Glossary
Item difficulty
Definition
Item difficulty is how hard a single test question is. In item response theory it is a number on the same scale as ability: the ability level at which a person has an even, one in two chance of answering the item correctly. Higher values mean harder items.
Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.
Why it matters for IQ scores
A score built from item difficulties can compare people who saw different questions. If you solve an item whose difficulty sits well above average ability, that tells the scoring model more than solving an easy one. This is the core idea behind the Rasch model.
What makes a puzzle harder
In the IQ Octopus puzzles, difficulty mostly comes from structure. A matrix with one rule, such as a shape count that goes up across each row, is easy. One with three rules acting at once, across both rows and columns, is hard. Wrong options that differ from the answer in only one detail, called distractors, also make an item harder. You can see the difference by comparing easy matrix puzzles with hard ones.
How the numbers work
On the test, design difficulties run roughly from -1.5 for the easiest items to +2.0 for the hardest, on the logit scale where average ability sits near 0. As real answers accumulate, those design values can be replaced with fitted ones.
Common confusions
A hard item is not a trick item. Good hard items are fair: every rule is visible and the answer is unique. See theta, the puzzle library and how the test works.
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 2 is the original figure turned a quarter turn counterclockwise.
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 counterclockwise gives option 2.
- 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.