1. The blue trolley
Every plant on the blue trolley needs daily watering. The fern is on the blue trolley. What must be true of the fern?
Show a hint
One sentence is a general rule; the other names a case that falls under it.
Puzzles · difficulty 1–5
Deduction and clues
Twenty-five puzzles about what actually follows. You work from stated rules, comparisons and statements to a single fact — and, on the last rung, to the honest verdict that the clues do not settle it. Each explanation names the technique so you can spot the same shape next time.
What this category trains
- Valid steps and their invalid look-alikes
- Quantifier care: all, no, most, some
- Ordering and scheduling under constraints
- Truth-teller and liar bookkeeping
- Recognising when clues underdetermine the answer
25 puzzles · about 55 minutes end to end, as a guide only · untimed
The ladder
The puzzles below run in difficulty order, easiest first. Each one checks on its own and shows its explanation straight away, so you get the method for one rung before you attempt the next.
Work down the ladder in order. The early puzzles need one rule applied once; the last three need a named technique — a counting bound, an assumption driven to a contradiction, or a check for whether the clues settle the question at all. Nothing here is timed and nothing is scored. Read the explanation after every puzzle, including the ones you get right: the method it names is the part that transfers. Pen and paper start to help from about the middle of the set.
2. The badge rule
At one office, everyone who attends the Monday briefing collects a visitor badge from reception. Priya did not collect a visitor badge. What follows?
Show a hint
Suppose for a moment that she had attended, and see what the rule would then force.
3. Three parcels on the scales
The green parcel is heavier than the red parcel. The red parcel is heavier than the grey parcel. Which ordering, heaviest first, is correct?
Show a hint
Both comparisons mention the same parcel; use it to join them into one chain.
4. This morning's loaves
All the loaves baked this morning are wholemeal. Some of the loaves baked this morning were sold before noon. Which conclusion is guaranteed?
Show a hint
Take the loaves sold before noon and ask what the rule lets you call them.
5. Before seven at the depot
No lorry enters the depot before seven in the morning. A vehicle entered the depot at half past six. What must be true of that vehicle?
Show a hint
The sentence describes what happens at the depot, not what would be permitted.
6. The alarm that stayed silent
If the alarm sounds, the doors lock automatically. This morning the alarm did not sound. What follows about the doors?
Show a hint
Ask whether the rule says anything at all about mornings when the alarm stays silent.
7. The wet path
If the sprinkler runs, the path becomes wet. This evening the path is wet. What follows about the sprinkler?
Show a hint
List two other ways a path gets wet, then ask whether the rule rules them out.
8. Four runners, three comparisons
Four runners finished with no ties. Who won?
Ivo, Jen, Kofi and Lena finished a race in some order. 'Ahead of' means in a better finishing position.
- Jen finished ahead of Kofi.
- Ivo finished behind Kofi.
- Lena finished ahead of Jen.
Show a hint
Turn each comparison into a link and join all three into one line before reading off the front.
9. One of them is lying
Exactly one of the two always tells the truth. On which day did the delivery arrive?
Tom and Vera work in the same store. One of them always tells the truth and the other always lies.
- Tom says: 'Vera and I both tell the truth.'
- Vera says: 'The delivery arrived the day after the meeting, and the meeting was on Monday.'
Show a hint
Start with the speaker whose claim would break the stated setup if it were true.
10. Tray one
All the seedlings in tray one are marigolds. No marigold has been treated with feed. What follows about the seedlings in tray one?
Show a hint
Relabel the tray-one seedlings using the first sentence, then apply the second to that label.
11. At least as many
Four quiz teams finished on four different scores. Which team came last?
Ash, Brook, Clay and Dawn each finished the quiz with a points total.
- Ash scored more than Brook.
- Brook scored more than Dawn.
- Dawn scored at least as many points as Clay.
- No two teams finished on the same score.
Show a hint
One clue leaves room for a tie; another closes it. Read those two together.
12. Three statements, one of them false
Exactly one of the three statements below is false. Who forgot to lock up?
Nia, Owen, Ravi and Sara share the closing duty. Exactly one of the four forgot to lock up last night, and three of them have spoken.
- Nia says: 'Owen forgot to lock up.'
- Owen says: 'I did not forget to lock up.'
- Ravi says: 'Nia forgot to lock up.'
Show a hint
Test each person in turn as the one who forgot, and count how many statements come out false.
13. Three workshops, three mornings
Which schedule fits every constraint?
A community centre runs three workshops — pottery, coding and first aid — one on each of three mornings.
- Each workshop runs on exactly one morning: Monday, Tuesday or Wednesday.
- First aid does not run on Monday.
- Coding runs on the morning immediately before pottery.
Show a hint
Place the pair that must sit side by side first, then see which morning is left over.
14. The supervisor's leap
Which criticism of the supervisor's conclusion is the correct one?
Notes from a depot meeting.
- Every van in the fleet was serviced in March.
- Two vans broke down in April.
- The supervisor concludes that the March service was carried out badly.
Show a hint
Ask what else, apart from a poor service, could put a van off the road in April.
15. A rule inside a rule
If the ferry is cancelled, then if the bridge is open the coach takes the bridge route. Today the ferry was cancelled and the coach did not take the bridge route. What follows?
Show a hint
Use the given fact to unlock the inner rule, then run that inner rule backwards.
16. Who brought the tart
Four neighbours each brought exactly one item to a shared lunch. Who brought the tart?
Beth, Cormac, Dilip and Esme brought the bread, the cheese, the olives and the tart between them, one item each.
- Cormac brought neither the bread nor the cheese.
- Beth brought neither the olives nor the tart.
- Dilip brought the cheese.
- Cormac did not bring the tart.
Show a hint
Find the person ruled out of three of the four items and give them what is left.
17. Most is not all
Most members of the walking group own waterproofs. Everyone who owns waterproofs has walked the coast path. Which conclusion does not follow?
Show a hint
Picture a group where a clear majority, but not everyone, owns waterproofs.
18. Four statements, two of them false
Exactly one of the four booked the room, and exactly two of their statements are false. Who booked it?
Hana, Idris, Jo and Kemi each say one thing about who booked the meeting room.
- Hana says: 'I did not book the room.'
- Idris says: 'Jo booked the room.'
- Jo says: 'Idris booked the room.'
- Kemi says: 'It was Idris who booked the room.'
Show a hint
Take each name in turn as the one who booked, and count the false statements that follow.
19. Five in the queue
Five people stand in a single queue. Who is second?
Amara, Bo, Cai, Dev and Elin stand in a queue. Position one is at the front; 'ahead of' means closer to the front.
- Cai is at the back of the queue.
- Dev stands immediately ahead of Amara.
- Elin is somewhere ahead of Bo.
- Amara is not second.
- Bo is not fourth.
Show a hint
Start with the clue that fixes a position outright, then try the welded pair in each place it can start.
20. Only if you have paid
A club rule says: you may enter the tournament only if you have paid the annual fee. Farrah has paid the annual fee. What follows about her entry?
Show a hint
Rewrite the rule as an arrow: does it run from entry to payment, or the other way?
21. The clue that does no work
The four clues fix the rota exactly. One of them could be deleted with the rota still fixed. Which clue is it?
Priya, Quill, Rosa and Ted each work exactly one day of the week: Monday, Tuesday, Wednesday or Thursday.
- Priya works on Monday.
- Quill does not work on Monday.
- Rosa works the day immediately after Quill.
- Ted does not work on Thursday.
Show a hint
Cover each clue in turn and check whether the other three still pin down every day.
22. What Priya could not tell
What can Quinn work out from Priya's remark?
A bag of counters, and two friends holding one each.
- The bag held three red counters and one blue counter.
- Priya and Quinn each drew one counter and hold it so that only the other person can see it.
- Both of them know exactly what the bag held.
- Priya, looking at Quinn's counter, says: 'I cannot tell what colour mine is.'
Show a hint
Ask what she would have said if the counter she was looking at had been the blue one.
23. Five statements, at least four true
Exactly one of the five switched the boiler off. Who was it, and how many statements are false?
Ana, Ben, Cara, Dai and Eve were the only people in the building. At least four of the five statements below are true.
- Ana says: 'It was Ben or Cara.'
- Ben says: 'I did not switch it off.'
- Cara says: 'Ana is telling the truth.'
- Dai says: 'Ben is telling the truth.'
- Eve says: 'Cara is lying.'
Show a hint
Work through the five candidates one at a time and tally which statements survive in each case.
24. Assume it, then break it
Four runners finished with no ties. Who finished last?
Farid, Gwen, Hugo and Ines finished in first, second, third and fourth place.
- Gwen finished ahead of Hugo.
- Farid finished either first or last.
- If Farid finished first, then Ines finished ahead of Gwen.
- Ines did not finish second.
Show a hint
The clue offering two possibilities is where to start: try one branch and see whether it survives.
25. Four weeks, four colleagues
Each colleague takes a different week of leave. Which week does Mira take?
Mira, Noor, Otto and Pia each take one week of leave, in weeks one, two, three and four of the month.
- Otto takes an earlier week than Pia.
- Mira does not take week one.
- Noor takes week three.
Show a hint
Before settling on a week, try to build two different rotas that both obey every clue.
Skills these puzzles practise
Each category maps onto the shared aptitude constructs, so a puzzle that interests you has a lesson and a larger practice bank behind it:
- Deductive reasoning
Applying stated rules and constraints to reach valid conclusions.
- Critical thinking
Evaluating evidence, assumptions, arguments, credibility, and alternative explanations.
- Case analysis
Synthesizing multiple documents and making a reasoned recommendation.
- Logical reasoning
Conditional logic, syllogisms, ordering, grouping, argument structure, and constraint problems.
- Problem solving
Selecting methods, combining information, troubleshooting, and reaching practical solutions.
- Planning and scheduling exercises
Resources, dependencies, deadlines, constraints, and contingency planning.
- Working memory
Holding, updating, and manipulating short sequences, rules, or instructions.
Other puzzle categories
- Logic grids — 25 puzzles · Constraint tracking
- Number sequences — 25 puzzles · Inducing a rule from a short run
- Word and letter — 25 puzzles · Letter-position reasoning
- Lateral thinking — 25 puzzles · Surfacing hidden assumptions
- Spatial and visual — 25 puzzles · Mental rotation and reflection
- Maths puzzles — 25 puzzles · Multi-step arithmetic without a calculator
- Codes and ciphers — 25 puzzles · Substitution and transposition systems