Logic grids: open practice pack: 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.