Codes and Matrices

This lesson covers two related NVR question types: shape codes and matrices. Both require you to identify patterns and rules, but they present them in different ways. Shape codes use letters to represent properties, while matrices use grids of shapes with a missing piece.

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Part 1: Shape Codes

In a code question, each shape is labelled with a set of code letters. Each letter stands for one property of the shape (such as its size, colour, or type). Your task is to crack the code — work out what each letter means — and then apply it to a new shape.

How It Works

You are given several shapes, each with a code:

Shape	Description	Code
Shape 1	Large black circle	P R
Shape 2	Small black circle	Q R
Shape 3	Large white circle	P S
Shape 4	Small white square	Q S

Question: What is the code for a large black square?

Step-by-Step Decoding

Step 1: Compare Shape 1 (large black circle, P R) and Shape 2 (small black circle, Q R). They differ only in size — large vs small. The code that changed is P to Q. So P = large and Q = small.

Step 2: Compare Shape 1 (large black circle, P R) and Shape 3 (large white circle, P S). They differ only in colour — black vs white. The code that changed is R to S. So R = black and S = white.

Step 3: Notice that Shape 4 is a square (not a circle) and its code is Q S. There is no extra letter for "circle" or "square." In this example the shape type is not coded. This happens sometimes — not every property gets a code letter.

Step 4: Apply the decoded table to the question. A large black square = P R.

Decoding Table

Code	Meaning
P	Large
Q	Small
R	Black
S	White

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Tips for Cracking Codes

1. Always compare two shapes that differ in exactly ONE property. This isolates the code letter for that property.
2. Build a table as you decode each letter. Write down what each letter means.
3. Verify your table against ALL given shapes. If any shape does not match your decoded table, you have made an error.
4. Watch for three-letter codes. These usually mean three properties are coded (e.g. size, colour, and shape type).

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Part 2: Matrices

A matrix is a grid of shapes (usually 3 rows and 3 columns) with one shape missing. You must find the pattern in each row and each column and use it to work out the missing shape.

How Matrices Work

Think of a matrix as a table:

	Column 1	Column 2	Column 3
Row 1	Circle	Square	Triangle
Row 2	Square	Triangle	Circle
Row 3	Triangle	Circle	?

Row rule: Each row contains one circle, one square, and one triangle (all three shapes appear once).

Column rule: Each column also contains one circle, one square, and one triangle.