Counting Figures and Visual Enumeration
Count every simple and composite figure systematically—without double-counting or missing larger combinations.
Count by size, then by position
A reliable grid formula
In an r × c rectangular grid, the number of rectangles is r(r+1)c(c+1) ÷ 4. For squares, count each possible size separately.
Do not stop at the smallest figures
A 2 × 2 grid contains 4 small squares and 1 large square, for 5 squares. It contains 9 rectangles in total because the non-square 1 × 2 and 2 × 1 rectangles also count.
Find your starting level
Practice in stages
Foundations
Grids, segments, and separate figures.
Core
Overlaps and composite figures.
ACET Transfer
Layered diagrams and near totals.
Can you enumerate without scaffolding?
Counting Figures FAQ
What is the most common mistake?
Counting only the smallest figures and forgetting larger composite ones.
How do I avoid double-counting?
Separate figures by size and type, keep subtotals, and use one fixed scan direction.
Do tilted figures count?
Yes, when they satisfy the named shape’s defining properties.
Should I use a formula?
Use formulas for regular grids; use organized enumeration for irregular or overlapping figures.
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