Rotation Puzzles
Turn the figure and pick what you would see. Or say how far it has already gone. Or spot which one has been flipped over instead of turned — the mistake this whole item type is built to catch. Sixty patterns, with the turn worked out after every attempt.
Also known as rotation of figures and group rotation.
What A Figure Looks Like Turned
A rotation puzzle asks you to turn a whole figure by some amount — usually 90°, 180° or 270° — and pick the result. Nothing is hidden and nothing is inferred: the difficulty is entirely in turning the picture accurately in your head, and in not mistaking a mirrored version for a turned one.
Rotation Is Not Reflection
Everything in this item type comes back to one distinction. A rotation turns the figure on the spot; you could slide a paper cut-out round the table and reach it without ever lifting the paper. A reflection flips the figure over, and no amount of turning will ever get you there.
The property that tells them apart is handedness. Pick two details — the ringed marker and the corner dot, say — and ask which side of one the other sits on. Turning the figure never changes that answer. Flipping it always does. That single test settles almost every question on this page.
Why every figure here carries a marker. A plain regular polygon has a mirror line through each corner, which means its reflection is one of its own rotations — the two are literally indistinguishable. A question built on such a figure would have two right answers. Every figure on this page is checked before it is shown, and only ones with a genuine handedness are used.
| Rotation | Reflection | |
|---|---|---|
| What it preserves | Handedness — the figure is never flipped | Nothing; left and right swap |
| Clockwise features | Stay clockwise | Become anticlockwise |
| How to test it | Follow one marked corner around | Check which side the odd feature sits on |
| The trap | A shape with a mirror line has a reflection that IS one of its rotations | Which would make a reflection distractor secretly correct |
| How this site avoids it | Every figure carries a handedness-breaking feature | And is rejected unless a chirality check confirms it |
Follow One Marked Corner Around
- Follow one detail, not the whole figure. The ringed marker appears exactly once, which makes it the natural thing to track.
- Count in quarter turns first. Get to the nearest 90°, then adjust by 45° if the detail has landed between positions.
- Remember the outline may not help. A square is unchanged by a quarter turn and a hexagon by a sixth of one. When the silhouette looks the same, the details are the only evidence.
- Check handedness last. Once an option has the right angle, confirm it has not also been flipped. This is where most marks are lost.
When A Shape Hides Its Own Rotation
A shape with rotational symmetry maps onto itself, and the outline stops being evidence:
- A square looks identical after every quarter turn.
- A hexagon looks identical after every 60°.
- A triangle looks identical after every 120° — but changes obviously at 45° or 90°.
Several patterns here use exactly those shapes on purpose, because they force the habit that actually generalises: read the details, not the silhouette.
The Four Question Types
- Show the turn — the figure and a stated angle; pick what you would see.
- Which is a rotation — three options have been flipped as well as turned.
- Which is not a rotation — the reverse, and harder, because three genuine turns look reassuringly varied.
- How far has it turned — two pictures and the angle between them.
Why Every Figure Here Is Chiral
A regular polygon with a single marked corner has a mirror line running through that corner — which means its reflection is also one of its rotations. Build a puzzle on a shape like that and the "reflected" wrong answer is secretly right. Every figure used here carries a handedness-breaking feature (an off-centre dot, an uneven number of spokes, an off-axis inner mark) and is rejected unless no mirrored view matches any plain rotation. It is the sort of thing you never notice when it is done and immediately notice when it is not.
Rotation Puzzles Frequently Asked Questions
How do I tell a rotation from a reflection?
By handedness. Pick two details and note which side of one the other sits on. Turning never changes that; flipping always does.
Why does the outline sometimes not help?
Because shapes with rotational symmetry map onto themselves. A square is unchanged by a quarter turn, so only the marker and other details show that anything moved.
Is a 270° clockwise turn the same as 90° anticlockwise?
Yes — they land in the same place. The puzzles here state turns clockwise, but you are free to count whichever way is shorter.
How many puzzles are there?
There is no fixed number. Each puzzle is rebuilt from the short seed in the page address, so the supply is effectively unlimited.
How do I work out how far a figure has turned?
Pick one detail that appears only once — the ringed marker is ideal — and follow it from the first picture to the second. Count round clockwise in quarter turns first, then in eighths if it lands between them. Do not try to hold the whole figure in your head.
Why do some figures look the same after being turned?
A shape with rotational symmetry maps onto itself. A square looks identical after a quarter turn and a hexagon after a sixth of a turn, so the outline tells you nothing. In those questions the answer has to come from a detail such as the marker or a corner dot, which is exactly why every figure here carries one.
Is it free and does it need an account?
It is completely free and there is no account. Nothing is uploaded; your score is kept only in your own browser.
What is rotational symmetry?
A figure has rotational symmetry when turning it lands it back on a picture identical to the one you started with. The order is how many times that happens in a full turn — a square has order 4, an equilateral triangle order 3. It matters here because a figure with rotational symmetry cannot make a fair rotation question: several different turns would give the same picture, so more than one option would be right.