Lateral Thinking curriculum

A puzzle that seems impossible usually rests on a detail you supplied yourself: that a person is an adult, that "dead" means a person, that a room has a window. Write down what you are assuming about who, where, when and what. Then test each one against the exact words. The answer is usually ordinary once the wrong assumption is gone.

Trick questions often hide the answer in plain sight. "Write nineteen without using any numbers" is satisfied by writing the word "nineteen", because a word is not a numeral. Reading quickly, the mind supplies the harder question it expected. Slow down and answer the one actually written.

Some questions build on a premise that cannot be true, such as asking for the change from a payment that was never made, or the shadow of something with no light on it. If an answer seems to need a calculation about something impossible, the correct option usually points out the impossibility instead.

Situation puzzles describe something that sounds sinister or impossible, then hide a plain cause: a game, a job, a performance, a photograph. Ask which everyday setting would make every detail normal at once. An explanation that fits most of the details but not all is the wrong one.

Many hard puzzles have one idea that makes them easy: a clever ordering, a symmetry, a parity, or using one thing in two ways at once. If a solution is turning into a long list of cases, stop and ask what feature of the puzzle you have not used yet. The intended route is almost always short.

"A shelf holds 12 books and you borrow 5. How many books do you have?" The answer is 5, the books you took, not the 7 left on the shelf. Asking what remains and asking what you hold are different questions about the same setup, so find whose count the question names.

"A baker made 30 rolls, and all but 8 were sold. How many are left?" All but 8 were sold, so 8 are left. The number 30 is there to tempt a subtraction, 30 − 8 = 22, which answers a question nobody asked. Rephrase the sentence as "8 were not sold" before you do any arithmetic.

Turning a tangled sentence into a plain one takes a second and removes the pull of the arithmetic. "You are third in a queue and two people join behind you. What place are you?" becomes "nobody joined in front of me", so you are still third. Most wording traps fall apart once the sentence is paraphrased.

Items such as "what kind of 'press' has no buttons?" name a word and rule out one meaning. List the other contexts the word lives in: the press can mean news reporters, a press is a machine that squeezes or prints, and a press is also a lift in a gym. Then keep the sense that fits every part of the clue.

A word often has a technical meaning inside one setting. A "menu" on a screen lists commands rather than dishes, and to "fold" egg whites in a kitchen is to mix them in gently. When a clue names a setting, start from that setting and ask what the word means there.

You can break a habit, hold a grudge and draw a conclusion without touching anything. When a riddle rules out physical handling, switch to the abstract sense of the verb. Ask what can be broken or held without being picked up.

A notebook and a pen cost $3.40 together, and the notebook costs $3.00 more than the pen. The tempting answer for the pen is $0.40. Remove the difference: $3.40 − $3.00 = $0.40, then halve, so the pen costs $0.20 and the notebook $3.20.

Plug your answer back into the story. If the pen costs $0.40, the notebook costs $3.40 and the total is $3.80, not $3.40, so the intuitive answer fails at once. With $0.20, the notebook is $3.20 and the total is $3.40, as stated. One line of checking catches the trap every time.

A bowl of rising dough doubles every 10 minutes and fills the bowl at 4:00. When was it half full? At 3:50, one doubling earlier, not at the halfway point of the time. Run doubling puzzles backward from the end, where the answer takes one step.

A frog climbs 7 feet each day and slips back 2 each night, in a 40-foot well. Net progress is 5 feet a day, so after 7 days and nights it sits at 35 feet. On day 8 it climbs 7 feet to the top and is out, with no slip. Dividing 40 by 5 to get 8 is right here only by luck, so always handle the last day separately.

A 60-meter fence with a post every 5 meters, including both ends, has 60 ÷ 5 = 12 gaps and 13 posts. Three doses taken an hour apart span two hours, not three. Decide whether the question counts the marks or the spaces between them, and sketch a short case to check.

Each of 40 people shakes 39 hands, which gives 40 × 39 = 1,560, but that counts every handshake twice, once from each side. So there are 1,560 ÷ 2 = 780 handshakes. The same count gives the number of games when every team plays every other team once.

For 11 + 12 + … + 30, pair the first with the last: 11 + 30 = 41, then 12 + 29 = 41, and so on. There are 20 numbers, so 10 pairs, and the sum is 10 × 41 = 410. Count the terms carefully: from 11 to 30 inclusive is 30 − 11 + 1 = 20 numbers.

The minute hand moves 6° a minute and the hour hand 30° an hour, which is 0.5° a minute. At 7:12 the minute hand is at 12 × 6 = 72° and the hour hand at 7 × 30 + 12 × 0.5 = 216°. The angle between them is 144°. Forgetting the hour hand's drift, and putting it exactly on the 7, is the usual error.

At 1:52 the minute hand is at 312° and the hour hand at 30 + 26 = 56°. The raw gap is 256°, which is the long way around. The smaller angle is 360° − 256° = 104°. Always check the raw gap against 180° before you choose.

A passenger walking forward at 5 km/h on a train moving at 100 km/h moves at 105 km/h to someone on the platform, but at 5 km/h to the other passengers. Puzzles about motion go wrong when one quantity is measured from the ground and another from the vehicle. Fix one observer first.

Riding 30 km at 10 km/h takes 3 hours and riding back at 15 km/h takes 2. That is 60 km in 5 hours, an average of 12 km/h, not 12.5. More time is spent at the slower speed, so it pulls the average down. Never average the two speeds directly.

Light travels in straight lines, a shadow falls on the far side from the light, and a mirror swaps left and right in what it shows. In a dark place, nothing is seen until something gives light. Following the light usually exposes the detail the puzzle hoped you would overlook.

Ice melts, water evaporates and heat fades. A clue that has vanished by the time someone arrives may have been something that changed state, such as a block of ice that is now a puddle. Ask what each material in the scene would look like an hour later.

Some puzzles let you look only once. The solution is to make an action that leaves evidence you can read afterward: a warm surface, a melted edge, a footprint, a moved marker. Ask what you can change now that will still be visible when you look.

If a person does something on some days and not on others, compare the days. The answer is the single thing that is there on the days it happens and missing on the days it does not, such as rain, a companion or a holiday. List the differences and test each against every detail of the story.

With a 7-liter jug and a 4-liter jug, fill the 4, pour it into the 7, fill the 4 again and pour until the 7 is full. That takes 3 liters, leaving 1 in the smaller jug. Differences between containers, or burning something from both ends to halve its time, produce amounts no single tool gives.

At a dinner there are two uncles and two nephews, yet only three people are present. One of them is both: an uncle to the youngest and a nephew to the oldest. When a count of roles seems too high for the people available, look for someone who is both a parent and a child, or a buyer and a seller.

Puzzles let you picture an average adult with average senses and an ordinary job. List what the story never says about the person: age, height, health, profession, whether they can see or hear. One of those unstated facts usually explains the scene, so check them before inventing anything stranger.

If a puzzle seems contradictory about who is related to whom, check whether you assumed that a doctor is a man, that a parent is a father, or that "grand" means one generation. The words rarely state these things. Draw the people and label only what the sentence actually says.

Money puzzles invite you to add a sum that is already counted on the other side. Follow one wallet or one till from start to finish. If Jo borrows $10, repays $6 and then borrows $4 more, Jo owes $10 − $6 + $4 = $8. Every amount should enter once, with its sign.

Tickets cost $12 each, with $5 off the second ticket only. Two tickets cost $12 + $7 = $19, not $14 and not $24 − $10. Pricing puzzles hide the trap in a rule that covers only part of the purchase, so apply it item by item.

How many hours does a person sleep in a lifetime? About 8 hours a night, 365 nights a year, for about 80 years: 8 × 365 × 80 is roughly 230,000 hours. Each factor may be off a little, but the answer lands in the right order of magnitude, which is what these questions ask for.

Cut a painted 4 × 4 × 4 cube into 64 small cubes. The 8 corners have 3 painted faces, each of the 12 edges has 2 middle cubes with 2 painted faces (24), each of the 6 faces has 4 center cubes with one painted face (24), and the inner 2 × 2 × 2 block of 8 has none. The four counts add to 64.

Intuition about chance is unreliable, so write out every equally likely case, mark the ones that fit, and divide. Two children with at least one girl gives the cases girl-girl, girl-boy and boy-girl, so the chance both are girls is 1 in 3, not 1 in 2. The list does the reasoning for you.

A grid 5 cells long and 2 cells wide holds more than 10 squares: 10 of size 1 and 4 of size 2, 14 in all. Questions that add "of all sizes" or "in total" want the larger shapes too. Count by size, from smallest to largest, and add.

Calendar and clock puzzles work on edges. A shop open from 9 p.m. Monday to 5 a.m. Tuesday is open for 8 hours, across midnight. A date "a year from February 29" has no matching day in most years. Draw a short timeline and mark where the day, month or year turns over.