PSLE Number Pattern Questions, Shown Working

Q: Can I get worked solutions for more question types?

Yes. Genius Plus Academy publishes a worked solution and a video for PSLE Paper 2 questions across all ten question types, and parents can request the free cheat sheet that names each type with its lock and key, from the worked-solutions library.

PSLE number pattern questions, shown working.

The short version

PSLE number pattern questions show a growing sequence of figures and ask about a figure far too large to draw. You solve them by finding the rule, often a square number or a steady step, then writing the nth figure as a formula. Any split, such as grey against white, is handled as half the total plus or minus half the gap.

Figures from GPA's tagged index of 709 PSLE questions, on a 664 sat-paper basis, with the MOE Specimen reported separately · the worked example was solved independently then checked against the verified GPA key · Mrs Eileen Toh signs off the mathematics · last reviewed 22 Jun 2026

One move does the heavy lifting: turn a figure sequence into a formula.

Number pattern questions reward one move above all, turning a figure sequence into a formula. Once you have the rule, a figure you could never draw, like Figure 250, becomes a single calculation. The second habit is to handle any split, such as grey against white, as half the total plus or minus half the gap.

Find the rule

Look first for a square number or a steady step between figures. The rule is what survives past the figures you can draw.

Write the nth figure

Express the nth figure as a formula, then a figure too large to draw, like Figure 250, becomes one calculation.

Split as a gap on a total

A difference between two groups is a small gap on a large total. The larger group is half the total plus half the gap.

These are the habits we see open almost every figure-pattern question. They describe how past papers have worked, not a forecast of the next one. Source: GPA tagged index, 664 sat-paper basis.

Find the rule, then make the difference small.

A number pattern question never expects a child to draw Figure 250. It expects the child to notice how each figure is built from the one before, then to name that rule. Most often the rule is a square number, like \(n^2\) small triangles in Figure \(n\), or a steady step, where the same amount is added each time. Once the rule is on the page, the nth figure is a formula, and a figure too large to draw becomes a single calculation.

The second idea is the one that earns the last mark: a part of the figure, such as the grey triangles, is handled as a small gap on a large total. If you know the total and the gap between grey and white, the grey is half the total plus half the gap, and the white is half the total minus half the gap. Two clean ideas, one about the whole and one about the difference, and the question is finished.

2019 · Paper 2 · Q17 figure to formula

The triangle that grows by odd numbers

The question

A pattern of triangles: Figure 1 is one small triangle, and each new figure adds a row, so Figure \(n\) is a big triangle made of \(n^2\) small triangles, alternately white and grey by row. (a) Complete the table for Figure 5. (b) How many small triangles are in Figure 250 altogether? (c) In Figure 250, what percentage are grey?

We reproduce this one because it made national news — one of the 2019 PSLE questions widely shared online, covered by Mothership. For other questions our pages point you to your Ten-Year Series instead.

Video: a Genius Plus Academy teacher solving PSLE 2019 Paper 2 Question 17

Teacher video · 2019 P2 Q17

The lock

A child can fill the next column by drawing, but Figure 250 cannot be drawn. The lock is spotting that the total is a square number and that the grey-minus-white gap grows in a steady, countable way.

The key

Find the rule, then handle grey and white as a small gap on a large total: grey is half the total plus half the gap.

Worked steps

(a) Figure 5 adds a fifth row of 9 white triangles to Figure 4: white \(= 6 + 9 = 15\), grey stays 10 (total 25).
(b) Figure \(n\) holds \(n^2\) small triangles, so Figure 250 holds \(250^2 = 62\,500\).
(c) For even-numbered figures, grey exceeds white by \(n\) (Figure 2: \(3-1=2\); Figure 4: \(10-6=4\)). For Figure 250 the gap is 250.
Grey \(= (62\,500 + 250) \div 2 = 31\,375\), so grey % \(= 31\,375 \div 62\,500 \times 100\% = 50.2\%\).

Answer: (a) white 15, grey 10. (b) 62 500. (c) 50.2%.

What makes it click. Two ideas, neatly separated: the total is a square, and grey is just half the total plus half the gap. Hard problems often split into one idea about the whole and one about the difference.

Independently solved, matches the GPA marking-scheme key. Open the full worked solution →

Do not try to draw what cannot be drawn. Find the formula instead.

The most expensive mistake in a number pattern question is to keep extending the drawing. A child fills the table for Figure 5 by hand, feels confident, and then tries the same thing for Figure 250. There is no time, and there is no need. The early figures exist only to reveal the rule. Once you can write the nth figure as a formula, the large figure is a single line of arithmetic, not a drawing.

The second slip is to compute grey and white from scratch in the big figure. Treat the difference as a small gap on a large total instead: the larger group is half the total plus half the gap. Name the rule, name the gap, and the final mark falls out cleanly.

Questions parents ask

What is a PSLE number pattern question?

It shows a sequence of figures that grow in a fixed way, then asks about a figure too large to draw, such as Figure 250. The skill is to find the rule, often a square number or a steady step, and write the nth figure as a formula. A later part usually asks for a split, such as the percentage that is grey.

How do you handle the grey-against-white part?

Treat it as a small gap on a large total. Once you know the total and the gap between the two groups, the larger group is half the total plus half the gap, and the smaller is half the total minus half the gap. That separates one idea about the whole from one about the difference, and the final mark falls out cleanly.

Is the worked solution here reliable?

Yes. The 2019 Paper 2 Q17 example was worked independently and then checked against the verified GPA marking-scheme key, and the two agree on every part. Mrs Eileen Toh signs off the mathematics. This is honest analysis of a past paper, not a prediction of the next one.

Can I get worked solutions for more question types?

Yes. We publish a worked solution and a video for PSLE Paper 2 questions across all ten question types, and you can request the free cheat sheet that names each type with its lock and key. Browse them all in our worked-solutions library.

PSLE number pattern questions, shown working.

One move does the heavy lifting: turn a figure sequence into a formula.

Find the rule, then make the difference small.

The triangle that grows by odd numbers

Do not try to draw what cannot be drawn. Find the formula instead.

The 10 PSLE Question Types, cheat sheet

This trains one move. The Intensive trains all ten.

Keep reading

Questions parents ask

See how your child reads a pattern.