Puzzles · difficulty 15

Logic grids

Constraint puzzles solved by ticking and crossing a grid. Each one gives you a small cast, a set of attributes, and clues that never state the whole answer — so you close the board by elimination, negative inference, and, at the top of the ladder, a hypothesis you deliberately break.

What this category trains

25 puzzles · about 70 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 through the ladder in order — the early puzzles teach the notation the later ones assume. Sketch the grid, tick a cell when a clue confirms a pairing, and cross the rest of that cell's row and column straight away; most of the work in a logic grid is done by the crosses, not the ticks. Nothing here is timed, and checking an answer shows you the method, so read the explanation even when you were right.

1. Two at the counter

Difficulty 1 of 5 · Warm-up

Iris and Owen each collect one drink from the counter. Which pairing satisfies both clues?

Two colleagues, two drinks, one drink each.
RowTeaCoffee
Irisblankblank
Owenblankblank

Clues

  1. Iris and Owen order different drinks.
  2. Iris does not order the coffee.
Show a hint

Start from the clue that rules something out. With only two drinks on the board, it settles everything.

Answers for Two at the counter

2. Repainting the lane

Difficulty 1 of 5 · Warm-up

Two houses on the same lane are repainted, one in green and one in cream. Which pairing fits the clues?

Two houses, two colours, one colour each.
RowGreenCream
House 4blankblank
House 6blankblank

Clues

  1. One house is painted green and the other is painted cream.
  2. House 6 is painted green.
Show a hint

One clue fills a cell on its own. Place that tick first, then see what it removes from the rest of the grid.

Answers for Repainting the lane

3. A two-runner finish

Difficulty 1 of 5 · Warm-up

Two runners finish a short race. Using the clues, which pairing of runners to places is correct?

Two runners, two finishing places.
RowFirstSecond
Priyablankblank
Raviblankblank

Clues

  1. Only two runners finished, and they took first and second place.
  2. Ravi crossed the line before Priya.
Show a hint

Turn the comparison into a plain ordering — who is ahead of whom — before you touch the grid.

Answers for A two-runner finish

4. Two boxes on the shelf

Difficulty 1 of 5 · Warm-up

A striped box and a plain box sit on a shelf. One holds a ribbon and the other holds buttons. Which pairing is correct?

Two boxes, two items, one item each.
RowRibbonButtons
Striped boxblankblank
Plain boxblankblank

Clues

  1. Each box holds exactly one of the two items.
  2. The plain box does not hold the ribbon.
Show a hint

Rewrite the negative clue as a positive statement about the other box before you fill anything in.

Answers for Two boxes on the shelf

5. Covering the two shifts

Difficulty 1 of 5 · Warm-up

A shop runs an early shift starting at 7am and a late shift starting at 2pm. Hana and Marek cover one shift each. Which rota fits the clues?

Two shifts, two staff, one shift each.
RowEarly shift (7am)Late shift (2pm)
Hanablankblank
Marekblankblank

Clues

  1. Each shift is covered by exactly one person, and nobody covers both.
  2. Hana is unable to start work before midday.
  3. Marek is happy to take whichever shift is left.
Show a hint

Convert the sentence about when Hana can start into a cross in one cell, then read the grid.

Answers for Covering the two shifts

6. Three friends, three fruits

Difficulty 2 of 5 · Straightforward

Bea, Callum and Dilan each take one piece of fruit from a bowl holding an apple, a pear and a plum. Which set of pairings is correct?

Three friends, three fruits, one fruit each.
RowApplePearPlum
Beablankblankblank
Callumblankblankblank
Dilanblankblankblank

Clues

  1. Each friend takes exactly one fruit, and no two friends take the same fruit.
  2. Bea takes the pear.
  3. Dilan takes the apple.
Show a hint

Two of the three fruits are handed out directly. Count what is left rather than reasoning about it.

Answers for Three friends, three fruits

7. Three vehicles, three colours

Difficulty 2 of 5 · Straightforward

A hire firm keeps a hatchback, an estate and a van, each a different colour: silver, navy or red. Which set of pairings is correct?

Three vehicles, three colours, one colour each.
RowSilverNavyRed
Hatchbackblankblankblank
Estateblankblankblank
Vanblankblankblank

Clues

  1. Each vehicle is a different colour.
  2. The van is red.
  3. The hatchback is not silver.
Show a hint

Place the vehicle whose colour is stated outright, then re-read the exclusion against what remains.

Answers for Three vehicles, three colours

8. Three deliveries, three days

Difficulty 2 of 5 · Straightforward

Books, plants and tiles are delivered to a workshop on Monday, Tuesday and Wednesday, one delivery a day. Which set of pairings is correct?

Three deliveries, three days, one delivery a day.
RowMondayTuesdayWednesday
Booksblankblankblank
Plantsblankblankblank
Tilesblankblankblank

Clues

  1. The three deliveries arrive on three different days.
  2. The plants arrive on Tuesday.
  3. The tiles arrive earlier in the week than the books.
Show a hint

Fix the delivery whose day is stated, then apply the ordering clue only to the days still open.

Answers for Three deliveries, three days

9. Three pets, three owners

Difficulty 2 of 5 · Straightforward

Eve, Femi and Grace each own one of a cat, a rabbit and a parrot. Every clue below is a denial. Which set of pairings is correct?

Three owners, three pets, one pet each.
RowCatRabbitParrot
Eveblankblankblank
Femiblankblankblank
Graceblankblankblank

Clues

  1. Each person owns exactly one pet, and each pet has exactly one owner.
  2. Eve does not own the parrot.
  3. Grace does not own the parrot.
  4. Eve does not own the rabbit.
Show a hint

Two clues talk about the same pet. Read down that column and count how many owners are ruled out.

Answers for Three pets, three owners

10. Desks on three floors

Difficulty 2 of 5 · Straightforward

Ines, Jonah and Kemi have desks on the first, second and third floors of the same building, one desk to a floor. Which set of pairings is correct?

Three people, three floors, one desk on each floor.
RowFirst floorSecond floorThird floor
Inesblankblankblank
Jonahblankblankblank
Kemiblankblankblank

Clues

  1. Each person's desk is on a different floor.
  2. Jonah's desk is on the second floor.
  3. Kemi's desk is higher up than Ines's desk.
Show a hint

Place the desk whose floor is stated first; the comparison then has only two floors to sort out.

Answers for Desks on three floors

11. Three teams, three scores

Difficulty 2 of 5 · Straightforward

The Larks, the Otters and the Swifts scored 12, 18 and 24 points in a quiz, in some order. Which set of pairings is correct?

Three teams, three scores, one score each.
Row12 points18 points24 points
Larksblankblankblank
Ottersblankblankblank
Swiftsblankblankblank

Clues

  1. The three teams scored 12, 18 and 24 points, with no two teams on the same score.
  2. The Otters scored the most points of the three.
  3. The Larks did not score 18.
Show a hint

Superlatives name a single cell. Work out what scoring the most can only mean before reading on.

Answers for Three teams, three scores

12. Subjects and study days

Difficulty 3 of 5 · Tricky

Amara, Bo and Cleo each study one subject and each attend on one day. Which subject does Bo study, and on which day does Bo attend?

Three students, each with one subject and one study day.
RowSubjectDay
Amarablankblank
Boblankblank
Cleoblankblank

Clues

  1. The subjects are geology, statistics and poetry; the days are Monday, Wednesday and Friday. No subject and no day is shared.
  2. Amara studies statistics.
  3. Bo does not study poetry.
  4. Cleo attends on Monday.
  5. Amara does not attend on Friday.
Show a hint

No clue here links a subject to a day. Solve the two attributes as separate grids, then read them together.

Answers for Subjects and study days

13. Three shops, three streets

Difficulty 3 of 5 · Tricky

Dara, Esme and Frank each run one shop selling one product on one street. What does Dara sell, and on which street does that shop stand?

Three shopkeepers, each with one product and one street.
RowProductStreet
Darablankblank
Esmeblankblank
Frankblankblank

Clues

  1. The products are candles, cheese and cameras; the streets are Bridge Street, Mill Street and Quay Street. No product and no street is shared.
  2. Esme's shop sells cheese.
  3. The camera shop is not on Mill Street.
  4. Dara's shop is on Mill Street.
  5. Frank's shop is not on Bridge Street.
Show a hint

One clue crosses out a product-and-street pairing. Work out which shopkeeper stands on that street.

Answers for Three shops, three streets

14. Players and their towns

Difficulty 3 of 5 · Tricky

Rosa, Sami and Tomas each play one instrument and each live in one town. Which instrument does Sami play, and in which town does Sami live?

Three musicians, each with one instrument and one town.
RowInstrumentTown
Rosablankblank
Samiblankblank
Tomasblankblank

Clues

  1. The instruments are the cello, the flute and the oboe; the towns are Ashford, Brindle and Calder. No instrument and no town is shared.
  2. Tomas plays the flute.
  3. The cellist lives in Brindle.
  4. Tomas lives in Ashford.
  5. Sami does not play the cello.
Show a hint

One clue names an instrument and a town but no person. Work out who plays that instrument first.

Answers for Players and their towns

15. Three morning departures

Difficulty 3 of 5 · Tricky

Three trains leave a station at 09:10, 09:25 and 09:40, each from a different platform and each to a different town. From which platform does the 09:40 leave, and where is it going?

Three departures, each with one platform and one destination.
RowPlatformDestination
09:10blankblank
09:25blankblank
09:40blankblank

Clues

  1. The platforms are 1, 2 and 3; the destinations are Fenwick, Garrow and Hollin. No platform and no destination is shared.
  2. The 09:25 leaves from platform 2.
  3. The Fenwick train leaves from platform 3.
  4. The 09:10 does not go to Garrow.
  5. The Garrow train leaves from a lower-numbered platform than the Hollin train.
Show a hint

Work out which two platforms are still in play before you use the higher-and-lower comparison.

Answers for Three morning departures

16. Three lockers at the pool

Difficulty 3 of 5 · Tricky

Iva, Jae and Kit each use one of lockers 1, 2 and 3, and each locker holds one item. Which locker does Jae use, and what is inside it?

Three people, each with one locker and one item inside it.
RowLockerContents
Ivablankblank
Jaeblankblank
Kitblankblank

Clues

  1. The lockers are 1, 2 and 3; the items are boots, a helmet and a towel. No locker and no item is shared.
  2. The towel is in locker 2.
  3. Kit uses neither locker 1 nor locker 2.
  4. Iva has the boots.
Show a hint

One clue rules the same person out of two lockers. Mark both crosses before you read anything else.

Answers for Three lockers at the pool

17. Three morning appointments

Difficulty 3 of 5 · Tricky

Lena, Mo and Nils have appointments at 10:00, 10:30 and 11:00, one each. Who is seen at 10:30, and who is seen at 11:00?

Three people, three appointment times, one appointment each.
Row10:0010:3011:00
Lenablankblankblank
Moblankblankblank
Nilsblankblankblank

Clues

  1. The three appointments are at 10:00, 10:30 and 11:00, one person each.
  2. Nils is seen immediately before Mo.
  3. Lena is not seen at 11:00.
Show a hint

Treat the two consecutive appointments as one block and list every position that block could occupy.

Answers for Three morning appointments

18. Four flats, four floors

Difficulty 4 of 5 · Hard

A block has one flat on each of floors 1 to 4, and Priya, Quinn, Rafe and Suki live one to a flat. Who lives on the top floor?

Four floors, four residents, one resident to a floor.
RowPriyaQuinnRafeSuki
Floor 4 (top)blankblankblankblank
Floor 3blankblankblankblank
Floor 2blankblankblankblank
Floor 1blankblankblankblank

Clues

  1. Each resident lives on a different floor.
  2. Priya lives on floor 3.
  3. Suki lives on neither floor 1 nor floor 4.
  4. Rafe does not live on floor 4.
Show a hint

The person on the top floor is never named by any clue. Place everyone who is named and see who is left over.

Answers for Four flats, four floors

19. Four scores, four roles

Difficulty 4 of 5 · Hard

Tara, Ubaid, Vera and Wren each took one role and each scored 61, 68, 74 or 80 on a shared exercise. Which role did Vera take, and what did she score?

Four candidates, each with one score and one role.
RowScoreRole
Tarablankblank
Ubaidblankblank
Verablankblank
Wrenblankblank

Clues

  1. The scores are 61, 68, 74 and 80 and the roles are analyst, designer, editor and planner. No score and no role is shared.
  2. Vera scored higher than Tara but did not score the highest.
  3. The editor scored 80.
  4. Ubaid scored the lowest of the four.
  5. Tara is the designer.
  6. The planner scored the lowest of the four.
Show a hint

That comparison carries two restrictions at once. Write both of them down before you place any score.

Answers for Four scores, four roles

20. Four books on a shelf

Difficulty 4 of 5 · Hard

Four books — Salt Road, Winter Ledger, Paper Kites and Quiet Fen — each have a different author and a different genre. Who wrote the romance, and which book is it?

Four books, each with one author and one genre.
RowAuthorGenre
Salt Roadblankblank
Winter Ledgerblankblank
Paper Kitesblankblank
Quiet Fenblankblank

Clues

  1. The authors are Ade, Bex, Cass and Dov; the genres are crime, history, romance and travel. No author and no genre is shared.
  2. Salt Road is neither the crime novel nor the history book.
  3. Bex wrote Quiet Fen.
  4. The travel book was written by Cass.
  5. Winter Ledger is the crime novel.
  6. Quiet Fen is not the history book.
  7. Dov wrote the history book.
Show a hint

Split the neither-nor clue into two separate crosses and see which title is left holding history.

Answers for Four books on a shelf

21. Four stalls in a row

Difficulty 4 of 5 · Hard

Four market stalls stand in a row at positions 1 to 4, counting from the entrance. Which stall is at position 2?

Four stalls, four positions in a row, one stall to a position.
RowBreadCheeseFlowersHoney
Position 1blankblankblankblank
Position 2blankblankblankblank
Position 3blankblankblankblank
Position 4blankblankblankblank

Clues

  1. The four stalls occupy positions 1 to 4, one stall to a position.
  2. The bread stall is directly to the left of the cheese stall.
  3. The honey stall is at position 4.
  4. The flower stall is not next to the cheese stall.
Show a hint

Two stalls must stand side by side. List every place that pair could sit, then test each against the rest.

Answers for Four stalls in a row

22. Four projects, four deadlines

Difficulty 4 of 5 · Hard

A team runs a survey, a rebuild, an audit and a launch. Each has a different lead and is due in a different month. Which project does Nia lead, and when is it due?

Four projects, each with one lead and one deadline month.
RowLeadDue month
Surveyblankblank
Rebuildblankblank
Auditblankblank
Launchblankblank

Clues

  1. The leads are Kai, Lin, Moss and Nia; the deadlines are March, April, May and June. No lead and no month is shared.
  2. Kai leads the audit.
  3. The rebuild is due neither in March nor in June.
  4. The survey is due in March.
  5. Lin's project is due in June.
  6. Moss's project is due in May.
Show a hint

One clue closes two months for the same project. Shrink that project's row first, then test what remains.

Answers for Four projects, four deadlines

23. Four labs, four topics

Difficulty 5 of 5 · Toughest

Anya, Boris, Cato and Dena each work in one of labs 1 to 4 and each study one topic. Which topic does Boris study, and in which lab?

Four researchers, each with one lab and one topic.
RowLabTopic
Anyablankblank
Borisblankblank
Catoblankblank
Denablankblank

Clues

  1. The labs are 1, 2, 3 and 4; the topics are algae, basalt, coral and resin. No lab and no topic is shared.
  2. Anya works in lab 1.
  3. If Boris works in lab 2, then Dena studies basalt.
  4. Dena studies coral.
  5. Cato does not work in lab 2.
  6. Boris works in a higher-numbered lab than Cato.
  7. The algae study is carried out in lab 1.
  8. Cato does not study resin.
Show a hint

One clue is an if-then. Check whether its second half is already false before you try to use its first half.

Answers for Four labs, four topics

24. The clue you can spare

Difficulty 5 of 5 · Toughest

Four flights each leave from a different gate at a different time. The timetable below has exactly one solution, and exactly one of the last four clues can be deleted without making it ambiguous. Which clue is that?

Four flights, each with one gate and one departure time.
RowGateDeparture
Ardal flightblankblank
Brenn flightblankblank
Corve flightblankblank
Duns flightblankblank

Clues

  1. The gates are 1, 2, 3 and 4; the departures are 06:00, 07:00, 08:00 and 09:00. No gate and no time is shared.
  2. The Ardal flight leaves at 06:00.
  3. The Corve flight leaves from gate 4.
  4. The flight at gate 1 leaves at 07:00.
  5. The Duns flight leaves later than the Corve flight.
  6. The Ardal flight leaves from gate 3.
  7. The Brenn flight does not leave from gate 2.
Show a hint

Delete one clue at a time and ask whether the timetable still has exactly one solution without it.

Answers for The clue you can spare

25. Four households, one assumption

Difficulty 5 of 5 · Toughest

Four households each live on a different street and keep a different vehicle. Which household keeps the bicycle, and on which street do they live?

Four households, each with one street and one vehicle.
RowStreetVehicle
Ahernblankblank
Brillblankblank
Cowanblankblank
Drayblankblank

Clues

  1. The streets are Larch Row, Marsh Lane, Nettle Way and Oak Rise; the vehicles are a bicycle, an estate car, a motorbike and a van. No street and no vehicle is shared.
  2. At least one of these two statements is true: the van is kept on Larch Row, or Dray lives on Marsh Lane.
  3. Ahern lives on neither Larch Row nor Nettle Way.
  4. Cowan lives on neither Nettle Way nor Oak Rise.
  5. Neither Brill nor Cowan keeps the van.
  6. Dray keeps neither the motorbike nor the van.
  7. The estate car is kept on Nettle Way.
Show a hint

Nothing is placed outright. Take one half of the either-or clue as true and follow it until something breaks.

Answers for Four households, one assumption

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:

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