Lateral Thinking Mini Workshop

Edward De Bono coined the term lateral thinking. It is about reasoning beyond what general logic reveals.

Sharpening your lateral thinking skills will open new opportunities simply because you will start looking at a problem/situation in completely new angles.

Rather than giving you theories about lateral thinking, I have chosen three problems that cannot be solved by traditional thinking. Please try to solve the problems by yourself before attempting to look at the solutions.

Think of this as a “Lateral Thinking Mini Workshop”

Problem #1: Billiard Ball

You have eight billiard balls. One of them is “defective,” meaning that it weighs more than the others. You have a balance. What is the minimum number of weighings to determine the faulty ball?

Problem #2: Contaminated Pill

You have five jars of pills. All the pills in one jar only are “contaminated.” The only way to tell which pills are contaminated is by weight. A regular pill weighs 10 grams; a contaminated pill is 9 grams. You are given a weighing machine and allowed to make one measurement with it. How do you tell which jar is contaminated?

The above two problems are from a book called “How Would You Move Mount Fuji?” by William Poundstone ( I have slightly modified them, though )

Problem #3: The total distance

A train travels from point A to Point B. The distance between Point A to Point B is 100 miles. The train travels at 10 miles per hour. At the same time a bird flies from Point A towards Point B. The bird is an adventurous bird. It travels at 20 miles per hour. When it reaches point B (way early as compared to the train) it turns back and travels toward the train. When it meets the train, it turns back and travels back to point B. And then it keeps repeating his journey back and forth to the train. What is the total distance traveled by the bird?

The above problem was shared with me by Raj Raheja, founder and chairman of Heartwood Studios.

Now the solutions:






Solution for Problem #1

The correct answer is two weighings.

You start with 3 balls each. Two outcomes are possible.

a. If the weights are equal, the faulty ball is one of the two remaining balls. One more weighing will reveal the faulty ball.

b. If the weights are not equal, you have already identified that it is one of the three balls on the scale. Now take the three balls and weigh one ball each and keep a ball aside. If the weights are unequal, you have identified the faulty ball. If the weights are equal, the ball you set aside is the faulty ball.

Solution for Problem #2

Let us assume that the bottles are labeled as A, B, C, D and E.

Take 1 pill from A, 2 pills from B, 3 pills from C, 4 pills from D and 5 pills from E. Weigh them all on the weighing machine. If none of the pills were contaminated, the weight would have been 150 grams ( 15 * 10 grams) However, since pills from one of the bottles are contaminated, the weight will be less than 150 grams. If the weight is less by 2 grams, then bottle B is contaminated. If the weight is less by 5 grams, then bottle E is contaminated.

Solution for Problem #3

The answer is 200 miles.

The solution is rather simple as you will see. The distance between point A and point B is 100 miles. The train travels at 10 miles per hour so it has traveled 10 hours to reach the destination. That is the same time the bird has traveled. But since the bird is traveling at 20 miles per hour, it has traveled 200 miles.

Have a great day!

Photo Courtesy: aishepmcr on Flickr