Guide
Spatial reasoning, explained
Spatial reasoning is the ability to hold a shape in mind and work with it: turn it, flip it, compare it with another. On an IQ test it usually appears as mental rotation and odd-one-out puzzles. Here is what those puzzles measure, how they are built, and how to approach them.
Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.
What spatial puzzles measure
Spatial reasoning items give you a figure and ask you to transform it mentally. You cannot pick it up and turn it over, so you have to build a mental picture accurate enough to rotate and compare. Like other nonverbal puzzles, they lean on fluid reasoning, working with material you have not seen before (Wikipedia: Fluid and crystallized intelligence), and they add a strong visual component.
On IQ Octopus, the Spatial Reasoning section has 5 puzzles: three mental rotation items and two odd-one-out items. There is a worked example on the Spatial Reasoning practice page.
Mental rotation
You see a target figure, usually an irregular shape made of a few squares with one square marked. Four options follow. One is the target turned by a quarter, a half or three quarters of a turn. The other three are mirror images, also turned, so they look similar at a glance.
The shape is always chiral, meaning it is not the same as its own mirror image, the way a left hand differs from a right hand. That is what makes the puzzle work: no amount of turning in the flat plane turns a left hand into a right hand.
How to solve it
- Find a landmark. Use something unique: the marked square, the longest arm, an odd corner.
- Read around it. Starting at the landmark, list the parts you meet going clockwise around the figure: “marked square, then the long arm, then the short stub”.
- Do the same for each option. Find the landmark, read clockwise.
- Compare the order. A rotation keeps the clockwise order. A mirror image reverses it, so you read the same parts in the opposite direction.
Some people prefer to imagine the turn directly: rotate the target a quarter turn at a time and see whether it lands on an option. That works well for small turns. The landmark method is more reliable for half turns and awkward angles, and it is faster once it becomes a habit.
Try one · Spatial Reasoning
Which option is the same shape, only rotated?
Tap the option you think is right, or show the answer.
Show the answer
Option 4 is the original figure turned a quarter turn clockwise.
How to solve it
- Pick a landmark: the marked cell or the end of the longest arm.
- Turn the figure in your head and watch where that landmark goes, and which side the other cells end up on.
- Turning the figure a quarter turn clockwise gives option 4.
- Each of the other options is a mirror image: flipping it over would match, but no turn does.
That was 1 puzzle. The full test has 25.
Odd one out
You see six figures. Five share a property and one does not. Your job is to find the one that breaks the rule. The hard part is that the shared property is rarely the first thing you notice. The figures may differ in size, angle and position precisely so that those surface differences distract you.
Properties that odd-one-out puzzles commonly use:
- Number of sides or corners. Five figures are pentagons of different shapes; one has six sides.
- Symmetry. Five figures have a line of symmetry; one does not.
- Crossings. Five figures have lines that cross a set number of times; one has a different number.
- Enclosed regions. Count the closed spaces inside each figure.
- Relations. The hardest version: five figures have a dot inside the shape, one has it outside. The property is about how two parts relate, not about either part alone.
How to solve it
- Ignore size, angle and position first. Those are usually there to distract.
- Go through the list above, one property at a time, and count or check it for every figure.
- Stop when exactly one figure differs. If two differ, you have not found the rule yet.
Common mistakes
- Choosing the first match. In rotation puzzles, a mirror image can look right if you check only the outline. Always check the order of parts.
- Turning the wrong way. A quarter turn clockwise and a quarter turn counterclockwise give different results. If you rotate mentally, track the direction.
- Stopping at a surface difference. In odd one out, the figure that looks most different is often a decoy.
Practice and familiarity
Spatial puzzles can feel strange the first time, and familiarity with the format helps. Retaking cognitive tests raises scores by about a quarter of a standard deviation on average (Hausknecht et al., 2007), mostly from knowing what to expect. One worked example is enough to remove the surprise; see the practice page, then read about the related pattern recognition and matrix puzzles, where rotation often appears as one rule among several.
Sources
- Fluid and crystallized intelligence. Wikipedia. en.wikipedia.org/wiki/Fluid_and_crystallized_intelligence
- Hausknecht, J. P., Halpert, J. A., Di Paolo, N. T., & Moriarty Gerrard, M. O. (2007). Journal of Applied Psychology, 92(2), 373-385. doi.org/10.1037/0021-9010.92.2.373