Non-Verbal Reasoning › Analogies & grids
Analogies & grids
The same idea in four costumes: work out the rule that links some pictures, then use it to find the one that is missing. Each type starts with a short explanation and a worked example.
Start here
All four types on this page ask the same question in different ways: what is the rule, and what is missing? You are shown some pictures that follow a hidden rule, with one left blank. Find the rule, apply it, and pick the picture that fits the gap.
The rule is always one of the six things from the last topic — a change of shape, shading, size, number, position or rotation — so keep that check handy. The only new part is where to look: across a pair, along a row, down a column, or around a shape.
- Analogies — “this changes to that, so this changes to…”
- Matrices — a grid of pictures with one square empty.
- Similar triangles — a pattern carried from one big triangle to another.
- Star matrices — a pattern running around the points of a star.
1. Analogies
An analogy shows you one picture changing into another, then a third picture that must change in the very same way. It is written as A → B :: C → ? and read as “A is to B as C is to what?”. Work out what happened between A and B, then do exactly that to C.
- Look at A → B. The arrow has turned a quarter-turn clockwise, from pointing up to pointing right. Nothing else changed.
- Name the rule. “Turn a quarter-turn clockwise.”
- Apply it to C. The triangle points up; a quarter-turn clockwise makes it point to the right.
Your go: analogies
Find the rule from the first pair, then tap the picture that completes the second pair.
2. Matrices
A matrix is a grid — usually two-by-two here — with one square left empty. The pictures change by a rule as you move across each row, and often the same is true down each column. Find the rule, then fill the empty square.
- Read across the top row. The white circle becomes a solid circle. So the rule across is “the shape fills in solid.”
- Read down the columns. The circle becomes a square down the left column, so the shape changes from circle to square.
- Put it together. The bottom row is squares; the empty square is on the “solid” side. So it is a solid square.
Your go: matrices
Work out the rule across the rows, then tap the picture for the empty square.
3. Similar triangles
Here you are shown two large triangles, each split into four smaller ones. The second triangle follows the first by a rule, and one small piece is left blank. The commonest rule is the simplest: the second triangle copies the first, so the missing piece matches the same corner of the first triangle. Always check the pieces you can see first, to be sure it is a straight copy.
- Check the pieces you can see. Top, left and centre are the same in both triangles, so the second really is a copy.
- Find the blank. It is the bottom-right piece.
- Match it to the first triangle. In the first, the bottom-right piece is solid, so the missing piece is solid.
Your go: similar triangles
The second triangle copies the first. Tap the small triangle that belongs in the blank piece.
4. Star matrices
A star matrix has a picture at each of six points, with one point blank. The rule runs around the star. Two rules are common: the pictures may alternate as you go round, or points opposite each other may match. Check the pairs of opposite points first — it is the quickest way in.
- Pair up opposite points. Top and bottom are both circles. Upper-right and lower-left are both squares.
- Find the blank’s partner. The blank is at the upper-left; its opposite point, the lower-right, is a triangle.
- Match it. Because opposite points are the same, the blank must be a triangle.
Your go: star matrices
Work out the rule running around the star, then tap the picture for the blank point.
That is analogies & grids
Four shapes of the same puzzle: find the rule, then find what is missing. When you are ready, head back and try another topic.
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