A single figure sits in the top-left field. In the next matrix it is one field to the right, then one further right again, and by the fourth matrix it has reached the top-right corner.

Figure Sequences

Work out the rule governing each figure in a 4 x 4 matrix series, then pick the next two matrices.

What the task asks

You are shown a series of matrices. From one matrix to the next, the figures inside can shift position, change colour and change orientation, always according to a consistent rule that holds across the whole series.

Your job is to work out the rule governing each figure and decide what the next two matrices look like.

Track one property at a time: first where each figure moves, then whether it turns, then whether its colour changes. Rules combine, but each figure follows its own.

Rules

A figure may change colour, cycling through two or more colours in a fixed order.
A figure may rotate about its own axis, a quarter turn at a time.
A figure may move horizontally, vertically or diagonally. A figure that moves diagonally keeps moving diagonally and never switches to another kind of movement.
A figure may travel around the outer border of the matrix, clockwise or anticlockwise.
A rule may grow by one each step (x + 1). A figure that moves one field between the first two matrices moves two between the next pair, then three, and so on. The same growth can apply to how far it turns.
Figures never disappear, and no two figures ever occupy the same field.
Figures never leave the matrix. On meeting an outer edge, a figure either bounces back the way it came or carries on along the edge.

Worked example

A single figure sits in the top-left field. In the next matrix it is one field to the right, then one further right again, and by the fourth matrix it has reached the top-right corner.

Solution. The figure moves one field at a time along the top row. It has now reached the right-hand edge, so the boundary rule decides what happens next: either it bounces and comes back left, or it turns the corner and continues down the right-hand edge. Whichever the earlier matrices show it doing at an edge is what it will do here.

Timing

The subtest gives you 25 minutes for 20 series, about 75 seconds each. Answer every question: a guess costs nothing, and an unanswered question scores the same as a wrong one. No notes are allowed.

How this app presents it

The matrix is 4 × 4. Matrices 1 to 4 are shown; matrices 5 and 6 are hidden.
You choose one of three response options for Image 1 (matrix 5) and, separately, one of three for Image 2 (matrix 6). Both must be right for the question to count as correct.
Low uses one figure; Medium uses three; High uses four, including identical shapes. Track them by their starting cells. High combines growing 90°, 180°, 270° turns with diagonal steps of 2, 3, 4 and so on. Steps bounce at boundaries, sometimes returning to the same cell.
Some options share every position but differ in rotation or colour. Check all properties before answering.
Only figures whose orientation is visible are ever given a rotation rule, since a rotating square would be unanswerable.

Practise this task type Timed 20-question set

The other Core Module task types

Mathematical Equations Find the whole number each letter stands for so every equation in the system holds at once.
Latin Squares Deduce the letter in the question-mark field of a 5 x 5 grid using only row and column elimination.

This is an unofficial practice tool, not affiliated with or endorsed by g.a.s.t. or the TestDaF-Institut. The description above is written for this project; always check the official preparatory materials for the authoritative instructions.