The puzzles in IQ tests, explained
Intelligence tests look very different from one another, but most of them are built from the same handful of puzzle types. Each type was designed to measure one kind of reasoning while depending as little as possible on what you happened to learn at school. This guide goes through the types you'll meet most often, explains what each is measuring, and shows how people who are good at them tend to work. Every example below is a real puzzle of the kind used in the IQ Centre test, and you can open the answer under each one.
In short: most IQ tests mix pattern grids (matrices), number sequences, spatial puzzles such as mental rotation and paper folding, verbal reasoning, and a working memory task. The best general strategy for all of them is the same: find one rule at a time, check it everywhere, and only then look at the answer options.
Pattern grids (matrix reasoning)
A matrix puzzle shows a grid, usually three by three, with the last piece missing. The pieces follow rules along each row (and often down each column too), and you choose the piece that completes the grid. The format is most closely associated with Raven's Progressive Matrices, first published by the British psychologist John C. Raven in 1938, and matrix puzzles now appear in almost every major intelligence test. They're popular with test designers because they need no language and no knowledge, only the ability to spot structure and hold several rules in mind at once.
The rules are almost always one of three kinds:
- Stays the same. Something is constant along a row, such as every shape in the row being a triangle, even if it changes from one row to the next.
- Changes step by step. Something goes up or down by the same amount along the row: one shape, then two, then three; or large, medium, small.
- Three of a kind. Each row contains the same three values in a different order: one black, one grey and one striped shape, for example.
Easy matrices have one rule. Hard ones have three or four rules running at the same time, each on a different feature of the shapes (their number, size, shading, and the shape itself). That is what makes them hard: none of the rules is difficult on its own, but you have to track them all without losing any.
Which piece completes the pattern?
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E. 2 rules work at once. In each row, the number of shapes goes down by one each step; the shapes are grey in one box, empty in another and striped in the third. Each row also keeps the same shape all the way along. Only one piece fits every rule.
How to solve them
- Don't look at the options first. It's tempting, but the options are designed so that each one is almost right. Work out what the missing piece must be, then find it.
- Take one feature at a time. Ask: what happens to the number of shapes along each row? Then the shading. Then the size. Then the shape. Write each rule down if it helps.
- Check every row. A rule only counts if it works in all three rows. Many wrong answers come from a rule that fits the top row but not the others.
- Eliminate. Once you know two features of the answer, most options are gone. In a well-made puzzle every wrong option is wrong in at least one feature, so you can't find the answer by spotting what the options have in common.
Line patterns: laying one square on another
A second family of matrix puzzles uses lines rather than solid shapes. Here the rule usually combines the first two squares in a row to make the third. Sometimes the third square is the first two laid on top of each other. In harder versions, lines that appear in both of the first two squares cancel out, and only the lines that appear in exactly one of them survive. Spotting which version you're looking at is half the puzzle: check a line that appears in both of the first two squares, and see whether it's still there in the third.
Which piece completes the pattern?
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D. In each row, the third square keeps the lines that appear in only one of the first two. Lines that appear in both cancel out.
Number sequences
Number sequence puzzles show a row of numbers and ask what comes next. They measure inductive reasoning, working out a general rule from a few examples, and they use only basic arithmetic, so a calculator wouldn't help. What makes them hard is that the rule isn't always a single step.
The rules you'll meet most often, roughly from easiest to hardest:
| Rule | Example | Next |
|---|---|---|
| Add the same amount | 4, 9, 14, 19 | 24 |
| Multiply by the same amount | 3, 6, 12, 24 | 48 |
| The gap grows by the same amount | 2, 3, 5, 8, 12 | 17 |
| Two sequences taking turns | 1, 20, 3, 18, 5, 16 | 7 |
| Each number is the two before added together | 2, 3, 5, 8, 13 | 21 |
| Two operations in turn | 2, 4, 7, 14, 17 | 34 |
What number comes next?
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F. The gap doubles each time (+4, +8, +16 ...). So the next number is 138.
How to solve them
- Write the gaps underneath. Subtract each number from the next. If the gaps are all equal, you're done. If they grow steadily, look at the gaps between the gaps.
- If the numbers grow fast, try dividing. Doubling or tripling sequences get big quickly; additive ones don't.
- If the sequence zigzags, split it. Look at every other number. Two simple sequences taking turns look chaotic until you separate them.
- Check your rule on every step, not just the last two. A rule that only explains the end of the sequence is usually the trap the wrong options are built around.
Mental rotation
Mental rotation puzzles show a three-dimensional object, often built from cubes, and ask which of several options is the same object seen from a different angle. The classic version comes from a 1971 study by the psychologists Roger Shepard and Jacqueline Metzler, who found that the time people take to decide grows steadily with the angle between the two views, as if people really do turn the object in their heads.
The wrong options are usually mirror images. A mirror image of an object can look identical from many angles, but no amount of turning will make it match, in the same way that a left glove can never be turned into a right glove. That's why these puzzles use objects that are "handed": their mirror image is a genuinely different object.
Which option is the same object as the one shown, just turned around?
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B. Pick a landmark, such as the end of the longest arm, and follow the bends from there. Only the right answer makes the same bends in the same order. One of the others is its mirror image: it matches until one bend goes the other way, and no amount of turning can fix that, just as a left glove never becomes a right glove. The other two have a cube in a different place.
How to solve them
- Find a landmark. Pick the most distinctive part, such as the end of the longest arm or a place where the object bends, and find it in each option.
- Follow the path. From the landmark, trace the object one turn at a time: "three cubes, then turn up, then two cubes, then turn towards me." Compare that sequence of turns with each option.
- Watch the last turn. Mirror images usually match until the final bend, which goes left instead of right. If everything matches except one direction, it's the mirror image.
Paper folding
In a paper folding puzzle, a square of paper is folded one or more times, a hole is punched through all the layers, and you choose what the sheet looks like when it's opened out. It's a classic test of spatial visualisation, the ability to imagine a series of changes to an object, and versions of it have been used in reasoning tests for decades.
The paper is folded as shown, then holes are punched through every layer. What does it look like opened out?
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C. Unfold one step at a time, starting with the last fold. Each hole gets a mirror twin across that fold line, but only where the folded flap was lying under the punch. 2 holes → 4 holes → 6 holes. Here the corner-to-corner fold only covered part of the folded strip, so some holes get no twin from it.
How to solve them
- Unfold in reverse. Undo the last fold first. Every hole gets a twin, reflected across that fold line. Then undo the fold before that, reflecting every hole you now have.
- Count first. Each fold doubles the number of layers, so one hole punched after two folds becomes four holes. Options with the wrong number of holes can be crossed out straight away.
- Diagonal folds swap rows and columns. A hole near the top edge reflects to a hole near the left edge. This is where most mistakes happen.
Verbal reasoning
Verbal reasoning puzzles use words, but the best ones test reasoning rather than vocabulary. Three formats are common.
Analogies take the form "glove is to hand as sock is to …". The skill is naming the exact relationship in the first pair (a glove covers a hand) and applying it to the second (a sock covers a foot). Wrong options are usually words that are associated with the second word in some other way, like "shoe" or "wool".
Odd one out asks which word doesn't belong. The trick is to find the most specific category that fits all but one: violin, cello, harp and guitar are all string instruments; a trumpet is brass.
Deduction gives you statements and asks what must follow. Good tests use made-up words so that what you know about the world can't help or mislead you: "All blems are tarks. Some tarks are green. Which statement must be true?" The answer is only what the statements guarantee. Here, whether any blem is green is not settled, because the green tarks might not be blems.
Because verbal puzzles depend on language, they're less fair to people taking a test in a second language. That's one reason many modern tests lean more heavily on matrices and spatial puzzles.
Working memory
Working memory is the ability to hold a few things in mind and work with them for a short time. Most full IQ tests measure it, usually with a span task: you see or hear a sequence and repeat it back, and the sequences get longer until you can't. Digit span (repeating strings of numbers) is the best known. The block-tapping version, often called the Corsi task after Philip Corsi, who described it in 1972, uses a board of blocks that light up in turn, and you tap them back in the same order.
Most adults can repeat back somewhere between five and seven blocks. Span tasks are useful in an IQ test because working memory supports almost every other kind of reasoning: a matrix with four rules is hard partly because you have to keep four rules in mind at once.
Two habits help: chunk the sequence into small groups rather than remembering single items, and trace the path as a shape rather than remembering individual positions.
How the puzzles are turned into a score
Professional tests don't simply count right answers. Each puzzle has a difficulty, worked out from how thousands of people answered it, and getting a hard puzzle right tells the test more than getting an easy one right. Many modern tests also adapt to you, giving harder puzzles to people who are doing well, so that a short test can still measure accurately at every level. The IQ Centre test works the same way: the second half is chosen from how the first half went, and your score is calculated from which puzzles you got right, not just how many. You can read more about the scale itself in what IQ scores mean.
Try them for real
The IQ Centre test has twenty puzzles of the kinds described here, plus the block-tapping memory game. It takes about 15 minutes.