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NSW SelectiveYear 7 entry

Switch and state puzzles in Selective Thinking Skills

Independent. Not affiliated with the NSW Department of Education.

Switch and state puzzles follow a system, such as lights and buttons, through a run of steps. In Selective Thinking Skills, your child can write the state after every step in a table, or count presses: odd flips, even cancels.

Watch the full lessonPlay the preview

The full lesson is in the SelectiveReady app. A free account opens How and Why Authors Write; this lesson needs a paid plan.

Updated 16 October 2026 · Facts checked 12 October 2026

Systems, Switches & State Changes (lesson preview)

A short preview from the SelectiveReady lesson “Systems, Switches & State Changes”, on switch and state puzzles for the NSW Selective test.

Published:

Read the video transcript

Okay, step one, we press button A. Now, what did our rules say? A toggles lights one and three. They were both off, so boom, they both turn on. Our new setup is on, off, on, off. All right, next we hit button B. This one affects lights two, three, and four. So lights two and four, they were off, now they're on. But wait, what about light three? It was already on. So toggling it means it goes back off. See how that works? Our new state is on, on, off, on. And now for the grand finale. We press button A one more time. It hits lights one and three. Light one was on, so now it's off. Light three was off, so now it's on. And remember, button A doesn't touch lights two and four, so they just stay put. And just like that, we're done. After that whole A-B-A sequence, what's our final answer? Light one is off. Lights two, three, and four are all on. Puzzle, solved.

Systems, Switches & State Changes is a full lesson in the SelectiveReady app. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published. The preview below has English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns to see a puzzle as a system: a set of things that follow simple rules. They'll be able to track the state after each step, use the odd-or-even shortcut, and avoid the slips that lose track.

The clip presses button A, then B, then A again on four lights. The full lesson adds the rules of the system, the shortcut, a full state table and the common traps.

3

How do switch and state puzzles show up in Selective Thinking Skills?

These puzzles are among the Thinking Skills question types. The Department doesn't publish a fixed list of types 2NSW Education · 12 October 2026 · Published, so the system can be lights, codes, seats or moves.

The testWhat it means for switch puzzles
Each child gets 23NSW Education · 12 October 2026 · Published sheets of working-out paperSpace for a state table, one row per step
402NSW Education · 12 October 2026 · Published questions in 402NSW Education · 12 October 2026 · Published minutesA neat table is quicker than starting again
42NSW Education · 12 October 2026 · Published options per questionWrong options often show a state after a missed step
Thinking Skills checks critical thinking and problem solving, with no previous knowledge needed2NSW Education · 12 October 2026 · PublishedThe rules are all in the question
4

What are switch and state puzzles?

A switch and state puzzle gives your child a system, its rules and a sequence of actions. The question asks what the system looks like at the end.

A toggle is the key idea. Pressing it turns something on if it was off, and off if it was on.

Kind of systemWhat changesThe tool that helps
Lights and buttonsOn or offCount presses for each light
Secret codesEach letter shifts by a set amountFind the shift, then apply it
Passing round a circleWho holds the ballFind when it comes back to the start
Moves on a gridWhere a counter standsTrack one move at a time
5

What is the method for switch and state puzzles?

Write the starting state, apply one step at a time, and record the new state after every step. The lesson's big message is to be methodical, not a genius.

One step, one row: write the start, record the lights after every press; odd presses flip a light, even presses cancel.

  1. Read the rules

    Note exactly which button changes which part. On working paper, mark any part touched by more than one button.

  2. Write the start

    Make a table with one column per part and write the starting state.

  3. One step, one row

    Apply a single step and write the whole new state before moving on.

  4. Check with the shortcut

    Count how often each part was switched. Odd means flipped; even means back where it started.

6

What does a worked switch puzzle look like?

We wrote this puzzle to show the method. Three fans, red, blue and green, start off.

Switch P flips the red and blue fans. Switch Q flips the blue and green fans.

Question: Your child presses P, Q, Q, P, Q. Which fans are on at the end?

PressRed fanBlue fanGreen fan
Startoffoffoff
Pononoff
Qonoffon
Qononoff
Poffoffoff
Qoffonon

The blue and green fans are on. The shortcut agrees: red is switched twice (even, so off), blue five times (odd, so on) and green three times (odd, so on).

7

Which traps catch children on switch puzzles?

The most common trap is trying to hold the whole sequence in your head. The lesson's advice is plain: write it down after each step.

TrapWhat goes wrongThe fix
All in the headOne step is lost and every later state is wrongOne row per step on working paper
Toggle goes one wayA light that is already on is turned on againToggle means on to off as well as off to on
Misread rulesA button is given the wrong lightsList each button's parts on working paper first
8

Can my child try one on their own?

Here is a lamps puzzle from our free Thinking Skills set. It is a bigger version of the clip, with three buttons and five lamps.

Practice question · SEL-TS-TST-26

Five lamps in a row are numbered 1 to 5. At the start, all five are off. Each button switches some of the lamps: a lamp that is off turns on, and a lamp that is on turns off.

  • Button X switches lamps 1, 3 and 5.
  • Button Y switches lamps 2 and 3.
  • Button Z switches lamps 3, 4 and 5.

Thanh presses X, then Y, then Z, then X again. Which lamps are on at the end?

  1. A

    Lamps 1, 3 and 5

  2. B

    Lamps 2 and 4

  3. C

    Lamps 1, 2, 3 and 4

  4. D

    Lamps 2, 4 and 5

Show answer and explanation

Answer: D

Answer: D (Lamps 2, 4 and 5)

Count how many times each lamp is switched. An odd number of switches leaves it on; an even number leaves it off.

  1. Lamp 1: X and X again, 2 times, so off.
  2. Lamp 2: Y, 1 time, so on.
  3. Lamp 3: X, Y, Z and X again, 4 times, so off.
  4. Lamp 4: Z, 1 time, so on.
  5. Lamp 5: X, Z and X again, 3 times, so on. Lamps 2, 4 and 5 are on.

Why the other options are wrong

  • A (Lamps 1, 3 and 5): These are only the lamps the last button switches; the earlier presses also matter.
  • B (Lamps 2 and 4): Lamp 5 is switched three times, by X, Z and X again, so it ends up on.
  • C (Lamps 1, 2, 3 and 4): This is the result after X, Y and Z only; the second press of X has been missed.

  1. Count, don't replay

    Count how many times each lamp is switched across X, Y, Z and X again. Odd leaves it on; even leaves it off.

  2. Lamps 1 and 2

    Lamp 1 is switched by X twice, so it's off. Lamp 2 is switched once by Y, so it's on.

  3. Lamps 3, 4 and 5

    Lamp 3 is switched four times: off. Lamp 4 once: on. Lamp 5 three times: on.

  4. Match the option

    Lamps 2, 4 and 5 are on, which is option D. Option C is the state before the last press of X.

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How can my child practise switch puzzles at home?

Any on-off game works. The habit to build is writing the state after each step.

Cup flips

Line up a few cups. Call out rules such as "flip the first and third", then predict before checking.

Secret codes

Shift each letter of a word two places along the alphabet and swap coded notes.

Board game tracking

Keep a quick table of where each counter is after every turn.

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Questions parents ask about switch puzzles for Selective

What if the puzzle has many steps?

Look for a repeat. When the system comes back to where it started, the pattern begins again, so your child only needs the steps left over.

My child is good at mental work. Why write it down?

Long sequences trip up strong thinkers too. A table takes seconds and makes each step easy to check.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published.

Next questions

Selective Thinking Skills →Lesson: Solving Logic Puzzles →Lesson: If-Then Reasoning →Free Selective practice test →The NSW Selective test explained →

Sources and checks

  1. SelectiveReady

    SelectiveReady · Checked 13 October 2026

  2. Selective high school practice tests

    NSW Department of Education · Checked 12 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Page text: CC BY 4.0.

  3. Placement test

    NSW Department of Education · Checked 12 October 2026 · CC BY 4.0 (NSW Department of Education copyright notice); quotes credited

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