OC ordering under conditions: 6 queue puzzles

Quick Answer

Draw a blank for each place in the queue. Place the clue that fixes a spot first. Then write out every order that is still possible and cross out any that breaks a clue. What is left is the answer, and your child can see which clue removed which order.

Who are these ordering puzzles for?

Children in Years 3 and 4 who are preparing for the NSW Opportunity Class test and who sometimes get a "who is in which place" question right by luck and wrong by luck. The six puzzles are ours and are written for practice. They are not copied from or modelled on any official paper.

The Department of Education lists the OC test as three multiple-choice components: Reading, Mathematical Reasoning and Thinking Skills (NSW Department of Education, OC practice tests). It does not publish a list of question types inside Thinking Skills, so we do not say that ordering puzzles are a named question type. What they train is reading each condition exactly and keeping every possibility in view.

How do we solve an ordering puzzle without guessing? A worked queue

Four children, Ali, Bree, Cam and Dot, stand in a queue. The front of the queue is on the left.

1. Dot is last.
2. Bree is next to Cam.
3. Ali is after Bree.
4. Cam is before Bree.

Three words do the work in these puzzles, so we define them once:

• Next to means touching, on either side. Bree next to Cam means they are in places that are one apart, in either order.
• Before means somewhere ahead of, not necessarily directly in front. "Cam is before Bree" is true if Cam is first and Bree is third.
• After means somewhere behind, not necessarily directly behind.

Step 1: place the clue that fixes a spot. Clue 1 puts Dot in the fourth place, so the rest are in places 1 to 3.

Step 2: write every order that is left. Three people can stand in six orders in places 1 to 3:

1. Ali → Bree → Cam → Dot
2. Ali → Cam → Bree → Dot
3. Bree → Ali → Cam → Dot
4. Bree → Cam → Ali → Dot
5. Cam → Ali → Bree → Dot
6. Cam → Bree → Ali → Dot

Step 3: check each order against every clue.

Order	Clue 1	Clue 2	Clue 3	Clue 4	Result
Ali, Bree, Cam, Dot	✓	✓	✗	✗	Rejected by clue 3
Ali, Cam, Bree, Dot	✓	✓	✗	✓	Rejected by clue 3
Bree, Ali, Cam, Dot	✓	✗	✓	✗	Rejected by clue 2
Bree, Cam, Ali, Dot	✓	✓	✓	✗	Rejected by clue 4
Cam, Ali, Bree, Dot	✓	✗	✗	✓	Rejected by clue 2
Cam, Bree, Ali, Dot	✓	✓	✓	✓	Valid

Step 4: read the answer. Only Cam → Bree → Ali → Dot passes all four clues. Notice that clue 2 alone ("next to") would have kept two orders, because Bree and Cam can touch either way round. It was clue 4 that picked between them.

The puzzles

Write the places on paper as blanks, then list the orders before you decide. Answers are in the next section, so cover them for now.

Puzzle 1

In this queue the people are Dev, Ava, Ben and Cal. The first name in your list is the front of the queue.

1. Dev is first.
2. Ava is before Ben.
3. Cal is next to Ben.
4. Cal is after Ben.

Who is second in the queue?

Puzzle 2

In this queue the people are Kim, Leo, Mia, Noor and Omar. The first name in your list is the front of the queue.

1. Mia is last.
2. Kim is next to Leo.
3. Kim is before Leo.
4. Noor is before Kim.
5. Omar is before Noor.

Who is fourth in the queue?

Puzzle 3

In this queue the people are Sam, Pia, Quin, Raj and Tia. The first name in your list is the front of the queue.

1. Sam is first.
2. Pia is next to Quin.
3. Pia is before Quin.
4. Raj is after Tia.
5. Tia is not next to Sam.

Which statement must be true?

• A. Quin is next to Sam
• B. Raj is before Tia
• C. Pia is next to Sam
• D. Tia is third

Puzzle 4

In this queue the people are Uma, Vic, Wen and Xav. The first name in your list is the front of the queue.

1. Uma is next to Vic.
2. Vic is before Uma.
3. Xav is last.
4. Vic is not first.

Which statement must be true?

• A. Wen is next to Uma
• B. Vic is second
• C. Uma is before Vic
• D. Xav is third

Puzzle 5

In this queue the people are Eli, Fay, Gus, Hana and Ivy. The first name in your list is the front of the queue.

1. Ivy is last.
2. Gus is next to Hana.
3. Gus is before Hana.
4. Fay is before Eli.
5. Eli is not next to Fay.

Which statement cannot be true?

• A. Fay is first
• B. Hana is next to Eli
• C. Gus is second
• D. Eli is before Gus

Puzzle 6

In this queue the people are Jo, Kai, Lia and Max. The first name in your list is the front of the queue.

1. Max is next to Lia.
2. Max is before Lia.
3. Jo is before Kai.

How many different orders are possible?

Answers with every possibility shown

For each puzzle the list of possibilities comes from the clues that fix places, and the table shows every clue against every order. A ✗ means that clue is broken, and the first ✗ is the reason the order is rejected.

Puzzle 1 answer: Ava

Clue 1 fixes the shape of the queue. It leaves 6 possible orders, listed and checked below.

Order	Clue 1	Clue 2	Clue 3	Clue 4	Result
Dev, Ava, Ben, Cal	✓	✓	✓	✓	Valid
Dev, Ava, Cal, Ben	✓	✓	✓	✗	Rejected by clue 4
Dev, Ben, Ava, Cal	✓	✗	✗	✓	Rejected by clue 2
Dev, Ben, Cal, Ava	✓	✗	✓	✓	Rejected by clue 2
Dev, Cal, Ava, Ben	✓	✓	✗	✗	Rejected by clue 3
Dev, Cal, Ben, Ava	✓	✗	✓	✗	Rejected by clue 2

Only one order passes every clue: Dev → Ava → Ben → Cal.

Puzzle 2 answer: Leo

Clues 1 to 3 fix the shape of the queue. They leave 6 possible orders, listed and checked below.

Order	Clue 1	Clue 2	Clue 3	Clue 4	Clue 5	Result
Kim, Leo, Noor, Omar, Mia	✓	✓	✓	✗	✗	Rejected by clue 4
Kim, Leo, Omar, Noor, Mia	✓	✓	✓	✗	✓	Rejected by clue 4
Noor, Kim, Leo, Omar, Mia	✓	✓	✓	✓	✗	Rejected by clue 5
Noor, Omar, Kim, Leo, Mia	✓	✓	✓	✓	✗	Rejected by clue 5
Omar, Kim, Leo, Noor, Mia	✓	✓	✓	✗	✓	Rejected by clue 4
Omar, Noor, Kim, Leo, Mia	✓	✓	✓	✓	✓	Valid

Only one order passes every clue: Omar → Noor → Kim → Leo → Mia.

Puzzle 3 answer: C. Pia is next to Sam

Clues 1 to 3 fix the shape of the queue. They leave 6 possible orders, listed and checked below.

Order	Clue 1	Clue 2	Clue 3	Clue 4	Clue 5	Result
Sam, Pia, Quin, Raj, Tia	✓	✓	✓	✗	✓	Rejected by clue 4
Sam, Pia, Quin, Tia, Raj	✓	✓	✓	✓	✓	Valid
Sam, Raj, Pia, Quin, Tia	✓	✓	✓	✗	✓	Rejected by clue 4
Sam, Raj, Tia, Pia, Quin	✓	✓	✓	✗	✓	Rejected by clue 4
Sam, Tia, Pia, Quin, Raj	✓	✓	✓	✓	✗	Rejected by clue 5
Sam, Tia, Raj, Pia, Quin	✓	✓	✓	✓	✗	Rejected by clue 5

Only one order passes every clue: Sam → Pia → Quin → Tia → Raj.

Puzzle 4 answer: B. Vic is second

Clues 1 to 3 fix the shape of the queue. They leave 2 possible orders, listed and checked below.

Order	Clue 1	Clue 2	Clue 3	Clue 4	Result
Vic, Uma, Wen, Xav	✓	✓	✓	✗	Rejected by clue 4
Wen, Vic, Uma, Xav	✓	✓	✓	✓	Valid

Only one order passes every clue: Wen → Vic → Uma → Xav.

Puzzle 5 answer: D. Eli is before Gus

Clues 1 to 3 fix the shape of the queue. They leave 6 possible orders, listed and checked below.

Order	Clue 1	Clue 2	Clue 3	Clue 4	Clue 5	Result
Eli, Fay, Gus, Hana, Ivy	✓	✓	✓	✗	✗	Rejected by clue 4
Eli, Gus, Hana, Fay, Ivy	✓	✓	✓	✗	✓	Rejected by clue 4
Fay, Eli, Gus, Hana, Ivy	✓	✓	✓	✓	✗	Rejected by clue 5
Fay, Gus, Hana, Eli, Ivy	✓	✓	✓	✓	✓	Valid
Gus, Hana, Eli, Fay, Ivy	✓	✓	✓	✗	✗	Rejected by clue 4
Gus, Hana, Fay, Eli, Ivy	✓	✓	✓	✓	✗	Rejected by clue 5

Only one order passes every clue: Fay → Gus → Hana → Eli → Ivy.

Puzzle 6 answer: 3 orders

Clues 1 to 2 fix the shape of the queue. They leave 6 possible orders, listed and checked below.

Order	Clue 1	Clue 2	Clue 3	Result
Jo, Kai, Max, Lia	✓	✓	✓	Valid
Jo, Max, Lia, Kai	✓	✓	✓	Valid
Kai, Jo, Max, Lia	✓	✓	✗	Rejected by clue 3
Kai, Max, Lia, Jo	✓	✓	✗	Rejected by clue 3
Max, Lia, Jo, Kai	✓	✓	✓	Valid
Max, Lia, Kai, Jo	✓	✓	✗	Rejected by clue 3

Three orders pass every clue: Jo → Kai → Max → Lia; Jo → Max → Lia → Kai; Max → Lia → Jo → Kai. The answer is 3. A child who stops at the first valid order and writes "1" has not answered the question that was asked.

What mistake patterns should we look for?

• "Next to" read as "somewhere before." The child places Cam anywhere ahead of Bree when the clue says they touch. Ask them to point at the two places that are touching.
• "Before" and "after" swapped. The order comes out reversed. Have them say the clue as "who is nearer the front?" before they place anyone.
• Stopping at the first order that works. Puzzle 6 is built for this. An order that satisfies most clues but breaks one is still wrong.
• Placing every clue at once. Fix one place first, then list. Children who try to hold the whole queue in their head tend to lose a clue.
• Trusting a sensible-looking order. If the table shows one ✗, the order goes, however natural it looks.

Can my child write a clue that leaves only one answer?

Give your child these three clues for Abe, Bea, Cleo and Dan:

1. Dan is last.

2. Bea is before Cleo.

3. Abe is next to Cleo.

4. Ask them to list every order that passes all three clues. There are two.

5. Ask them to write a fourth clue that rules out one of the two and keeps the other.

6. Ask them to check it with a table, the same way as above.

The two orders are Bea → Abe → Cleo → Dan and Bea → Cleo → Abe → Dan. Several fourth clues work, such as "Abe is after Cleo" (which keeps the second) or "Cleo is after Abe" (which keeps the first). A fourth clue is correct only if it removes exactly one of the two orders, so a clue like "Dan is last" fails because it removes neither.

What should we do after this set?

• If your child got the answers by listing, try the same method on a Thinking Skills question in our OC sample questions.
• To see how a full practice paper is put together, read the OC practice tests guide and the OC past papers page.
• For a timed run through the paper, there are free mock tests.
• If you would like structured practice across all three OC components, you can compare the Opportunity Class practice packs. This is optional; these puzzles are free either way.

Sources and review

About the puzzles: all six puzzles, the worked queue and the write-a-clue task are original to Braintree Coaching Australia. Every list of possibilities and every table was produced by checking all possible orders of the people involved, not only the ones shown.

Exam facts used: the three OC components and their multiple-choice format come from the NSW Department of Education OC practice tests page, read on 15 October 2026.

Author: James Rush, content writer, Braintree Coaching Australia.

Review status: the puzzles have not yet been solved blind by a reviewer outside the team, and a named teacher review has not yet been recorded. If an answer looks wrong to you, please tell us.

Last updated: 2026-10-15.