Counting-Based Complex Rules

Counting-based rules appeared in the previous course as straightforward patterns — "always 4 shapes" or "total sides is even." In harder UCAT questions, counting becomes considerably more demanding. You might need to count sides across multiple shapes, compare the ratio of two different counts, or track a running total. This lesson covers the advanced counting patterns that appear in medium-to-hard AR questions.

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Advanced Counting Rule 1: Total Sides Equals a Specific Number

We encountered this briefly before, but in complex questions the total is higher and the shape combinations are less obvious.

Worked Example: Total Sides = 16

Set A:

• Box 1: Two pentagons (5+5) + one hexagon (6) = 16 ✓
• Box 2: Four squares (4+4+4+4) = 16 ✓
• Box 3: One octagon (8) + two squares (4+4) = 16 ✓
• Box 4: One hexagon (6) + one pentagon (5) + one triangle (3) + one circle (0) + one square (0? No — wait, that would be wrong)

Let me recalculate Box 4: hexagon (6) + pentagon (5) + triangle (3) + a shape with 2 sides? There is no common 2-sided shape. Let me redesign: