How to solve figure analogies

A method that works on every item

1. Inventory A

Before comparing, describe A completely: the main shape, its size, its fill, which way it points, and every small shape with its position (top, top-right corner, right side and so on). Most mistakes come from never noticing a small part.

2. Name each change to B

Go through the inventory one feature at a time and ask whether it changed. Write each change as a short sentence: “the whole figure turns a quarter turn clockwise”, “the large shape becomes hatched”. If something looks different but you cannot say how, test the two candidates that are easiest to confuse: a turn and a flip.

3. Separate turns from flips

Pick a landmark that is not symmetrical, such as the tip of an arrow or a single small shape at one corner. A quarter turn clockwise moves the top to the right side. A left-to-right mirror keeps the top at the top but swaps left and right. A top-to-bottom flip keeps left and right but swaps top and bottom. A half turn swaps both. Following one landmark settles it.

4. Watch what moves together

When the whole figure turns, the small shapes turn with it. When only the main shape spins, the small shapes stay put. When the small shapes move around the edge, the main shape stays put. Deciding which parts moved together is often the key to a hard item.

5. Apply the changes to C and nothing else

Inventory C the same way, apply each change in turn, and describe the result before you look at the options. Then find the option that matches your description exactly.

A worked example in words

A is a small outlined arrow pointing up. B is a small outlined arrow pointing right. C is a large hatched triangle pointing left, with a small circle at the top.

1. Inventory A: small, outlined, arrow, pointing up, no small shapes.
2. From A to B, only the direction changed: up to right is a quarter turn clockwise.
3. Apply it to C: the whole figure turns a quarter turn clockwise. The triangle now points up, and the circle that was at the top moves to the right side.
4. Answer: a large hatched triangle pointing up, with a small circle on the right side.

The traps here are an option where the triangle turns but the circle stays at the top (the spin-only change, which is not what A to B showed) and an option that is a mirror image instead of a turn.

Common traps

• The partial match. An option applies two of three changes. Check every change against your choice.
• The mirror twin. An option is the right answer reflected. Use a landmark to tell turn from flip.
• The extra change. An option also changes the fill or size when the first pair did not. Nothing should change except what changed from A to B.
• The wrong anchor. An option moves the small shapes when the first pair spun only the main shape, or the reverse.

How analogies relate to other puzzle types

An analogy is a matrix puzzle in miniature: a rule found in one row and applied to the next. Matrix puzzles in the tradition of Raven's Progressive Matrices use the same move across a 3x3 grid (Wikipedia: Raven's Progressive Matrices). The matrix reasoning guide covers that bigger version, and the spatial reasoning guide goes deeper on turns and mirror images.

To practice, open the figure analogy puzzle library, where every item shows its changes step by step, or take the timed logical reasoning practice test. The Logical Reasoning practice page walks through one example from the test itself.