Learn by Novus · Open practice pack v1

Deduction and clues: open practice pack: learner worksheet

25 untimed puzzles on a difficulty 1–5 ladder.

Puzzles are an untimed educational and entertainment activity. They are not a clinical, diagnostic, standardized, or professionally recognized assessment. Solving puzzles here does not produce an IQ score and cannot be used for Mensa qualification, diagnosis, giftedness identification, educational placement, employment selection, disability applications, accommodations, legal matters, or medical decisions. Puzzle items are never used as unseen scored questions in any Novus Learn assessment.

Learner worksheet

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.

Choose one answer for each item. Keep the authored hints, answer key, and worked explanations separate until you are ready to check your work.

Difficulty 1

Start here and establish the method before moving up the ladder.

1. puz-deduction-and-clues-01: The blue trolley · Difficulty 1

Every plant on the blue trolley needs daily watering. The fern is on the blue trolley. What must be true of the fern?

  1. It needs daily watering.
  2. It is the only plant on the trolley that needs daily watering.
  3. Any plant that needs daily watering is on the blue trolley.
  4. It will stop needing daily watering once it leaves the trolley.

Answer:

2. puz-deduction-and-clues-02: The badge rule · Difficulty 1

At one office, everyone who attends the Monday briefing collects a visitor badge from reception. Priya did not collect a visitor badge. What follows?

  1. Priya collected a badge somewhere other than reception.
  2. Priya attended the briefing without a badge.
  3. Priya did not attend the Monday briefing.
  4. Nobody who collected a badge attended the briefing.

Answer:

3. puz-deduction-and-clues-03: Three parcels on the scales · Difficulty 1

The green parcel is heavier than the red parcel. The red parcel is heavier than the grey parcel. Which ordering, heaviest first, is correct?

  1. Red, green, grey.
  2. Green, red, grey.
  3. Grey, red, green.
  4. Green, grey, red.

Answer:

4. puz-deduction-and-clues-04: This morning's loaves · Difficulty 1

All the loaves baked this morning are wholemeal. Some of the loaves baked this morning were sold before noon. Which conclusion is guaranteed?

  1. Every wholemeal loaf was sold before noon.
  2. Some loaves sold before noon were not wholemeal.
  3. Every loaf sold before noon was baked this morning.
  4. Some wholemeal loaves were sold before noon.

Answer:

5. puz-deduction-and-clues-05: Before seven at the depot · Difficulty 1

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?

  1. It was the only vehicle to enter early that day.
  2. It was not a lorry.
  3. It was a lorry, and it broke the rule.
  4. It was a van.

Answer:

Difficulty 2

Continue in order; use the worked explanations from earlier rungs when needed.

6. puz-deduction-and-clues-06: The alarm that stayed silent · Difficulty 2

If the alarm sounds, the doors lock automatically. This morning the alarm did not sound. What follows about the doors?

  1. They stayed unlocked all morning.
  2. They locked anyway, because locking is automatic.
  3. Nothing follows: they may have been locked or unlocked.
  4. They lock only when the alarm sounds.

Answer:

7. puz-deduction-and-clues-07: The wet path · Difficulty 2

If the sprinkler runs, the path becomes wet. This evening the path is wet. What follows about the sprinkler?

  1. It ran this evening.
  2. It did not run this evening.
  3. It runs whenever the path is wet.
  4. Nothing follows: a wet path has other possible causes.

Answer:

8. puz-deduction-and-clues-08: Four runners, three comparisons · Difficulty 2

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.

  1. Jen finished ahead of Kofi.
  2. Ivo finished behind Kofi.
  3. Lena finished ahead of Jen.
  1. Lena
  2. Jen
  3. Kofi
  4. Ivo

Answer:

9. puz-deduction-and-clues-09: One of them is lying · Difficulty 2

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.

  1. Tom says: 'Vera and I both tell the truth.'
  2. Vera says: 'The delivery arrived the day after the meeting, and the meeting was on Monday.'
  1. Sunday
  2. Monday
  3. Tuesday
  4. Wednesday

Answer:

10. puz-deduction-and-clues-10: Tray one · Difficulty 2

All the seedlings in tray one are marigolds. No marigold has been treated with feed. What follows about the seedlings in tray one?

  1. Some of them have been treated with feed.
  2. None of them has been treated with feed.
  3. Every untreated plant is in tray one.
  4. Any plant treated with feed is a marigold.

Answer:

11. puz-deduction-and-clues-11: At least as many · Difficulty 2

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.

  1. Ash scored more than Brook.
  2. Brook scored more than Dawn.
  3. Dawn scored at least as many points as Clay.
  4. No two teams finished on the same score.
  1. Ash
  2. Brook
  3. Dawn
  4. Clay

Answer:

Difficulty 3

Continue in order; use the worked explanations from earlier rungs when needed.

12. puz-deduction-and-clues-12: Three statements, one of them false · Difficulty 3

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.

  1. Nia says: 'Owen forgot to lock up.'
  2. Owen says: 'I did not forget to lock up.'
  3. Ravi says: 'Nia forgot to lock up.'
  1. Nia
  2. Owen
  3. Ravi
  4. Sara

Answer:

13. puz-deduction-and-clues-13: Three workshops, three mornings · Difficulty 3

Which schedule fits every constraint?

A community centre runs three workshops (pottery, coding and first aid) one on each of three mornings.

  1. Each workshop runs on exactly one morning: Monday, Tuesday or Wednesday.
  2. First aid does not run on Monday.
  3. Coding runs on the morning immediately before pottery.
  1. Coding Monday, first aid Tuesday, pottery Wednesday.
  2. First aid Monday, coding Tuesday, pottery Wednesday.
  3. Coding Monday, pottery Tuesday, first aid Wednesday.
  4. Pottery Monday, coding Tuesday, first aid Wednesday.

Answer:

14. puz-deduction-and-clues-14: The supervisor's leap · Difficulty 3

Which criticism of the supervisor's conclusion is the correct one?

Notes from a depot meeting.

  1. Every van in the fleet was serviced in March.
  2. Two vans broke down in April.
  3. The supervisor concludes that the March service was carried out badly.
  1. The facts cover the whole fleet, so nothing can follow about one van.
  2. A breakdown after a service does not by itself show the service failed.
  3. Two breakdowns is too small a number to support any conclusion at all.
  4. The conclusion is safe, since the vans were serviced and then failed.

Answer:

15. puz-deduction-and-clues-15: A rule inside a rule · Difficulty 3

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?

  1. The bridge was open and the driver ignored the rule.
  2. The ferry was running after all.
  3. The bridge is always closed when the ferry is cancelled.
  4. The bridge was not open.

Answer:

16. puz-deduction-and-clues-16: Who brought the tart · Difficulty 3

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.

  1. Cormac brought neither the bread nor the cheese.
  2. Beth brought neither the olives nor the tart.
  3. Dilip brought the cheese.
  4. Cormac did not bring the tart.
  1. Esme
  2. Beth
  3. Cormac
  4. Dilip

Answer:

17. puz-deduction-and-clues-17: Most is not all · Difficulty 3

Most members of the walking group own waterproofs. Everyone who owns waterproofs has walked the coast path. Which conclusion does not follow?

  1. Most members of the group have walked the coast path.
  2. Every member of the group has walked the coast path.
  3. At least one member of the group has walked the coast path.
  4. Some people who own waterproofs have walked the coast path.

Answer:

Difficulty 4

Continue in order; use the worked explanations from earlier rungs when needed.

18. puz-deduction-and-clues-18: Four statements, two of them false · Difficulty 4

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.

  1. Hana says: 'I did not book the room.'
  2. Idris says: 'Jo booked the room.'
  3. Jo says: 'Idris booked the room.'
  4. Kemi says: 'It was Idris who booked the room.'
  1. Hana
  2. Idris
  3. Jo
  4. Kemi

Answer:

19. puz-deduction-and-clues-19: Five in the queue · Difficulty 4

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.

  1. Cai is at the back of the queue.
  2. Dev stands immediately ahead of Amara.
  3. Elin is somewhere ahead of Bo.
  4. Amara is not second.
  5. Bo is not fourth.
  1. Bo
  2. Dev
  3. Amara
  4. Elin

Answer:

20. puz-deduction-and-clues-20: Only if you have paid · Difficulty 4

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?

  1. She may enter the tournament, because the condition is satisfied.
  2. She has entered the tournament.
  3. Anyone who has paid the annual fee may enter the tournament.
  4. Paying is required for entry, but on its own it need not be enough.

Answer:

21. puz-deduction-and-clues-21: The clue that does no work · Difficulty 4

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.

  1. Priya works on Monday.
  2. Quill does not work on Monday.
  3. Rosa works the day immediately after Quill.
  4. Ted does not work on Thursday.
  1. Priya works on Monday.
  2. Quill does not work on Monday.
  3. Rosa works the day immediately after Quill.
  4. Ted does not work on Thursday.

Answer:

22. puz-deduction-and-clues-22: What Priya could not tell · Difficulty 4

What can Quinn work out from Priya's remark?

A bag of counters, and two friends holding one each.

  1. The bag held three red counters and one blue counter.
  2. Priya and Quinn each drew one counter and hold it so that only the other person can see it.
  3. Both of them know exactly what the bag held.
  4. Priya, looking at Quinn's counter, says: 'I cannot tell what colour mine is.'
  1. That her own counter is blue.
  2. That Priya's counter is blue.
  3. That her own counter is red.
  4. Nothing: an admission of ignorance carries no information.

Answer:

Difficulty 5

Continue in order; use the worked explanations from earlier rungs when needed.

23. puz-deduction-and-clues-23: Five statements, at least four true · Difficulty 5

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.

  1. Ana says: 'It was Ben or Cara.'
  2. Ben says: 'I did not switch it off.'
  3. Cara says: 'Ana is telling the truth.'
  4. Dai says: 'Ben is telling the truth.'
  5. Eve says: 'Cara is lying.'
  1. Ana, with two false statements.
  2. Ben, with three false statements.
  3. Dai, with two false statements.
  4. Cara, with one false statement.

Answer:

24. puz-deduction-and-clues-24: Assume it, then break it · Difficulty 5

Four runners finished with no ties. Who finished last?

Farid, Gwen, Hugo and Ines finished in first, second, third and fourth place.

  1. Gwen finished ahead of Hugo.
  2. Farid finished either first or last.
  3. If Farid finished first, then Ines finished ahead of Gwen.
  4. Ines did not finish second.
  1. Farid
  2. Hugo
  3. Ines
  4. Gwen

Answer:

25. puz-deduction-and-clues-25: Four weeks, four colleagues · Difficulty 5

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.

  1. Otto takes an earlier week than Pia.
  2. Mira does not take week one.
  3. Noor takes week three.
  1. Week one.
  2. Week two.
  3. It cannot be determined from the clues.
  4. Week four.

Answer: