Last reviewed 22 Sept 2026 · 5 min read
Look for six things, in this order
Any change between two figures is one or more of:
- Rotation — the whole figure turns, usually , or , clockwise or anticlockwise.
- Reflection — the figure is flipped about a line; a rotation can never turn a shape into its mirror image.
- Movement — one element moves a fixed number of positions round the figure each step.
- Addition or removal — a line, dot or arm appears or disappears.
- Shading — a shaded part moves, swaps with an unshaded one, or spreads.
- Counting — the number of sides, dots or lines increases or decreases by a fixed amount.
Say the change in one sentence — "the arrow turns 90° clockwise and the dot moves one corner anticlockwise" — before you look at the options. A described rule can be applied; an unspoken impression cannot.
Figure series
Four or five figures follow a rule; the next one is asked for. Two habits make this quick:
- Track one element at a time. Follow only the dot through all the figures, then only the arrow. A rule that applies to two elements at once is really two simple rules.
- Use the step count. If a shape moves two positions each time round an eight-position frame, it returns to its start after four steps — which often identifies the answer without drawing.
Figure analogy
Figure A becomes B in some way; apply the same change to C. The change is described exactly as above. Watch two things: whether the size changed, and whether the change is a rotation or a reflection — the two look alike for symmetric shapes and are told apart by any asymmetric mark.
Figure classification
Four figures share a property and one does not. Common properties: the number of lines or sides, the presence of a curve, symmetry, whether the shape is closed, whether all elements are of the same type, and whether the figure can be drawn without lifting the pen.
Rotation versus reflection
Rotation preserves the order of elements going clockwise; reflection reverses it. So if three marks read A, B, C clockwise in the first figure and A, C, B clockwise in the second, it is a reflection, however much it looks like a turn.
Worked examples
An arrow points north in figure 1, north-east in figure 2, east in figure 3. Where does it point in figure 4?
Solution. It turns clockwise each time → south-east.
A square has a dot in the top-left corner and a line along the top edge. In the next figure the dot is top-right and the line along the right edge. What comes next?
Solution. Both move one position clockwise → dot at bottom-right, line along the bottom edge.
The figures contain 3, 5, 7 and 9 lines. How many lines does the next figure contain?
Solution. Two more each time → 11.
Each figure gains one arm and loses one dot. If figure 3 has 5 arms and 2 dots, what does figure 5 have?
Solution. Two steps later → 7 arms and 0 dots.
In a circle divided into four, the shaded quarter moves one place anticlockwise each step, starting at the top-right. Where is it in the fourth figure?
Solution. Top-right → top-left → bottom-left → bottom-right.
A right-pointing triangle with a dot at its apex becomes a left-pointing triangle with the dot at its apex. Apply the same change to a right-pointing arrow with a circle at its tail.
Solution. The figure is reflected left-to-right, carrying its parts with it → a left-pointing arrow with the circle at its tail.
Which is the odd one out: a square, a rectangle, a rhombus, a scalene triangle?
Solution. The first three have at least two lines of symmetry; the scalene triangle has none.
A figure has marks P, Q, R reading clockwise. In the next figure they read P, R, Q clockwise. Is this a rotation or a reflection?
Solution. The clockwise order has reversed → a reflection.
A dot moves three positions clockwise round an eight-position frame in each step. After how many steps does it return to its starting position?
Solution. It needs a multiple of 8: → 8 steps.
The rule is "rotate anticlockwise and shade the smaller shape". Two options show the correct rotation but only one shades the smaller shape.
Solution. Check the parts of the rule one at a time against every option: the first test usually removes two options and the second removes the rest.