Rethink the Premise

What "lateral" means

Edward de Bono coined the phrase "lateral thinking" in his 1967 book The Use of Lateral Thinking. His contrast was with "vertical" thinking, which digs the same hole deeper. Lateral thinking steps sideways to dig somewhere else. In puzzle terms: deduction asks what follows from the premises; lateral thinking asks whether you've got the premises right.

That makes the hidden constraint here an odd one. It's usually an assumption: something you added without noticing, which the puzzle never said.

The candle and the strings

In Karl Duncker's candle problem (published in his 1945 monograph On Problem-Solving), people get a candle, a box of drawing pins and matches, and must fix the candle to a wall so wax won't drip on the table. The solution: tip the pins out, pin the empty box to the wall as a shelf, and stand the candle in it. People struggle because the box is presented as a container. Duncker called this "functional fixedness": seeing an object only in its usual role. Later versions found the problem gets easier when the pins are presented outside the box.

Norman Maier's two-string problem (1931) is similar. Two strings hang from a ceiling, too far apart to hold both at once. Among the objects in the room is a pair of pliers. Tie the pliers to one string as a pendulum, set it swinging, grab the other string and catch the swinging one. The pliers' job description, "tool for gripping", was the barrier.

The nine dots

Arrange nine dots in a 3×3 square. Connect all of them with four straight lines without lifting your pen. The puzzle is often traced back to Sam Loyd's Cyclopedia of Puzzles (1914) and is said to be one source of the phrase "think outside the box".

Why it's hard

Almost everyone assumes the lines must stay inside the square formed by the dots. The instructions never say so. Once you let a line run past the edge and turn there, a four-line path becomes possible: start at one corner, run along an edge past the last dot, turn back diagonally, and continue zig-zagging through the remaining dots. The answer isn't clever drawing; it's deleting a rule that was never there.

Monty Hall: the premise that matters

In 1990 Marilyn vos Savant answered a reader's question in Parade magazine: you pick one of three doors; one hides a car, two hide goats. The host, who knows where the car is, opens a different door showing a goat and offers you a switch. Should you? She said yes, and switching wins two times in three. Thousands of letters insisted she was wrong. She wasn't.

The hidden constraint is in the bold phrase. Your first pick is right one time in three. If it's wrong (two times in three), the host is forced to reveal the only other goat, so the remaining door must hide the car. Switching wins exactly when your first pick was wrong: 2/3. If the host opened a door at random and happened to show a goat, the odds would be 1/2 each. Same doors, different premise, different answer.

Fair play and situation puzzles

"Situation puzzles" give a strange scenario and let you ask yes/no questions until you reconstruct the story. A good one is fair: every key fact is consistent with the setup and discoverable through questions. A bad one depends on a detail no reasonable solver could guess. If the reveal makes you groan with recognition, it was fair; if it makes you feel cheated, it wasn't.

1. List every assumption in the question, even obvious ones.
2. Cross out any the text doesn't state.
3. For each object, name three uses besides the usual one.
4. Ask who knows what. Knowledge changes probabilities.
5. Prefer explanations you can justify from the text over ones that merely surprise.

Sources

• de Bono, E. The Use of Lateral Thinking. Jonathan Cape, 1967.
• Duncker, K. "On Problem-Solving." Psychological Monographs 58 (1945). Candle problem
• Monty Hall problem · Nine dots and "outside the box"