Logic grids: open practice pack ############################### 25 untimed puzzles on a difficulty 1–5 ladder. Pack: puzzles-logic-grids Source: puzzles Pack version: v1 Worksheet items: 25 Authored hints: 25 Worked explanations: 25 ! 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. ! The answer key and worked explanations in this file belong only to this public, untimed educational practice source. No active aptitude suite or Novus Reasoning Challenge answer key is ever included in any download. Learner worksheet ================= 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. 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-logic-grids-01: Two at the counter ----------------------------------------- Difficulty: Difficulty 1 Iris and Owen each collect one drink from the counter. Which pairing satisfies both clues? Two colleagues, two drinks, one drink each. Row Tea Coffee ---- --- ------ Iris - - Owen - - 1. Iris and Owen order different drinks. 2. Iris does not order the coffee. - A. Iris: coffee; Owen: tea - B. Iris: tea; Owen: coffee - C. Iris: tea; Owen: tea - D. Iris: coffee; Owen: coffee Your answer: ______ 2. puz-logic-grids-02: Repainting the lane ------------------------------------------ Difficulty: Difficulty 1 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. Row Green Cream ------- ----- ----- House 4 - - House 6 - - 1. One house is painted green and the other is painted cream. 2. House 6 is painted green. - A. House 4: cream; House 6: green - B. House 4: green; House 6: cream - C. House 4: green; House 6: green - D. House 4: cream; House 6: cream Your answer: ______ 3. puz-logic-grids-03: A two-runner finish ------------------------------------------ Difficulty: Difficulty 1 Two runners finish a short race. Using the clues, which pairing of runners to places is correct? Two runners, two finishing places. Row First Second ----- ----- ------ Priya - - Ravi - - 1. Only two runners finished, and they took first and second place. 2. Ravi crossed the line before Priya. - A. Ravi: second; Priya: first - B. Ravi: first; Priya: second - C. Ravi: first; Priya: first - D. Ravi: second; Priya: second Your answer: ______ 4. puz-logic-grids-04: Two boxes on the shelf --------------------------------------------- Difficulty: Difficulty 1 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. Row Ribbon Buttons ----------- ------ ------- Striped box - - Plain box - - 1. Each box holds exactly one of the two items. 2. The plain box does not hold the ribbon. - A. Striped: buttons; Plain: ribbon - B. Striped: buttons; Plain: buttons - C. Striped: ribbon; Plain: ribbon - D. Striped: ribbon; Plain: buttons Your answer: ______ 5. puz-logic-grids-05: Covering the two shifts ---------------------------------------------- Difficulty: Difficulty 1 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. Row Early shift (7am) Late shift (2pm) ----- ----------------- ---------------- Hana - - Marek - - 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. - A. Hana: late shift; Marek: early shift - B. Hana: early shift; Marek: late shift - C. Hana: early shift; Marek: early shift - D. Hana: late shift; Marek: late shift Your answer: ______ Difficulty 2 ------------ Continue in order; use the worked explanations from earlier rungs when needed. 6. puz-logic-grids-06: Three friends, three fruits -------------------------------------------------- Difficulty: Difficulty 2 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. Row Apple Pear Plum ------ ----- ---- ---- Bea - - - Callum - - - Dilan - - - 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. - A. Bea: pear; Callum: apple; Dilan: plum - B. Bea: apple; Callum: plum; Dilan: pear - C. Bea: pear; Callum: plum; Dilan: apple - D. Bea: plum; Callum: pear; Dilan: apple Your answer: ______ 7. puz-logic-grids-07: Three vehicles, three colours ---------------------------------------------------- Difficulty: Difficulty 2 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. Row Silver Navy Red --------- ------ ---- --- Hatchback - - - Estate - - - Van - - - 1. Each vehicle is a different colour. 2. The van is red. 3. The hatchback is not silver. - A. Hatchback silver, estate navy, van red - B. Hatchback navy, estate silver, van red - C. Hatchback navy, estate red, van silver - D. Hatchback red, estate navy, van silver Your answer: ______ 8. puz-logic-grids-08: Three deliveries, three days --------------------------------------------------- Difficulty: Difficulty 2 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. Row Monday Tuesday Wednesday ------ ------ ------- --------- Books - - - Plants - - - Tiles - - - 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. - A. Books Monday, plants Tuesday, tiles Wednesday - B. Tiles Tuesday, plants Monday, books Wednesday - C. Tiles Monday, books Tuesday, plants Wednesday - D. Tiles Monday, plants Tuesday, books Wednesday Your answer: ______ 9. puz-logic-grids-09: Three pets, three owners ----------------------------------------------- Difficulty: Difficulty 2 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. Row Cat Rabbit Parrot ----- --- ------ ------ Eve - - - Femi - - - Grace - - - 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. - A. Eve cat, Femi parrot, Grace rabbit - B. Eve cat, Femi rabbit, Grace parrot - C. Eve rabbit, Femi parrot, Grace cat - D. Eve parrot, Femi cat, Grace rabbit Your answer: ______ 10. puz-logic-grids-10: Desks on three floors --------------------------------------------- Difficulty: Difficulty 2 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. Row First floor Second floor Third floor ----- ----------- ------------ ----------- Ines - - - Jonah - - - Kemi - - - 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. - A. Ines third, Jonah second, Kemi first - B. Ines first, Jonah third, Kemi second - C. Ines first, Jonah second, Kemi third - D. Ines second, Jonah first, Kemi third Your answer: ______ 11. puz-logic-grids-11: Three teams, three scores ------------------------------------------------- Difficulty: Difficulty 2 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. Row 12 points 18 points 24 points ------ --------- --------- --------- Larks - - - Otters - - - Swifts - - - 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. - A. Larks 18, Otters 24, Swifts 12 - B. Larks 12, Otters 24, Swifts 18 - C. Larks 12, Otters 18, Swifts 24 - D. Larks 24, Otters 18, Swifts 12 Your answer: ______ Difficulty 3 ------------ Continue in order; use the worked explanations from earlier rungs when needed. 12. puz-logic-grids-12: Subjects and study days ----------------------------------------------- Difficulty: Difficulty 3 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. Row Subject Day ----- ------- --- Amara - - Bo - - Cleo - - 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. - A. Geology, Wednesday - B. Poetry, Friday - C. Statistics, Friday - D. Geology, Friday Your answer: ______ 13. puz-logic-grids-13: Three shops, three streets -------------------------------------------------- Difficulty: Difficulty 3 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. Row Product Street ----- ------- ------ Dara - - Esme - - Frank - - 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. - A. Cameras, Mill Street - B. Candles, Quay Street - C. Candles, Mill Street - D. Cheese, Mill Street Your answer: ______ 14. puz-logic-grids-14: Players and their towns ----------------------------------------------- Difficulty: Difficulty 3 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. Row Instrument Town ----- ---------- ---- Rosa - - Sami - - Tomas - - 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. - A. Oboe, Calder - B. Cello, Brindle - C. Flute, Calder - D. Oboe, Brindle Your answer: ______ 15. puz-logic-grids-15: Three morning departures ------------------------------------------------ Difficulty: Difficulty 3 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. Row Platform Destination ----- -------- ----------- 09:10 - - 09:25 - - 09:40 - - 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. - A. Platform 3, Fenwick - B. Platform 1, Garrow - C. Platform 2, Garrow - D. Platform 1, Hollin Your answer: ______ 16. puz-logic-grids-16: Three lockers at the pool ------------------------------------------------- Difficulty: Difficulty 3 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. Row Locker Contents --- ------ -------- Iva - - Jae - - Kit - - 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. - A. Locker 1, boots - B. Locker 3, helmet - C. Locker 2, boots - D. Locker 2, towel Your answer: ______ 17. puz-logic-grids-17: Three morning appointments -------------------------------------------------- Difficulty: Difficulty 3 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. Row 10:00 10:30 11:00 ---- ----- ----- ----- Lena - - - Mo - - - Nils - - - 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. - A. Nils at 10:30, Lena at 11:00 - B. Mo at 10:30, Nils at 11:00 - C. Nils at 10:30, Mo at 11:00 - D. Lena at 10:30, Mo at 11:00 Your answer: ______ Difficulty 4 ------------ Continue in order; use the worked explanations from earlier rungs when needed. 18. puz-logic-grids-18: Four flats, four floors ----------------------------------------------- Difficulty: Difficulty 4 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. Row Priya Quinn Rafe Suki ------------- ----- ----- ---- ---- Floor 4 (top) - - - - Floor 3 - - - - Floor 2 - - - - Floor 1 - - - - 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. - A. Quinn - B. Rafe - C. Suki - D. Priya Your answer: ______ 19. puz-logic-grids-19: Four scores, four roles ----------------------------------------------- Difficulty: Difficulty 4 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. Row Score Role ----- ----- ---- Tara - - Ubaid - - Vera - - Wren - - 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. - A. Editor, 80 - B. Analyst, 74 - C. Designer, 68 - D. Analyst, 68 Your answer: ______ 20. puz-logic-grids-20: Four books on a shelf --------------------------------------------- Difficulty: Difficulty 4 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. Row Author Genre ------------- ------ ----- Salt Road - - Winter Ledger - - Paper Kites - - Quiet Fen - - 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. - A. Cass, Salt Road - B. Dov, Quiet Fen - C. Bex, Quiet Fen - D. Bex, Paper Kites Your answer: ______ 21. puz-logic-grids-21: Four stalls in a row -------------------------------------------- Difficulty: Difficulty 4 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. Row Bread Cheese Flowers Honey ---------- ----- ------ ------- ----- Position 1 - - - - Position 2 - - - - Position 3 - - - - Position 4 - - - - 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. - A. The cheese stall - B. The flower stall - C. The honey stall - D. The bread stall Your answer: ______ 22. puz-logic-grids-22: Four projects, four deadlines ----------------------------------------------------- Difficulty: Difficulty 4 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. Row Lead Due month ------- ---- --------- Survey - - Rebuild - - Audit - - Launch - - 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. - A. The rebuild, due in May - B. The survey, due in March - C. The audit, due in April - D. The launch, due in June Your answer: ______ Difficulty 5 ------------ Continue in order; use the worked explanations from earlier rungs when needed. 23. puz-logic-grids-23: Four labs, four topics ---------------------------------------------- Difficulty: Difficulty 5 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. Row Lab Topic ----- --- ----- Anya - - Boris - - Cato - - Dena - - 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. - A. Resin, lab 4 - B. Basalt, lab 4 - C. Resin, lab 2 - D. Basalt, lab 3 Your answer: ______ 24. puz-logic-grids-24: The clue you can spare ---------------------------------------------- Difficulty: Difficulty 5 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. Row Gate Departure ------------ ---- --------- Ardal flight - - Brenn flight - - Corve flight - - Duns flight - - 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. - A. The clue that the flight at gate 1 leaves at 07:00 - B. The clue that the Duns flight leaves later than the Corve flight - C. The clue that the Ardal flight leaves from gate 3 - D. The clue that the Brenn flight does not leave from gate 2 Your answer: ______ 25. puz-logic-grids-25: Four households, one assumption ------------------------------------------------------- Difficulty: Difficulty 5 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. Row Street Vehicle ----- ------ ------- Ahern - - Brill - - Cowan - - Dray - - 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. - A. Cowan, on Larch Row - B. Dray, on Nettle Way - C. Dray, on Marsh Lane - D. Brill, on Nettle Way Your answer: ______ Authored hints ============== Only hints supplied by the puzzle authors are included. Items without a source hint are listed as missing; no hint text is generated or inferred. 0 worksheet items do not have an authored hint. No hint text was generated for them. puz-logic-grids-01 Start from the clue that rules something out. With only two drinks on the board, it settles everything. puz-logic-grids-02 One clue fills a cell on its own. Place that tick first, then see what it removes from the rest of the grid. puz-logic-grids-03 Turn the comparison into a plain ordering, who is ahead of whom, before you touch the grid. puz-logic-grids-04 Rewrite the negative clue as a positive statement about the other box before you fill anything in. puz-logic-grids-05 Convert the sentence about when Hana can start into a cross in one cell, then read the grid. puz-logic-grids-06 Two of the three fruits are handed out directly. Count what is left rather than reasoning about it. puz-logic-grids-07 Place the vehicle whose colour is stated outright, then re-read the exclusion against what remains. puz-logic-grids-08 Fix the delivery whose day is stated, then apply the ordering clue only to the days still open. puz-logic-grids-09 Two clues talk about the same pet. Read down that column and count how many owners are ruled out. puz-logic-grids-10 Place the desk whose floor is stated first; the comparison then has only two floors to sort out. puz-logic-grids-11 Superlatives name a single cell. Work out what scoring the most can only mean before reading on. puz-logic-grids-12 No clue here links a subject to a day. Solve the two attributes as separate grids, then read them together. puz-logic-grids-13 One clue crosses out a product-and-street pairing. Work out which shopkeeper stands on that street. puz-logic-grids-14 One clue names an instrument and a town but no person. Work out who plays that instrument first. puz-logic-grids-15 Work out which two platforms are still in play before you use the higher-and-lower comparison. puz-logic-grids-16 One clue rules the same person out of two lockers. Mark both crosses before you read anything else. puz-logic-grids-17 Treat the two consecutive appointments as one block and list every position that block could occupy. puz-logic-grids-18 The person on the top floor is never named by any clue. Place everyone who is named and see who is left over. puz-logic-grids-19 That comparison carries two restrictions at once. Write both of them down before you place any score. puz-logic-grids-20 Split the neither-nor clue into two separate crosses and see which title is left holding history. puz-logic-grids-21 Two stalls must stand side by side. List every place that pair could sit, then test each against the rest. puz-logic-grids-22 One clue closes two months for the same project. Shrink that project's row first, then test what remains. puz-logic-grids-23 One clue is an if-then. Check whether its second half is already false before you try to use its first half. puz-logic-grids-24 Delete one clue at a time and ask whether the timetable still has exactly one solution without it. puz-logic-grids-25 Nothing is placed outright. Take one half of the either-or clue as true and follow it until something breaks. Answer key ========== ! The answer key and worked explanations in this file belong only to this public, untimed educational practice source. No active aptitude suite or Novus Reasoning Challenge answer key is ever included in any download. Logic grids: open practice pack answer key Item Choice Answer ------------------ ------ --------------------------------------------------------- puz-logic-grids-01 B Iris: tea; Owen: coffee puz-logic-grids-02 A House 4: cream; House 6: green puz-logic-grids-03 B Ravi: first; Priya: second puz-logic-grids-04 D Striped: ribbon; Plain: buttons puz-logic-grids-05 A Hana: late shift; Marek: early shift puz-logic-grids-06 C Bea: pear; Callum: plum; Dilan: apple puz-logic-grids-07 B Hatchback navy, estate silver, van red puz-logic-grids-08 D Tiles Monday, plants Tuesday, books Wednesday puz-logic-grids-09 A Eve cat, Femi parrot, Grace rabbit puz-logic-grids-10 C Ines first, Jonah second, Kemi third puz-logic-grids-11 B Larks 12, Otters 24, Swifts 18 puz-logic-grids-12 D Geology, Friday puz-logic-grids-13 C Candles, Mill Street puz-logic-grids-14 A Oboe, Calder puz-logic-grids-15 B Platform 1, Garrow puz-logic-grids-16 D Locker 2, towel puz-logic-grids-17 C Nils at 10:30, Mo at 11:00 puz-logic-grids-18 A Quinn puz-logic-grids-19 B Analyst, 74 puz-logic-grids-20 C Bex, Quiet Fen puz-logic-grids-21 D The bread stall puz-logic-grids-22 B The survey, due in March puz-logic-grids-23 A Resin, lab 4 puz-logic-grids-24 D The clue that the Brenn flight does not leave from gate 2 puz-logic-grids-25 C Dray, on Marsh Lane Worked explanations =================== puz-logic-grids-01 Negative inference is the engine of every grid: a clue saying what something is not settles as much as one saying what it is. Iris is barred from the coffee, and with only two drinks on the board that leaves her the tea. Because the pair order different drinks, the coffee then belongs to Owen. Handing Iris the coffee reads the exclusion backwards, as though it named her drink instead of ruling it out. The two pairings that give both people the same drink quietly drop the one-each rule: in a grid, ticking a cell also crosses out the rest of its row and its column. puz-logic-grids-02 Start with the clue that fills a cell outright, then let the uniqueness rule do the rest. House 6 is stated to be green, so that tick is placed and green is crossed off everywhere else; since the lane holds one green house and one cream house, cream is all that remains for house 4. Painting house 4 green reuses a colour that has already been spent, and giving both houses the same colour ignores the clue that splits the two colours between them. Placing a tick and then clearing its row and its column is the whole of grid notation in a single move. puz-logic-grids-03 A comparative clue does not name a place, it orders two entities, and when only two places exist, ordering them is the same as placing them. Crossing the line before someone puts Ravi ahead, so Ravi takes first and Priya second. Reversing that treats the comparison as if it described the order of the words in the sentence rather than the order in the race. The pairings that give both runners the same place ignore that first and second are each awarded once; treat every place as a column that can carry only one tick. puz-logic-grids-04 In a two-by-two grid, a negative clue about one entity is a positive clue about the other. The plain box is ruled out for the ribbon, so the ribbon must sit in the striped box, and the one-item-per-box rule then sends the buttons to the plain box. Attaching the exclusion to the wrong item swaps the whole board. The pairings that repeat a single item in both boxes forget that each item was counted once. A good habit is to cross out a cell's row and column the moment you tick it, so a repeat becomes impossible to write down. puz-logic-grids-05 Availability statements are exclusions in disguise, and translating them into crosses is the skill here. Hana cannot start before midday and the early shift begins at seven in the morning, so that cell is closed to her; the late shift is what remains, and the one-shift-each rule hands the early start to Marek. Reading her constraint as a preference for the early start inverts it completely. The rotas that put both people on the same shift ignore that each shift is covered once. Exactly the rule a grid encodes by allowing a single tick per row and per column. puz-logic-grids-06 When two of the three cells in a line are filled, the third is free. The pear is assigned outright and so is the apple, which crosses both fruits off everywhere else; the only fruit still on the board is the plum and the only friend still unserved is Callum. This is closing a line, and it is the cheapest move in any grid: count what has already been placed before you start reasoning about what has not. Any set that hands Callum the apple or the pear reuses a fruit that was already spoken for, which the one-each rule forbids. puz-logic-grids-07 Mix a positive clue with a negative one and the grid closes in two moves, provided you take them in the right order. The van takes red, which removes red from both the hatchback and the estate. The hatchback is then barred from silver, so it must be navy, and the estate inherits silver by elimination. Applying the exclusion before the certainty is what leads solvers to give the estate navy, after which nothing consistent is left for the hatchback. Place every stated fact first, then re-read the exclusions against the smaller board. puz-logic-grids-08 Ordering clues work on whatever gaps a fixed point leaves behind, so place the fixed point first. The plants take Tuesday, which means the tiles and the books must share Monday and Wednesday. Earlier in the week then decides between exactly those two days in one step: tiles on Monday, books on Wednesday. Reversing the relation is the common slip, and any arrangement that moves the plants off Tuesday has abandoned a clue that was already certain. Fixed point, then comparison, is the order that keeps this kind of puzzle to two moves. puz-logic-grids-09 A chain of exclusions can place something that no clue ever mentions positively. Two of the three owners are refused the parrot, so by elimination it belongs to Femi. That is closing a column rather than a row, and it is the move most solvers overlook when every clue is a denial. With the parrot gone, Eve is also barred from the rabbit, which leaves her the cat, and the rabbit falls to Grace. Attaching the two parrot denials to Femi rather than reading them as a column produces exactly the reversed set. When all the clues are negative, look for the line where the crosses already outnumber the blanks. puz-logic-grids-10 A comparative clue tells you very little until the board is small enough for it to bite. Jonah takes the second floor, which leaves the first and third floors for Ines and Kemi alone. Higher up then separates those two immediately: Kemi on the third floor, Ines on the first. Applying the comparison while all three floors are still open invites a spread that quietly contradicts the floor already stated. Fix the certainties, then let the relation arbitrate over the two cells that are left, and a three-way grid never needs more than two steps. puz-logic-grids-11 A superlative is worth more than an ordinary comparison because it names one cell exactly. Scoring the most of three teams can only mean 24, so the Otters take it and the other two share 12 and 18. The Larks are barred from 18, so they take 12 and the Swifts take 18. Reading the most as merely more than one other team weakens it into something several boards satisfy; treat superlatives as outright placements. Any arrangement that leaves the Otters off the top score has thrown away the strongest clue in the set. puz-logic-grids-12 With two attributes in play, keep two separate grids and refuse to mix them until each one is closed. On the subject grid, statistics is assigned outright and poetry is barred from Bo, so Bo takes geology and Cleo takes poetry. On the day grid, Monday is assigned and Friday is barred from Amara, so Amara takes Wednesday and Bo takes Friday. The mistake worth avoiding is importing a day clue into the subject grid: nothing in this set links a subject to a day, so each attribute is solved on its own evidence and the two results are only read together at the very end. puz-logic-grids-13 A clue that rules out one product-and-street pairing is a single cross, but a well-placed cross can settle a whole board. Mill Street belongs to Dara, and cameras are barred from Mill Street, so Dara does not sell cameras; cheese is already spoken for, so Dara sells candles. Frank is kept off Bridge Street and Mill Street is taken, so Frank is on Quay Street, Esme takes Bridge Street, and the cameras end up with Frank. The trap is to attach the camera exclusion to a person: it constrains a product and a street, and it only reaches a shopkeeper once that shopkeeper's street is known. puz-logic-grids-14 A clue that links two attributes without naming a person is a bridge, and a bridge only pays out once one of its ends is solid. The cellist lives in Brindle; Tomas is committed to the flute and Sami is barred from the cello, so Rosa is the cellist and therefore lives in Brindle. Tomas is in Ashford, which leaves Calder for Sami, and with the flute taken Sami has the oboe. Trying to place towns before instruments leaves the bridge clue idle and tempts you into putting Sami in Brindle simply because that town is still unclaimed. puz-logic-grids-15 A comparison that runs across two attributes can settle both of them at once, but only after the field has been narrowed. Fenwick sits on platform 3, so Garrow and Hollin must share platforms 1 and 2; the comparison then forces Garrow onto platform 1 and Hollin onto platform 2. Platform 2 belongs to the 09:25, so that service runs to Hollin. The 09:10 is barred from Garrow, so it takes Fenwick on platform 3 and the 09:40 takes Garrow on platform 1. Applying the comparison while all three platforms are still open is what leaves solvers holding several timetables instead of one. puz-logic-grids-16 A denial that names two cells does double duty, and both crosses have to be written down. Kit is kept out of two of the three lockers, so only the third is open to him. The towel's locker is stated, and since Iva has the boots she cannot be the person standing at the towel's locker either; with Kit already placed, Iva takes the one remaining locker and Jae is left holding the towel. The helmet then belongs to Kit by elimination. Solvers who apply only half of a compound denial leave two lockers open for Kit and stall. Read a clue that rules out several cells as several separate crosses. puz-logic-grids-17 Immediately before is a block clue: it fixes a shape rather than a position, so you place the shape by testing where it can sit. The pair occupies either ten and half past, or half past and eleven. The earlier placement pushes Lena to eleven, which a clue forbids, so the later one stands: Nils at half past ten, Mo at eleven, and Lena at ten. Listing the possible positions of a block and striking out the ones that break another clue is faster and safer than reasoning about the three people one at a time. puz-logic-grids-18 Four-way elimination is the same move as the three-way version, but at this size it pays to write every cross down. Floor 3 is assigned directly. Suki is barred from floors 1 and 4, and floor 3 is gone, so she takes floor 2; Rafe is barred from floor 4 and only floor 1 remains open to him. One floor and one resident are then unclaimed, so the top floor belongs to the resident no clue ever mentions. Reading Suki's double denial as though it placed her on floor 1 is the slip that produces the wrong name here. An exclusion removes cells, it never fills one. puz-logic-grids-19 Higher than one person but not the highest packs two restrictions into one sentence, and you need both. The lowest score is assigned outright, so the other three hold 68, 74 and 80. Vera is above Tara yet is not on 80, which leaves 74 for Vera and 68 for Tara, with 80 going to the remaining candidate. Roles then follow: 80 is the editor's, the lowest score is the planner's, one candidate is named as the designer, and the analyst is what is left, the 74. Dropping the not the highest half of the clue is what tempts solvers into handing Vera the 80. puz-logic-grids-20 A neither-nor clue is two crosses written as one sentence, and it is usually the cheapest clue in the set. Crime is assigned to one title outright; Salt Road is barred from crime and history, and a second title is barred from history, so history can only belong to the remaining book. Salt Road and Quiet Fen are then left sharing romance and travel. The travel book has a stated author who is not the author of Quiet Fen, so Quiet Fen is the romance and Salt Road is the travel book. Treating neither-nor as a single exclusion loses half its force and leaves the history slot ambiguous. puz-logic-grids-21 Adjacency clues are placed as blocks and then tested, never satisfied in advance. Two of the stalls must occupy neighbouring positions, and with position 4 already claimed the block can only sit at positions 1 and 2 or at positions 2 and 3. The earlier placement leaves the flower stall at position 3, directly beside the cheese stall, which a clue forbids; so the block sits at positions 2 and 3 and the flowers take position 1. That puts bread at position 2 and cheese at position 3. Turning not next to into a test you apply after each trial placement keeps row puzzles short. puz-logic-grids-22 When a clue rules a value out of two cells at once, spend it early to shrink the board. The rebuild cannot fall in March or June, and March already belongs to the survey, so the rebuild is due in April or May. Suppose April: the audit and the launch would then hold May and June, but May belongs to Moss and June to Lin, while the audit belongs to Kai, so the audit has nowhere to go and April fails. The rebuild is therefore due in May and led by Moss; the audit takes April under Kai, June is the launch under Lin, and the March survey is left to the fourth lead. puz-logic-grids-23 A conditional clue is not a fact about the world, it is a bridge you may cross in one direction only, and here it is crossed backwards. Its second half is already false, because Dena is committed to coral, so its first half must be false too: Boris does not work in lab 2. That is modus tollens. Lab 1 is taken and two researchers are now barred from lab 2, so lab 2 has a single occupant left, and the higher-than comparison sorts the remaining two labs. Topics follow: lab 1 studies algae, coral is assigned, and the last denial splits basalt from resin. Reading the conditional forwards, as though its first half were given, is the standard error. puz-logic-grids-24 A clue is redundant when the board is already forced without it, so test candidates by deleting one and re-solving. Delete the denial that keeps the Brenn service away from gate 2 and the timetable still closes: the Ardal service holds gate 3, so gate 1 belongs to Brenn or Duns; if it were Duns, that service would leave at 07:00, yet the only departure times left for the Corve service would both be later, contradicting the clue that Duns leaves after Corve. So Brenn holds gate 1 anyway. Delete any of the others instead and at least two timetables survive, which is exactly what makes a clue indispensable. puz-logic-grids-25 No clue here places anybody outright, so the only way in is to assume one half of the either-or clue and break it. Two households are barred from the van and a third keeps neither the motorbike nor the van, so the van belongs to Ahern. Now assume the van is kept on Larch Row: that puts Ahern on Larch Row, which a clue forbids: a contradiction, so the other half of the either-or must hold and Dray lives on Marsh Lane. Everything then falls out: Ahern takes Oak Rise, Cowan takes Larch Row, Brill takes Nettle Way with the estate car, Dray keeps the bicycle and Cowan the motorbike. Assume, propagate, contradict, conclude the opposite. That is the technique. Source: https://learn.novusstreamsolutions.com/puzzles/logic-grids