)
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|---|---|
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