13.4 Multi-Feature Shape Code Matching

2. Multi-Feature Shape Codes (Letter Codes)

In shape code questions, candidates are presented with a series of figures, each accompanied by a 2-letter or 3-letter code (e.g., KP, LQ, KQ, LP). A new mystery figure is then presented, and the candidate must determine its correct code.

Outline symbols are unfilled; solid symbols are black. Both shape and fill vary, allowing each letter position to be tested independently.

The Independent Variable Principle

For the independent-feature codes practised here, each letter position represents a separate feature. Read the instruction: not every possible code must use this model, and shape is not always the first position.

• Position 1 (First Letter): Encodes one specific visual variable (and only that variable), such as the base shape geometry.
• Position 2 (Second Letter): Encodes an entirely independent visual variable, such as the shading or interior pattern.
• Position 3 (Third Letter, if present): Encodes a third independent variable, such as pointer orientation or dot count.

The Systematic Tabular Decoding Protocol

Never attempt to guess the letters simultaneously. Isolate one letter position at a time using this structured 5-step protocol:

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1. Step 1: Pairwise First-Letter Isolation: Find two figures that share the identical first letter (e.g., Figure 1 KP and Figure 3 KQ both start with K). Ask: "What exact geometric feature is identical between Figure 1 and Figure 3?" Both are triangles! Therefore, K = Triangle.
2. Step 2: Contrast Verification: Check figures with a different first letter (e.g., Figure 2 LP and Figure 4 LQ). Both are squares! Therefore, L = Square.
3. Step 3: Pairwise Second-Letter Isolation: Find two figures that share the identical second letter (e.g., Figure 1 KP and Figure 2 LP both end with P). Ask: "What do Figure 1 and Figure 2 have in common?" Both are unshaded white! Therefore, P = White / Unshaded.
4. Step 4: Second Contrast Verification: Check figures ending with Q (Figure 3 KQ and Figure 4 LQ). Both are solid black! Therefore, Q = Solid Black.
5. Step 5: Code the Target Mystery Shape: If the target shape is a solid black triangle, look up its components: Triangle = K, Solid Black = Q. The code must be KQ.

Common Pitfalls in Shape Codes

• Accidental Co-Occurrence (Confounding Variables): In small sample sets, two features might accidentally coincide (e.g., all triangles happen to be large and all squares happen to be small). Look across the full set of figures to ensure the letter correlates strictly with the intended attribute.
• Letter Transposition: Mixing up the order of the letters (e.g., selecting QK instead of KQ). Pay strict attention to position: For this example, first letter = shape and second letter = shading; infer the order afresh in a new puzzle.

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Three-letter code example

Worked Example 3: Deciphering a 3-Letter Multi-Feature Shape Code

Problem Statement: Study the five reference figures and their assigned 3-letter codes below. Determine the correct code for the target test figure.

Figure 1: Large White Hexagon with 1 inner dot     ───►  Code: A X R
Figure 2: Small White Hexagon with 2 inner dots    ───►  Code: B X S
Figure 3: Large Black Hexagon with 2 inner dots    ───►  Code: A Y S
Figure 4: Small Black Octagon with 1 inner dot     ───►  Code: B Y R
Figure 5: Large White Octagon with 3 inner dots    ───►  Code: A X T

TARGET FIGURE: Small Black Hexagon with 3 inner dots  ───►  Code: ? ? ?

Visual Breakdown:

• Position 1 (First Letter: A vs B):
  • Compare figures with A: Figure 1 (Large), Figure 3 (Large), Figure 5 (Large). All are Large!
  • Compare figures with B: Figure 2 (Small), Figure 4 (Small). All are Small!
  • Deduction: A = Large, B = Small.
  • Target figure is Small $\implies$ First letter = B.
• Position 2 (Second Letter: X vs Y):
  • Compare figures with X: Figure 1 (White), Figure 2 (White), Figure 5 (White). All are White!
  • Compare figures with Y: Figure 3 (Black), Figure 4 (Black). All are Black!
  • Deduction: X = White, Y = Black.
  • Target figure is Black $\implies$ Second letter = Y.
• Position 3 (Third Letter: R, S, T):
  • Compare figures with R: Figure 1 (1 dot), Figure 4 (1 dot). Both have 1 dot!
  • Compare figures with S: Figure 2 (2 dots), Figure 3 (2 dots). Both have 2 dots!
  • Compare figures with T: Figure 5 (3 dots). Has 3 dots!
  • Deduction: R = 1 dot, S = 2 dots, T = 3 dots.
  • Target figure has 3 dots $\implies$ Third letter = T.
• Synthesize Target Code:
  • Small (B) + Black (Y) + 3 dots (T) = B Y T.