Think Around the Obvious
When straightforward mathematical calculation hits a dead end, lateral thinking opens a side door.
The Heritage of Lateral Deduction
In his long-running "Mathematical Games" column for Scientific American, Martin Gardner introduced millions of readers to the joy of non-obvious reasoning. Gardner showed that the hardest puzzles are often not those with fifty variables, but those with three variables where our intuition stubbornly makes a false premise.
Similarly, logician Raymond Smullyan authored classics like What Is the Name of This Book?, populated by knights who always tell the truth and knaves who always lie. In Smullyan's world, solving a dilemma does not require mind reading; it requires paying ruthless attention to self-referential statements.
Edward de Bono pointed out that vertical thinking is like digging the same hole deeper. Lateral thinking is like digging a new hole somewhere else. To escape mental traps, you must examine which rules were given in the problem, and which rules you unconsciously volunteered.
Figure 5.1 — Stepping Beyond Self-Imposed Borders
Three Classic Lateral Problems
The Two Ferryboats
Two boats start from opposite banks of a river at the same instant. They pass each other at 720 yards from the nearest shore, continue to the banks, rest for 10 minutes, and cross again, meeting 400 yards from the other shore.
The Hidden Insight
Rather than calculating complex speeds and time variables, notice the combined distance: on their first meeting, they have traversed exactly one river width combined. On their second meeting, they have covered three river widths!
The Three Light Switches
You are outside a closed room with three light switches. One switch operates an incandescent bulb inside. You may enter the room only once. How can you determine with certainty which switch controls the lamp?
The Thermal Variable
Turn switch 1 on for ten minutes. Turn it off, flip switch 2 on, and enter immediately. If the bulb is on, it is switch 2. If it is off but warm to the touch, it is switch 1. If it is cold and dark, it is switch 3.
The Counterfeit Coin
You have nine visually identical coins. One is slightly heavier than the other eight. Using an unweighted two-pan balance scale, how can you pinpoint the heavy coin in exactly two weighings?
Ternary Division
Divide into three groups of three (A, B, C). Weigh A against B. If they balance, the heavy coin is in C; if not, it is in the heavier pan. Weigh any two from that group to isolate the coin.