ShapeDance

What you see

The screen has three parts.

• Reference: a shape made of square cells joined edge to edge, always shown upright. It never moves.
• Candidates: a field of cards, each holding one shape. The field is a 3 by 3 grid of 9 cards at levels 1 to 5 and a 4 by 4 grid of 16 cards from level 6.
• No matches: a button under the board for the trials where no candidate is the reference turned.

The question on screen is short: find every candidate that is the reference turned (up to level 3 it also says how many there are). Click a card to mark it, click again to unmark it. With a keyboard, Tab to a card and press Space; press N for No matches. When you are happy, check your answer. A clock counts up while you work, but there is no deadline.

How a trial is built

Every trial is generated fresh from these rules, taken from the game's code.

• The reference is a connected shape of 6 cells at levels 1 to 3, 7 cells at levels 4 to 7, 8 cells at level 8 and 9 cells at levels 9 and 10. It is always chosen so that it has no rotational symmetry and is different from its own mirror image, so every turn and every flip gives a genuinely different picture.
• Matches are the reference turned by a quarter, a half or three quarters. There are one or two matches at levels 1 and 2 and one to three from level 3. From level 7, some trials have no matches at all: 15% of trials at levels 7 to 9 and 20% at level 10.
• Mirror images are the reference flipped, then turned any of the four ways. They are the lures that need real rotation to reject.
• Altered shapes are the reference with one cell moved to a different place on the outline. At levels 1 to 7 the moved cell lands at least two steps from where it was. At levels 8 to 10 it moves by at most two steps, so the change is small and easy to miss.
• Extra turning. From level 5, every card is also turned by a multiple of 30°, anywhere from 0° to 330°. Shapes stop sitting neatly on the grid and you have to rotate through less familiar angles.
• The cards never animate. The rotation happens in your head, by design.

At levels 1 to 3 the screen tells you how many rotations are hidden in the field. From level 4 it does not, and you have to decide for yourself when you have found them all.

What it measures

ShapeDance feeds the mental rotation facet of the Spatial dimension and carries 34% of that dimension. In the game's own design notes, 70% of what it measures is spatial visualisation and 30% is selective attention, because searching a field of 16 near-identical cards is also an attention task.

Its ancestry is direct. Shepard and Metzler showed that the time needed to match a turned figure rises in a straight line with the angle, at roughly 60° per second, and they used mirror images as the ‘different’ pairs so that only a real rotation could tell them apart. Vandenberg and Kuse turned those figures into the Mental Rotations Test, still the standard research measure. The two-dimensional version is older still: Project TALENT's 1960 test battery included an item type with one drawing and five similar ones, only one of which ‘exactly matches the drawing at the left if you turn it around’, while the rest ‘are backwards even when they are turned around’. ShapeDance keeps that logic and adds a larger field, a variable number of answers and a second kind of lure.

How it is scored here

Each trial is scored from your marks alone.

• When there are matches, your trial score is the number of matches you marked, minus the number of non-matches you marked, divided by the number of matches. It cannot go below zero. Find both of two matches and mark nothing else: 100%. Find both but also mark a mirror: (2 − 1) / 2 = 50%. Find one and mark one wrong card: 0%.
• When there are no matches (levels 7 and above only), the empty answer is the only correct one. Choose No matches and mark nothing for 100%; mark any card and the trial scores zero.
• Correct means perfect: every match, nothing else. A perfect trial moves you up one level. A Partly correct trial holds your level. A trial that scores zero, or is skipped, moves you down one level.

Time counts, but less than accuracy. Your time is compared with an expected time that grows with difficulty, and your trial credit is roughly accuracy to the power 0.75 times speed to the power 0.25. Being much slower than expected can shave about a quarter off a trial's credit; being much faster can add some. A wrong mark costs far more than a few extra seconds.

The trial's difficulty is measured from what you actually faced: the size of the shape, the share of mirror images, the average extra angle and the size of the field. Your ShapeDance score then compares the credit you earned, weighted by that difficulty, with what your difficulty predicts. On our scale, 50 means you performed exactly as expected for the difficulty you work at, and every 10 points is one spread-unit above or below. The score is held towards 50 until you have enough trials for it to mean something.

Your session report also shows three diagnostics: the share of rotated matches you found, mirror confusion (how often you marked cards that were not rotations, relative to the number of mirror images you were shown), and the extra time per degree of turning.

Where you will meet it

Rotation items are among the most common spatial questions in aptitude testing.

• Placement tests. TCS lists visual-spatial reasoning in the NQT Reasoning Ability section. Figure rotation items, where you pick the option that is the given figure turned and reject mirrored ones, are a staple of the visual reasoning topic lists that candidates report.
• GATE. The General Aptitude syllabus names rotation and mirroring under spatial aptitude.
• Employer tests. Criteria's CCAT includes spatial reasoning questions that ask you to rotate or flip images in your head.

ShapeDance is a close cousin of these items, not a copy of any of them. The differences cut in your favour: a multiple-choice rotation item has one right answer, while ShapeDance makes you judge every card, which is harder and makes the test items feel easy by comparison.

The method

1. Study the reference for three seconds

   Before you look at any candidate, pick an anchor (the most distinctive part, such as a long arm or an end cell) and a flag (an asymmetric part next to it: which side of the anchor does it sit on?). Say it in words: ‘long arm down, step to the right at the bottom’.

2. Reject the easy ones by count and outline

   Glance at each card for the obvious misfit: an arm that is clearly too long, a bump where the reference has none. At levels 1 to 7 altered shapes usually have a cell somewhere it plainly does not belong. Leave these unmarked and move on.

3. Turn the anchor the short way

   For each remaining card, find the anchor and ask how far it has turned. A quarter turn one way or the other, or a half turn. Never turn three quarters: that is one quarter the other way.

4. Check the flag's side

   With the anchor aligned in your head, is the flag on the same side as in the reference? Yes: a rotation. No: a mirror. This single check is what separates good scores from average ones.

5. Confirm, then decide the count

   Before marking, check one more part to catch a moved cell. When you have been through the whole field, count your marks; the line under the board says how many you have. At levels 1 to 3, it must equal the number in the question. From level 7, zero is a real possibility: if nothing survives, choose No matches.

Worked example 1: quarter turns only

This is the kind of field you meet at levels 2 to 4. Before opening the solution, decide which of the six cards are the reference turned.

Show the solution

Anchor: the column of three cells. Flag: the single cell sticking out to the left at the top. At the bottom, a cell sticks out to the right with a tail dropping from it.

• Card 1 is a mirror image. The column now runs across; turn it a quarter back and the flag lands on the right of the top, the wrong side.
• Card 2 is a match: the reference turned 180°. The flag that was top left is now bottom right, and the tail that hung down on the right now rises on the left, exactly what a half turn does. At a glance it looks almost like the reference, which is why it deserves a check rather than a quick dismissal.
• Card 3 is altered. It has two columns of three cells; the reference has only one.
• Card 4 is a match, turned a quarter anticlockwise (three quarters clockwise). The column has become a row, the flag hangs below its left end, and the tail rises from its right end.
• Card 5 is the plain mirror image, not turned at all. The flag sits on the right at the top.
• Card 6 is altered: a row of three across the top with a cell hanging from its middle, a T-junction the reference does not have.

Answer: cards 2 and 4. Marking a mirror as well would have cut the trial score to 50%.

Worked example 2: extra angles and near moves

From level 8 the altered shapes change by one small step and every card can sit at any multiple of 30°. This field uses a seven-cell reference.

Show the solution

Anchor: the row of three cells along the bottom. Flag: the 2 by 2 block, which sits above the left end of the row and overhangs it by one cell.

• Card 1 is altered. There is no 2 by 2 block any more; one cell has slid sideways by a single step.
• Card 2 is a mirror image. Turn it back and the block ends up at the right end of the row.
• Card 3 is the match, turned 210° clockwise in all, which is 150° the other way. Turn it back anticlockwise and the block sits above the left end of the row, overhanging it.
• Card 4 is altered. It has a 2 by 2 block, but the block sits over the row instead of overhanging its end, and a cell has moved to the top.
• Card 5 is a mirror image.
• Card 6 is altered: the block has been pulled apart into a column, so again there is no 2 by 2 square.

Answer: card 3 only. At this level the near moves are the main danger: confirm that the block is really a square and really overhangs before you mark.

Tips and traps

Levelling up

Four things get harder as you climb: the field grows from 9 to 16 cards at level 6, the answer can be zero from level 7, the altered shapes become subtle from level 8, and the shapes grow to 9 cells by level 9. The extra 30° turns arrive earlier, at level 5.

Adapt in order. At level 5, practise turning the short way until 150° feels as easy as 90°. At level 6, use a fixed scanning order (row by row) so you never lose your place in 16 cards. At level 7, commit to the empty answer when nothing survives, rather than marking the least bad card. From level 8, add the confirming cell to every check.

1. Week 1
   • Three sessions: anchor and flag on every card, even at low levels
   • After each session, read your mirror confusion figure and note it
2. Week 2
   • Three sessions: turn the short way; say the direction and amount before checking
   • Aim for perfect trials, not speed; perfect trials are what move you up
3. Week 3
   • Three sessions at level 5 or above: practise the 30° angles
   • Use a row-by-row scan and a final count check on every trial
4. Week 4
   • Three sessions at your highest stable level
   • Watch your extra time per degree; it should fall as the short-way habit sets in

Check yourself

5 practice questions

1. A trial has two matches. You mark both, and you also mark one mirror image. What does the trial score?
2. From which level can a ShapeDance trial contain no rotations of the reference at all?
3. A card is the reference turned 270° clockwise. What is the quickest way to check it?

and 2 more

Create a free account to answerSign in

Sources

1. Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171(3972), 701–703. doi.org/10.1126/science.171.3972.701
2. Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47(2), 599–604. doi.org/10.2466/pms.1978.47.2.599
3. Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains. Journal of Educational Psychology, 101(4), 817–835 (Project TALENT test descriptions). PDF
4. Khooshabeh, P., Hegarty, M., & Shipley, T. F. (2013). Individual differences in mental rotation: Piecemeal versus holistic processing. Experimental Psychology, 60(3), 164–171. doi.org/10.1027/1618-3169/a000184
5. TCS iON. National Qualifier Test. tcsion.com
6. GATE 2026, IIT Guwahati. General Aptitude (GA) syllabus. PDF
7. Criteria Corp. What to expect on the CCAT. criteriacorp.com

Put it into practice: ShapeDanceSign in to try it