Figure series for AFCAT: track one element at a time

In a figure series question you see four or five figures in a row, each a small box containing arrows, dots, lines or shapes. You pick, from four or five options, the figure that comes next. Candidates who find these hard are usually trying to take in the whole figure at once. Candidates who find them easy follow one element across the row, name its rule, and then move to the next element.

Non-verbal questions matter in AFCAT because the Air Force wants officers who can see how things turn and move. They are also quick marks: once you know the handful of rules, most series take under 40 seconds.

A language for describing figures

This site has no images, so every figure below is described in words. It is a good habit for the exam too: naming what you see is the fastest way to spot the rule.

Positions inside a figure are cells of a 3×3 grid, numbered like a phone keypad:

Going clockwise round the outer ring, the cells run 1 → 2 → 3 → 6 → 9 → 8 → 7 → 4 → back to 1. Anticlockwise is the reverse.

Directions for arrows use the compass: an arrow pointing to the top of the box points north, and a 45° clockwise turn takes it from north to north-east.

The rules that cover most series

The four-step method

1. List the elements. For example: an arrow, a dot, a shaded quarter.
2. Track one element across all figures. Write its state in each figure as a short row, such as "N, NE, E, SE".
3. Name the rule and predict that element in the next figure.
4. Eliminate options that break that prediction. Then repeat for the next element with the options left.

Often the first element alone cuts four options to two. The second element settles it.

Worked series

Example 1: rotation. An arrow points north, then north-east, then east, then south-east.

• Each step is a 45° clockwise turn. Next: south.

Example 2: movement round the ring. A dot sits in cell 1, then 2, then 3, then 6.

• The dot moves one cell clockwise round the outer ring each step. After 6 comes cell 9.

Example 3: two elements with different rules. Each figure contains a dot and a star.

• Dot: 1 → 3 → 9 → 7 is two cells clockwise each step, so it jumps from corner to corner. Next: cell 1.
• Star: 8 → 9 → 6 → 3 is one cell anticlockwise each step. Next: cell 2.
• Answer: the dot in cell 1 and the star in cell 2. An option with the dot in 1 but the star in 6 has moved the star the wrong way.

Example 4: growing count. A box contains 1, 2, 4 and 7 small circles.

• The differences are 1, 2, 3. The next difference is 4, so the next figure has 11 circles.

Example 5: shading plus alternation. A square is split into four quarters: top-left, top-right, bottom-right and bottom-left. In each figure one quarter is shaded, and there may be a dot at the centre.

• Shading moves one quarter clockwise each step, so figure 5 has the top-left quarter shaded.
• The dot alternates, so figure 5 has the dot.

Example 6: growing rotation. An arrow points north, then north-east, then south-east, then west.

• North to north-east is 45°. North-east to south-east is 90°. South-east to west is 135°. All clockwise.
• The next turn is 180°, so the arrow goes from west to east.

Speed habits for the exam

• Start with the element whose change is largest or clearest, usually an arrow or a single moving dot.
• Check options against your prediction, not the other way round. Looking at options first makes every option seem plausible.
• For a five-figure series, check whether figures 1, 3 and 5 follow one rule and 2 and 4 another. Alternation hides well.
• If two elements always move together, treat them as one element.
• A 180° turn looks the same whichever way it goes. A 90° turn does not, so check the direction.

Practice set

Use the 3×3 grid and compass directions above.

1. A line runs from the centre (cell 5) to cell 2, then from the centre to cell 3, then to cell 6, then to cell 9. Where does the line run in the next figure?
2. A triangle sits in cell 7, then cell 4, then cell 1, then cell 2. Where is it in the next figure?
3. A box contains 2, 3, 5, 8 and 12 dots. How many dots are in the next figure?
4. An arrow points north with a shaded circle on its tail. Then it points west with an unshaded circle, then south with a shaded circle, then east with an unshaded circle, then north with a shaded circle. Describe figure 6.
5. A dot moves two cells clockwise round the outer ring each step, and a cross moves one cell anticlockwise each step. In figure 1 the dot is in cell 1 and the cross is in cell 4. Where are they in figure 5?
6. Figure 1 has a circle in cell 1. Figure 2 has a square in cell 9. Figure 3 has a circle in cell 2. Figure 4 has a square in cell 8. Figure 5 has a circle in cell 3. Describe figure 6.

Answers:

1. Centre to cell 8. The line turns 45° clockwise each step, like a clock hand: north, north-east, east, south-east, then south.
2. Cell 3. The triangle moves one cell clockwise round the ring: 7 → 4 → 1 → 2 → 3.
3. 17. The differences are 1, 2, 3, 4, so the next is 5.
4. Arrow pointing west with an unshaded circle. The arrow turns 90° anticlockwise each step, and the shading alternates.
5. Dot in cell 1, cross in cell 6. Dot: 1 → 3 → 9 → 7 → 1. Cross: 4 → 7 → 8 → 9 → 6.
6. A square in cell 7. This is alternation. The odd figures hold a circle moving along the top row (1, 2, 3). The even figures hold a square moving along the bottom row (9, 8), so the next square is in cell 7.

What to do next

• Take any five series from a practice book and write each figure in words before solving. This builds the "one element at a time" habit.
• Do 10 figure series a day for a week. Note which rule each used, and see which rules you miss most often.
• Move on to figure analogy and classification, which use the same rules, and mirror and water images.