6.3 Count, Shape, Size and Shading Rules

Counting visible structure

Count can refer to whole objects, polygon sides, dots, line segments, occupied positions, shaded regions, or repeated symbols. Write the four values before guessing the next:

• 2, 3, 4, 5 suggests +1, so predict 6.
• 8, 6, 4, 2 suggests −2, so predict 0.
• 1, 3, 1, 3 alternates, so predict 1.
• 2, 1, 3 distributed across three columns may rotate as a group rather than change arithmetically.

Prefer the simplest rule that explains all frames. With only four given figures, many elaborate number sequences can be invented; the other visual features and answer choices determine the intended rule.

Relational count rules

Sometimes the absolute number changes unpredictably while a relationship stays fixed. An official sample explanation describes stacked shapes where the bottom shape always has one more side than the top, even though the top shape's side count varies.

Look for:

• one more or one fewer than another object;
• total count remaining constant while distribution changes;
• count moving between regions;
• two counts exchanging positions;
• one component disappearing as another appears.

If top has 3 sides and bottom has 4, then top 5 and bottom 6, the stable rule is bottom = top + 1—not a sequence of 3, 4, 5, 6 across time.

Shape sequences

Shape can follow a meaningful cycle: triangle → square → pentagon → hexagon predicts a seven-sided figure because side count increases. It can alternate curved and angular forms or repeat A-B-C-A.

But shape may be random. The official guide explicitly points out examples where stars, circles, squares, and other shapes change while location or count supplies the real rule. Test shape across every transition. If no consistent relationship survives, mark shape irrelevant and stop using it to eliminate choices.

Size rules

Size may:

• increase or decrease steadily;
• alternate large and small;
• cycle small → medium → large;
• transfer between two objects;
• depend on location or shading.

Judge relative size from the printed figure, not from imagined real-world scale. If one object grows while another shrinks, track them separately. A choice must preserve both directions.

Shading rules

Shading is highly visible and therefore easy to overvalue. Identify its exact behavior:

Alternation

Solid → hollow → solid → hollow predicts solid. The official guide uses alternating majority shading in a worked example.

Cycle

White → gray → black → white predicts gray. A three-state cycle should repeat after three frames.

Movement

A dark sector can travel around four quadrants while the figure stays otherwise constant. Treat this as a location rule applied to shading.

Transfer

One object becomes shaded as another becomes unshaded, preserving exactly one shaded object.

Conditional shading

Odd-numbered frames may shade the outer object while even-numbered frames shade the inner object. State the dependency explicitly.

Worked multi-feature example

Four frames contain:

• Outer polygon sides: 3, 4, 5, 6.
• Dots inside: 4, 3, 2, 1.
• Fill: dark, light, dark, light.
• A tiny decorative symbol: star, oval, cross, crescent.

Frame 5 should have a seven-sided outer polygon, zero dots, and dark fill. The decorative symbol has no repeated order and should not determine the choice. This example combines +1, −1, alternation, and irrelevant variation.

Verify against official-style choices

Suppose the choices differ as follows:

• Choice A: seven sides, zero dots, light fill.
• Choice B: six sides, zero dots, dark fill.
• Choice C: seven sides, one dot, dark fill.
• Choice D: seven sides, zero dots, dark fill.
• Choice E: eight sides, two dots, light fill.

D alone satisfies all three confirmed rules. Its decorative symbol need not match an invented pattern.

Error controls

• Count carefully when objects overlap. Two objects in the same position may still be two if both are visibly represented.
• Distinguish number of objects from number of sides.
• Do not assume bigger means later unless size changes repeatedly.
• Do not treat black, gray, hatched, and hollow as interchangeable.
• Check whether a count is attached to a moving region rather than to the frame as a whole.
• Recheck Frame 1 → 2 as well as the latest transition; recency can create a false rule.

Practice progression

Train one feature first, then combine two and three. For each solution, write a rule table and mark each feature as patterned, fixed, or random. This habit directly reflects the official warning that patterns may combine several factors while other features have no bearing.