Welcome to the new Independent website. We hope you enjoy it and we value your feedback. Please contact us here.


Dwarf on ice in lateral lift horror

Chris Maslanka explores the lures and flaws of lateral thinking puzzles
At the height of an otherwise pleasant party a somewhat intoxicated guest - let's dub him Justin Thyme - stumbles into me and regales me with the question: "Can a man living in Oxford be buried in Cambridge?" And then, without waiting for my reply, answers himself: "Course he can't; if he's living, there's no need to bury him." And before I can open my mouth to quibble with this he sets off on a random walk, which convinces me he will return just in time for the end of this article.

I hate lateral puzzles. Don't get me wrong. I don't mean all lateral puzzles, just the clever-clever ones - the smart-ass ones. You know the sort of thing: "What happens when an irresistible force meets an immovable object?" or, more laterally, try this one:

Puzzle One: Every morning, a man living in a skyscraper takes the lift down to go to work. Every evening he walks back up the stairs. Why?

Hint: Such puzzles tend to involve blocks of ice, one-armed ex-cannibals, dwarfs and people drowning in their own water beds. Here's another:

Puzzle Two: The suicide was hanging dead at the end of a rope in an empty room. The mysterious thing was that although his feet were two metres off the ground, there were no objects in the room for him to have stood on. The only door into the room had been locked from the inside. There was water on the floor. How did it happen?

Answers: The chap in the lift is a dwarf and can't reach the button for the floor he lives on. The suicide had stood on a block of ice, tied the rope around his neck, then jumped off. The ice subsequently melted.

Quibbles: If it's that much trouble, the dwarf would surely get a ground floor flat - or at least ensure that there are sometimes some vertically unchallenged people around to press the lift button for him. What sort of society do these puzzle-setters live in?

And how did that suicide smuggle so much ice up to his room. Quite apart from the question of how he got it under his arm and whether it tickled, a block of ice that size weighs more than a car. Perhaps he drove it up the stairs. Why had he bothered with ice anyway, when a chair wouldn't have melted and made such a mess? Was it so that he could change his mind if he got cold feet?

Let's get one thing straight at the outset: lateral puzzles are nothing new. Ancient texts are riddled with them. There is the question that Samson set the Philistines - "Out of the strong shall come forth sweet" - and the answer which Delilah treacherously passed over to them - "a dead lion in which wild bees had nested".

Then there is the riddle of the Sphinx, which stands up well even today: "What creature moves on all fours in the morning, on two feet at noon and on three toward the setting of the sun?"

The answer is not, of course, sheep living near a nuclear plant, but more enigmatically, a human being.

What is new is not lateral puzzles but the label "lateral", a term coined by Edward de Bono to distinguish the exploratory type of thinking from vertical thinking. There have always been two sorts of thinking. Logicians called them deductive and inductive; psychologists called them convergent and divergent. De Bono, in a deft exercise of new labels for old, renamed them "vertical and lateral thinking".

In deductive, vertical or convergent thinking you apply the rules of logic to the data and deduce conclusions. This is a purely mechanical procedure, in the sense that a machine could do it: nothing new is developed in the process. In a sense the conclusions are implied by the data, they are just not in the most user-friendly form.

In divergent, inductive or lateral thinking, by contrast, we invent, we create, we busk, we end up with more than we started with: the parts are greater than the whole. An apple falls on our head and we dream up the theory of universal gravitation.

In spite of what the trendy re-labelling might suggest, all good puzzles are in fact lateral. A good puzzle requires you to explore and discover for yourself a mode of solution; to invent and manipulate conceptual frameworks. That is why puzzles are such good exercises in learning. They facilitate problem-solving by encouraging mental flexibility. In short, it is precisely the laterality that distinguishes a good puzzle from a mere exercise in logic or rote learning.

But just because all good puzzles are lateral doesn't mean that all lateral puzzles are good. Here's another couple. Judge for yourself whether they are good or bad:

Puzzle Three: A woman was assured by a salesman that the parrot she was buying would repeat any word it heard. A week later, the parrot still hadn't uttered a single word. Given that the salesman had spoken the truth about the parrot's abilities, how did this happen?

Puzzle Four: A man adds height to the mailbox of his neighbour, who becomes so depressed he attempts suicide. Why?

Answers: The parrot was deaf. The suicidal neighbour was a basketball player whose mailbox difficulties convince him he is shrinking and that he will not be able to do dunk shots any more.

Quibbles: or maybe the parrot's owner was dumb, or the parrot spent all its time listening to instrumental music on its personal stereo.

Smart-ass puzzles don't teach you anything apart from pedantry. You feel no satisfying sugar-rush of recognition when you hit on the solution. If anything you feel cheated. When that happens it's because the setter isn't interested in the puzzle per se. He or she is interested in getting one over you. They take full advantage of ambiguity and using misleading language. For example:

Q: Why can't you photograph a man with a wooden leg in Winnipeg?

A: Because you take photographs with cameras. (groan)

Because right and wrong don't come into it, many rehashes of old puzzles are endlessly recycled and re-plagiarised complete with wrong answers.

Q: How far can you go into a wood?

A: Only half way: after that you're coming out again.

Not so, as the illustration verifies.

But hush, here comes Justin swaying from side to side, clearly still having difficulty thinking vertically. Now's my chance to set the record straight; to fight fire with fire, to outquibble the quibblers, to outsmart- ass the smart-asses.

Justin: If your peacock lays an egg in your neighbour's garden, is it your property or your neighbour's?

Me: The garden?

Justin: No, the egg. Is it yours or your neighbours?

Me: I expect so.

Justin: No, but which?

Me: Mine.

Justin (triumphantly): No, peacocks don't lay eggs!

Me: (slightly more triumphantly) I know. But you said "if".

Justin: Never mind, have a go at this one. A man turns his light out and leaves his house. As a result 60 souls perish. Explain.

Me: Let's see. He's a huge ex-strongman who compensates for over-eating by carrying his friends around on his shoulders at drunken parties. He turns the light out because he is shy and needs to go to the bathroom sooner than his friends can dismount. In the process he overbalances, toppling all his hangers-on off the balcony into the bay below. Sad really.

Justin (reading from his book): Nope. The answer is that he lives in a lighthouse.

Me: But you said he lives in a house, a lighthouse is a building, not a house. Besides, what's wrong with my answer?

Justin: It's not the answer.

And that's just the point: the authors of such puzzles claim these exercises can liberate your thought processes and make you more creative. So why are they so rigid about their solutions? Isn't a more considered answer to "Can a man living in Oxford be buried in Cambridge?" simply, "Yes, eventually."?

Time for another one:

Puzzle Five: The victim was lying dead on a bed, and on the floor beside the bed was a pair of scissors. The scissors were instrumental in the death, yet there is no trace of blood. There were no cuts or bruises. How could she have been murdered with the pair of scissors?

Answer: The killer had used the scissors to cut open the bed - it was a waterbed and the victim drowned.

Quibble: Hang on a minute. Wouldn't any decent hit-person have settled for stabbing as more reliable? What if the victim had been a strong swimmer. Besides, there are other more banal possibilities. I once, while practising origami (not normally considered a dangerous pursuit) almost cut through the lamp flex with my paper scissors. Shock horror!

In a world of deaf parrots, neurotic basket-ballers and suicides on ice, who can arbitrate between sensible answers and crazy ones? They are unreal, disconnected and almost schizophrenic. Such clever-clever problems can exist only by ignoring vast chunks of the real world, such as how we use language, or the laws of physics. Admittedly real-life problem-solving starts out being creatively wild, but always at the end it has to be checked against reality.

But Justin the immovable object is determined to resist the irresistible force of my logic and have the final word.

Justin: I have to cross this bridge over a precipice with three heavy balls. The bridge will only carry my weight plus one of the balls.

Me: Tough one that.

Justin (triumphantly): That's what you think; you see if I juggle them I'll only be holding one ball in my hand at any one time. That way I can cross in safety.

To my horror, I see he has run a plank out of the window across to the next skyscraper and has climbed out on to the window ledge with three huge balls. We are 50 floors up.

Me: But Justin, the average force you exert will be your weight plus three balls; throwing a ball up only serves to increase the reaction on the plank. As it isn't a steady force, the force on the plank will at times actually be greater than you and the three balls. That's physics.

Justin: No, no, you don't understand, this isn't a physics puzzle, it's a lateral puzzle ...

Illustrations by Kate Smiley