Shape Fitting

Identifying which piece correctly fills a given outline.

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Identifying which piece correctly fills a given outline.

Shape fitting puzzles require matching a piece to an outline or gap. This involves comparing the contours of available pieces with the shape to be filled, considering both size and exact geometry. This skill underlies tangram puzzles and practical tasks like packing and assembly.

match = find_piece(outline, available_pieces)

L-shaped piece fits L-shaped gap
Triangle fits only in triangular spaces
Rotated pieces may fit differently than expected

How to recognize it

Compare the outline perimeter with each piece's perimeter
Check corners and angles match between gap and piece
Consider if rotation might make a piece fit
Eliminate pieces with wrong area or impossible geometry

Common mistakes

Not considering that pieces might need rotation
Focusing only on area instead of exact shape
Missing subtle differences in angles or proportions

Step-by-step walkthrough

A T-shaped gap needs to be filled. Which of these pieces fits: an L-shape, a T-shape, or a plus sign?

Analyze the gap: a T-shape has one vertical bar with a horizontal bar at one end.
Check the L-shape: it has only two arms meeting at a corner - wrong geometry.
Check the plus sign: it has four arms extending from center - too many arms.
Check the T-shape: one vertical bar, one horizontal bar at the end - matches exactly.
The T-shape fits perfectly into the gap.

Answer: The T-shape fits the gap

Practice guidance

Spatial Reasoning