Lateral thinking: open practice pack: worked explanations

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The method is sense-splitting: when a scene reads as impossible, find the one word carrying the weight and list its ordinary senses. Here the word can mean jewellery, a phone call or a circular mark, and only the last one fits bare varnish, a hot mug used without a mat, and a housemate who has lost nothing. Reading it as jewellery forces you to invent a lost item the facts rule out, and the phone reading dies on an empty call list. Next time a short common noun sits at the centre of a puzzle, try its second sense before you doubt the facts.

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This is a narration gap. Two events written side by side feel adjacent in time, but nothing in the account says how long the middle lasted. Strip the story to what is stated: a fresh cup was poured, a door was answered, the tea was cold. The only unstated quantity is the length of the errand, and waiting with a neighbour for an engineer is exactly the kind of errand that runs for hours. Blaming the heating or the pot means contradicting a stated fact, which is always a worse move than filling in an unstated one.

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The technique is role-counting. Six posts and five people means somebody wears two hats, so a treasurer passing accounts to a librarian can be one person moving a ledger from one pile to another. Two named roles never entail two bodies. The tempting route is to doubt the record, but the minutes are stated to be accurate and complete, so any story needing them to be wrong is beaten before it starts, and a paper ledger with no computer in the room closes off the electronic route. Whenever a record describes a transfer nobody saw, check whether both roles could belong to one person.

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This is function-shifting: ask what an object can do, not what it is for. The volunteer's problem is a door that swings shut while both hands are full, and fixing anything to the door has been ruled out. Mass is the property being requested, and the only job in the scene that needs mass is holding a door. Weighing paper down is the right kind of idea but answers a problem nobody has, since there is no draught and the windows are shut. When a request names an odd property (heaviest, longest, coldest), let the property tell you the job.

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The assumption is a quiet singular. One flat coming free feels like one person arriving, but a flat holds a household, and the text never commits to a number. Both entries name flat four, both are accurate, and nobody moved in or out midweek, so the only reading that keeps every fact is two people sharing one home. A rapid change of tenant contradicts the stated fact that nobody moved, and calling Dana forgetful contradicts the entries being accurate. Whenever a puzzle turns on “the” new person, check whether the text ever said there was only one.

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This is the two-way trip test: equal effort over an equal distance should take equal time, so an unequal time means the medium itself is moving. The drifting stick shows water running away from the weir, which makes the outward leg an upstream leg and the return a downstream one. Tiredness and a short cut both need a stated fact to be false, since the effort was equal and the two points are fixed two kilometres apart, and still air rules out any wind. When the times differ and the route does not, look for something moving underneath.

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The assumption is that a voice implies a speaker present. Three stated facts break it: the same six words, the same minute every evening, and an empty building. Human speech does not repeat to the second, but a recording does, and ceiling speakers were fitted last month. A colleague upstairs contradicts her being alone, an echo needs her to have spoken first, and a radio would never deliver identical words at an identical time. When a repeated event is exact rather than merely similar, look for a machine before you look for a person.

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Track the label, not the tin. The labels live on the lids, and lids are interchangeable, so washing three tins and putting three lids back can shuffle every label without anyone touching one. The helper checked contents against labels as he filled, which rules out a filling error; the sacks are open and visible, which rules out a mislabelled sack; and doubting the cook's eyes contradicts a stated observation. When a container disagrees with its label, first ask which part of the container the label is attached to.

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The technique is separating a list from a timeline. Rosa's sentence joins her three events with “and”, not “then”, so it commits her to three things happening, not to the order they happened in. The photograph fixes the real order: Theo was already there while the cake was whole. Inventing a second cake or a second gathering contradicts stated facts, and calling Rosa mistaken contradicts her account being truthful. Where a witness's sequence seems to clash with hard evidence, check whether a sequence was ever claimed.

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This is a scale check. Four seconds between two points a walker would need an hour to cross only works if the points themselves are small. Three facts pin it down: the summit is within arm's reach, the whole valley is in view without a turn of the head, and nothing printed or on a screen is involved. That triangle describes a model laid out on the ground. A high viewpoint gives the view but never the touch, and a cable car would still take minutes. When a distance behaves oddly, question the size of the thing before the speed of the traveller.

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The move is to check what each side is counting. One count is of doors and the other is of tenancies, and a block contains doors that open onto a bin store and a stairwell as well as doors that open into homes, so the two totals were never counting the same objects. Every rival story needs a stated fact to fail: no flat is empty, no tenant holds two, and the file is complete. When two honest counts of “the same thing” disagree, write down what each one actually counts before you go looking for a mistake.

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This is elimination between rival stories, judged against every fact rather than the most vivid one. A person getting in needs a key, and the only other keyholder has been abroad for three weeks. The shed lighting itself needs a mechanism, and the switch is found off each morning while the light is on, which kills the sticking-switch idea and points at the one part that can act on its own: a sensing bulb with mice moving beneath the door. A painted window that does not open ends the borrowed-light story. A surviving explanation must fit all the facts, not most of them.

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The decisive detail is the one that reads as scenery: the building is unheated at weekends. Paper in an open rack against an outside wall takes up damp over two cold days, swells at the edges and misfeeds, then dries as the room warms, which is exactly why the trouble clears by lunchtime. Volume and paper stock are stated to be identical all week, so neither a heavy morning nor a wrong ream can be the difference, and the engineer found nothing to blame. When a fault keeps to a timetable, look for something else on the same timetable.

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This is a frame change rather than an object change. The crate is longer than any single side of the lift, but a box is not limited to its sides: the diagonal of a two-metre square floor is about 2.8 metres, comfortably more than 2.05. Nothing about the crate needs to change, only its angle. The stairs are stated to take nothing over 1.6 metres at any angle, so tilting there buys nothing, and dismantling contradicts the crate arriving unopened. When something will not fit, measure the longest line of the space rather than its width.

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This is reasoning from an absent negative: an event that always happens becomes evidence when it does not happen. The surgery texts every patient the evening before, her phone keeps everything and was receiving other messages that Monday evening, so the silence is real information rather than a gap in the record. Claim only what it licenses, though: it fixes the state of the booking system at the moment the texts went out, not the whole history. A Tuesday-morning cancellation would still have produced Monday's message, which is why that story does not fit. Absence proves something narrow; resist widening it.

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The method is the controlled comparison. All eight plants had the same feed at the stated strength, and the four outdoors were fine, so the feed cannot be what separates the healthy from the harmed. The vent jamming on the last day of May and being freed on the eleventh of June brackets the damage almost exactly, and a sealed greenhouse cooks in early summer. Soil worn out over nine years would not act within ten days, and inventing a glass-only disease adds a fact the scene never supplied. When two candidates share a timing, prefer the one that also matches the split between what was harmed and what was not.

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This is a common cause, not a chain. Takings and lost property both climb on gala and lesson days, and what gets handed in is towels, goggles and caps: swimming kit, not cafe kit. So the number of swimmers moves both totals and neither total acts on the other. Careless customers would leave cups and coats behind; a story about busy staff predicts fewer items reaching the desk, not more. Whenever two counts move together, look for the third quantity moving them both before you draw an arrow between them.

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Test necessity by deletion: take one fact away and ask whether more than one story still survives. This conclusion is reached by elimination. The access list closes the field to four people, and the train, the wrist and the badge time remove three of them. Delete any of those and a second suspect walks straight back in. Positive evidence that the survivor was present adds nothing, because elimination has already left him alone. That is the general shape: an argument from elimination needs its frame and its exclusions, never a confirmation of the one left standing.

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The count you need is never stated, but it is forced. Eighteen lunches went out with none spare and two of them went to the adult helpers, so sixteen children are on the trip. Now add the helpers back, because helpers occupy seats: eighteen people want a passenger seat and the licence allows sixteen. Two slips are common here: treating all eighteen lunches as children, and stopping at the sixteen children as though the adults travelled by magic. When a total is missing, look for a quantity that was handed out one to one.

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Two-stage inference: form the natural first guess, kill it, then rebuild from what is left. Water by an open door says rain, but nine dry days and dry ground outside close that route. What remains is already on the page: a heavy water cooler dragged out through the propped door, and a window wedged open at the far end, so opening the fire door creates a through-draught the moment it is propped. A ceiling leak explains the water but not the paper; a hurried search explains the paper but not the water. Prefer the story that covers every symptom rather than the loudest one.

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Separate the facts that enable from the facts that merely exclude. No cut marks and an untouched key close off routes; the lock still hanging shut on the rail restates the mystery rather than resolving it. Only one fact opens a door: the part sitting inside the lock comes off by hand, so the rest of the bicycle could be lifted away from its own lock in seconds. That also names the real error. The lock was securing a detachable component rather than the frame. When something apparently impossible has happened, list which facts could have made it possible, not which ones make it stranger.

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Build a knowledge timeline. The note names a particular chair in a cafe Yusuf had never used before, so its writer knew something that only came into existence at half past five. He told nobody, the flat has no telephone and her mobile was off, and she left at quarter to six and has not returned, so the knowledge had to be picked up in person inside that fifteen-minute window. A note written later contradicts her leaving time, and a lucky guess is closed off by his never having been to the place. Ask what each person could have known, and the exact moment they could have known it.

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Work knowledge claims as filters, one at a time. Twelve splits as 2×6, 3×4, 4×3, 6×2 and eighteen as 2×9, 3×6, 6×3, 9×2. A row count that fixes the total would have told Petra the answer, so her ignorance leaves rows of two, three or six. Treat the reply as two separate filters: “I could not before” removes per-row counts of four and nine, which were decisive on their own, and “now I can” removes six, since two rows of six and three rows of six both survive. What is left is two chairs a row giving twelve, or three a row giving eighteen, and both of those layouts have the same number of rows.

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The faulty step is treating spot checks as continuous observation. Three sightings at half past nine, one o'clock and six o'clock sit happily alongside the key being out from ten to nine until twenty past, and out again from twenty-five to ten in the evening. Precisely the windows the book records, and precisely the moments the doors were worked. Nothing else has to give: the sightings can all be accurate, the book can be honest, and the lock untouched. When a witness says something never happened, ask what they actually watched and for how long, then check whether the unwatched gaps are large enough to hold the event.

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Two constraints do the work here, one physical and one about knowledge. Nobody could enter the locked shed over the weekend, and the message names those boxes, so it was chalked inside before Friday evening. Tomas left before the van was even opened, so he could not have known the weight; Wren never came near the shed, so she could not have written on its inner face. That leaves one person, and his denial is testimony rather than a constraint: it rules nothing out. Sort your facts into what a person could do and what a person could know, and keep bare say-so out of both lists.