Abstract reasoning looks like the least learnable EPSO test: a row of figures, a question mark and ten minutes for ten questions. It is in fact the most learnable, because the rules behind the figures come from a short list. Once you know the ten families below, a new series stops being a puzzle and becomes a checklist: which elements are there, and which family is each one following?
A method that works on any series
- Take an inventory. Name every element in frame 1 and its attributes: position, angle, colour, number. Real items usually have two or three elements, each following its own rule.
- Solve one element at a time. Start with the quickest to check, usually a colour or a count. As soon as you have its rule, look at the options and cross out every one that breaks it.
- Let the options tell you where to look. When two options remain, find what differs between them. That difference is where the last rule lives.
- Guess when you are down to two. The AD5 notice sets no penalty for wrong answers, so a guess costs nothing. A clear rule for one element usually halves the options, which is worth a guess if the clock is running out.
For a general introduction to the test, see our abstract reasoning guide. Below, each family has a demonstration strip: five figures and, framed in gold, the one that comes next.
The ten rule families
1. Rotation
The rule. The black arrow turns 90° clockwise at every step; the white arrow turns 45° anticlockwise.
Spot it. Give each element its own clock. Note the angle and the direction for one element, then the other, and never assume they share a rate: two elements turning at different speeds, or in opposite directions, is one of the commonest ways a rotation item is made hard.
The typical wrong option. The option in which both arrows turn the same way. It looks right at a glance because each arrow has moved.
2. Movement with wrap-around
The rule. The dot moves two cells forward in reading order. From the last cell it wraps round to the first row.
Spot it. Number the cells in reading order (1–9, or 1–8 round the edge) and write down the dot’s position in each frame: 1, 3, 5, 7, 9. The step size is then obvious, and so is where it goes after the edge.
The typical wrong option. The option in which the dot stops at the edge or bounces back. Unless an earlier frame shows a bounce, assume the element wraps round.
3. Counting
The rule. One more black dot and one fewer white dot at every step. There are always six dots in total; their positions do not matter.
Spot it. Count each colour separately and write the counts down: 1–5, 2–4, 3–3… A total that stays the same while the elements move about is the giveaway that only the counts matter.
The typical wrong option. The option with the last frame’s counts (five black, one white) in new positions. The movement makes it look like progress; the counts show it is frame 5 again.
4. Colour cycles
The rule. The three colours move one shape to the right at every step; the colour of the triangle wraps round to the circle.
Spot it. Follow one colour, not one shape. The black fill goes triangle → circle → square → triangle: once you have its path, the other two colours follow.
The typical wrong option. The cycle run backwards: an option in which black moves to the left. Both look like “the colours rotate”.
5. Reflection
The rule. The figure is mirrored left-to-right, then top-to-bottom, then left-to-right again, alternating.
Spot it. Pick one small asymmetric detail (the ring at the foot of the pole) and ask where it is relative to the rest. A rotation keeps a figure’s “handedness”; a mirror image reverses it. If you cannot get from one frame to the next by turning the page, it is a reflection.
The typical wrong option. The same figure turned by 90° or 180° instead of mirrored. Rotation and reflection can land the flag in the same corner, but the ring then ends up on the wrong side.
6. Superimposition (adding and subtracting)
The rule. At every step a pair of neighbouring lines is laid over the figure. Where a line is already there it disappears; where there is none it appears. The pair moves 90° clockwise each time.
Spot it. Compare two neighbouring frames and list only what changed: here, always two neighbouring lines. When frames look unrelated, superimposition is the first thing to test: overlay frame 1 on frame 2, cancel what they share, and see what is left.
The typical wrong option. The option that keeps the lines it should remove. Candidates who read “lines are added” and never check for removals pick it.
7. Conditional rules
The rule. The triangle moves one cell clockwise round the edge. Its colour is decided by its row: black in the top row, grey in the middle row, white in the bottom row.
Spot it. When one attribute changes irregularly (black, black, black, grey, white), stop looking for a sequence in it and ask what it depends on: position, another element’s state, or whether the step number is odd or even. The condition is usually visible in the same frame.
The typical wrong option. An option with the colour that continues a guessed colour sequence. There is no colour sequence here, only a condition.
8. Lag and cross-reference
The rule. The big circle takes the colour that the small square had in the previous frame. The small square’s own colours follow no rule.
Spot it. If an element’s changes look random, compare it with the previous frame’s other elements, not with its own history. Write the two colour sequences one above the other and slide one along by a frame.
The typical wrong option. The option in which the circle copies the square of the same frame. It is the natural first guess and exactly one step too early.
9. Pointers and operators
The rule. The arrow is an instruction: the shape it points at changes colour in the next frame. The arrow then turns 90° clockwise. Nothing else changes.
Spot it. When one element points at others, check what happens to its target in the next frame, and confirm that everything it does not point at stays the same. That second check is what saves time: most of the figure is not moving.
The typical wrong option. The option in which every shape has changed colour, or the one where the shape the arrow points at now has already changed.
10. Noise and decoys
The rule. Only the black triangle follows a rule: one corner clockwise per step. The grey dots change number and place at random.
Spot it. After three frames, anything that has changed with no repeatable pattern is probably noise. Check whether the options differ in it: if they do not, ignore it; if they do, the answer cannot depend on it, so eliminate on the other elements first.
The typical wrong option. The option whose grey dots seem to “continue” a pattern you imagined in the noise, while the triangle is in the wrong corner.
Four practice questions
Real items combine families, so these do too. They are hard and very hard on purpose: each one uses a family that stops candidates who only know rotations and colour cycles. The real test allows one minute per question; give yourself up to two here, then open the answer and follow the elimination.
Options:
Show answer
Rule 2. The arrow turns 45° anticlockwise at every step.
Rule 3. The arrow’s colour cycles white → grey → black.
Answer: D.
Element by element. Start with the element that is quickest to check: the colour. White, grey, black, white, grey: the next is black, which rules out E. Then the arrow: up, up-left, left, down-left, down, so it turns 45° anticlockwise and must point down-right. That rules out A, which points down-left. Last, the dot: top-left, middle-right, bottom-left, top-middle, bottom-right. Count the stations between them: three every time, clockwise. Three stations on from bottom-right is middle-left, which rules out B (two stations) and C (three stations the wrong way).
What each wrong option does:
• A — near-miss: the arrow turned 45° clockwise.
• B — wrong magnitude: the dot moved two stations instead of three.
• C — wrong direction: the dot moved three stations anticlockwise.
• E — phase error: the arrow kept the grey of frame 5 instead of moving on to black.
Shortcuts and pitfalls. Counting stations is where time goes. Do it once, between frames 1 and 2, then check it on one more pair; do not re-count all four. And do not let the arrow’s changing colour distract you from its angle: they are separate rules.
Options:
Show answer
Rule 2. The small circle in the corner is an instruction for the next step: black means the arrow turns 90° clockwise, white means it turns 180°.
Rule 3. The circle’s colour in the answer frame decides only frame 7, so it is the same in all five options and does not decide anything.
Answer: B.
Element by element. The dots are the quick win: 1, 2, 3, 4, 5, so the answer has six, which rules out E. The arrow points up, right, down, left, then right again: three 90° clockwise turns, then one 180° turn. A rule that explains only three of the four turns is not the rule, so ask what was different before the 180° turn. The corner circle: it is white in frame 4 and black in every other frame. So black means 90° clockwise and white means 180°. In frame 5 the circle is black, so the arrow turns 90° clockwise, from right to down: B. A turns 180° as if the circle were white, C has not turned, and D turned 90° the wrong way.
What each wrong option does:
• A — a 180° turn, as if the circle in frame 5 were white.
• C — phase error: the arrow has not turned at all.
• D — right amount, wrong direction: 90° anticlockwise.
• E — the arrow is right, but the count of dots has not moved on from frame 5.
Shortcuts and pitfalls. Two traps sit in the timing. The circle acts on the next frame, not its own: the white circle is in frame 4, and the 180° turn happens between frames 4 and 5. And the circle shown in the options is irrelevant: its colour would only decide frame 7. Reading it as an instruction for frame 6 is the same timing mistake.
Options:
Show answer
Rule 2. The hexagon takes the colour the small circle had in the previous frame.
Rule 3. The circle’s own colour follows no rule, so it is the same in all five options.
Answer: E.
Element by element. The circle’s path is simple: top-left, bottom-left, bottom-right, top-right, top-left, so one corner anticlockwise, and next is bottom-left. That rules out C and D. Now the hexagon: white, grey, black, white, white. It starts like a cycle and then breaks it, so it has no rule of its own. The circle’s colours are grey, black, white, white, black; shift them one frame to the right and they match the hexagon from frame 2 onwards. So in frame 6 the hexagon takes the circle’s frame-5 colour: black. That is E. A copies the circle in the same frame, and B copies frame 4.
What each wrong option does:
• A — no lag: the hexagon copies the circle of the same frame.
• B — lag of two frames: the hexagon took the colour from frame 4.
• C — wrong direction: the circle moved clockwise.
• D — the circle has not moved from its corner.
Shortcuts and pitfalls. The tell-tale sign of a lag rule is an element whose sequence looks random while another element shows the same values in the same order. Write the two sequences under each other, slide one along, and the rule appears. Note the half-cycle here: white, grey, black invites you to predict white, grey next. Frame 5 already breaks it, which is your signal to look elsewhere.
Options:
Show answer
Rule 2. The double arrow moves one side clockwise at every step: top, right, bottom, left.
Rule 3. The grey dots in the middle are noise: their number and places are random, and they are the same in all five options.
Answer: A.
Element by element. Set the grey dots aside first: they come and go with no pattern, and the options all share them. The double arrow runs along the top, the right side, the bottom, the left side and the top again, so in frame 6 it is on the right side. That rules out E. Now compare neighbouring frames: exactly two shapes change each time, and they are the two the arrow linked in the frame before, which swap colours. In frame 5 the arrow links the top-left circle (black) and the top-right square (grey), so in frame 6 the circle is grey and the square black, and the bottom two stay white. That is A. B swaps the pair the arrow links in frame 6 instead, C swaps nothing, and D moves every colour one corner clockwise.
What each wrong option does:
• B — wrong timing: it swaps the two shapes the arrow links in frame 6.
• C — the arrow moved, but the two shapes it linked in frame 5 did not swap.
• D — every colour moved one corner clockwise, as if the whole figure had turned.
• E — right colours, but the arrow moved anticlockwise, to the left side.
Shortcuts and pitfalls. The black shape does move one corner clockwise at every step, and many candidates stop there. That description cannot tell you where the grey goes, and D is built for them. An operator rule explains every change at once; if your rule explains only one colour, keep looking.
These questions are written by EU Testing in the EPSO format. They are not official EPSO questions.
What makes an item hard
Busy figures are not what makes an item hard. Sixteen shapes rotating together are often easier than three elements where one of them follows a conditional rule. Difficulty comes from the kind of rule. Rotation, movement, counting and colour cycles are the everyday families. Conditional rules, lag, operators and noise are where the hardest questions come from, and they are also the ones most candidates have never practised. If you only have a few hours, spend them on those four families.
60 figure series at this level
The Abstract Reasoning Focus II card has 60 series built from these families, each with the rules and an element-by-element explanation.
Open Abstract Focus II → First 5 questions free · all 60 with PremiumFrequently asked questions
How many questions are in the EPSO abstract reasoning test?
In the AD5 competition (EPSO/AD/427/26), 10 questions in 10 minutes, scored from 0 to 10. It shares a combined pass mark of 10 out of 20 with the numerical reasoning test.
How many rules does an abstract reasoning item have?
Usually two or three, each applying to a different element or attribute. The rules are nearly always independent, which is why solving one element at a time works.
What should I do if I cannot see the rule?
Solve what you can and eliminate. One clear rule usually removes two or three options. If an element changes with no pattern after three frames, treat it as noise and check whether the options even differ in it.
Are rotation and reflection the same thing?
No. A rotation keeps a figure’s handedness; a reflection reverses it. Pick one asymmetric detail and check which side it is on: if you cannot reach the next figure by turning, it is a mirror image.
Figures drawn by EU Testing for this article, 29 September 2026. Pass marks: EPSO notice of competition EPSO/AD/427/26.