8  Creativity and Imagination: Puzzles that require creative thinking and imaginative solutions.

⚠️ This book is generated by AI, the content may not be 100% accurate.

8.1 Reframing

📖 Seeing a problem or situation from a new perspective to find a solution that may not have been obvious before.

8.1.1 Problem

You have a room with a table and three light switches outside the room. Each switch corresponds to a light inside the room. You can only enter the room once. How do you determine which switch controls which light?

  • Hint:
    • Consider the state of the lights after they have been on for a while
  • Answer:
    • Turn on two switches for 5 minutes. Turn off one of those switches and immediately enter the room. The light that is still on is controlled by the switch that is still on. The light that is warm to the touch but not on is controlled by the switch that was turned off. The remaining light is controlled by the switch that was never turned on.

8.1.2 Problem

You have two light bulbs and a 100-story building. You want to find out the highest floor from which you can drop an egg without breaking it. You can only drop the egg once. How do you do it?

  • Hint:
    • Think about the worst-case scenario
  • Answer:
    • Start from the 14th floor. If the egg breaks, drop it from the 13th floor. If it doesn’t break, drop it from the 27th floor. Keep doubling the floor number until the egg breaks. The highest floor from which you can drop the egg without breaking it is the floor below the one from which you dropped it and it broke.

8.1.3 Problem

You are in a dark room with a box of matches, a kerosene lamp, a candle, and a fireplace. Which do you light first?

  • Hint:
    • Think about the order in which you need to use the items
  • Answer:
    • The match

8.1.4 Problem

A man walks into a bar and asks for a glass of water. The bartender pulls out a gun and points it at the man. The man says “Thank you” and walks out. Why?

  • Hint:
    • Consider the man’s perspective
  • Answer:
    • The man had the hiccups and the bartender’s action scared him, curing his hiccups

8.1.5 Problem

There is a 10x10 grid of squares. How many squares are there?

  • Hint:
    • Think about the different sizes of squares
  • Answer:
    • 104 - 1 = 103 squares. This includes the 1x1 squares, the 2x2 squares, the 3x3 squares, and so on, up to the 10x10 square.

8.2 Analogical Thinking

📖 Drawing connections between seemingly unrelated things to generate new ideas and solutions.

8.2.1 Problem

A man is riding on a train looking out of the window. Across the tracks coming in the other direction is another train, where a beautiful woman can be seen looking out of the window. The two trains pass each other so quickly that they only make eye contact for a second. After the trains have passed, the man looks through his bag and discovers a lottery ticket that he’d forgotten he had. He fills out the ticket and wins the jackpot, quitting his day job and living a life of luxury. How did the woman on the other train contribute to his newfound wealth?

  • Hint:
    • Consider the connection between the man and the woman and how it could have contributed to his lottery win.
  • Answer:
    • The woman was holding a newspaper with the winning lottery numbers.

8.2.2 Problem

A farmer has 12 sheep. All but 9 die. How many sheep does he have left?

  • Hint:
    • Consider the meaning of ‘left’.
  • Answer:
    • 9

8.2.3 Problem

A man walks into a bar and asks for a glass of water. The bartender pulls out a gun and points it at the man. The man says ‘thank you’ and walks out. Why?

  • Hint:
    • Consider the relationship between the man, water, and the bartender’s action.
  • Answer:
    • The man had hiccups and the bartender’s action cured them.

8.2.4 Problem

What belongs to you, but other people use it more than you do?

  • Hint:
    • Consider something that is commonly shared or used by others.
  • Answer:
    • Your name

8.2.5 Problem

A man is found dead in a field. Next to him is a package of unopened crackers. How did he die?

  • Hint:
    • Consider the location and the cracker package.
  • Answer:
    • He stepped on a landmine and the crackers were his emergency rations.

8.3 Lateral Questioning

📖 Asking unexpected or challenging questions to break away from conventional thinking and explore new possibilities.

8.3.1 Problem

What is something you can hold without ever touching or using your hands?

  • Hint:
    • Consider the concept of ownership and possession.
  • Answer:
    • Your breath.

8.3.2 Problem

You measure my life in hours and I serve you by expiring. I’m quick when I’m thin and slow when I’m fat. The wind is my enemy.

  • Hint:
    • Think about objects that burn.
  • Answer:
    • A candle.

8.3.3 Problem

What has a bed but no head, a mouth but no teeth, and runs but never walks?

  • Hint:
    • Consider different types of bodies of water.
  • Answer:
    • A river.

8.3.4 Problem

What word becomes shorter when you add two letters to it?

  • Hint:
    • Think about the spelling of the word.
  • Answer:
    • Short.

8.3.5 Problem

I am always hungry, the more you feed me the more I grow, but when I’m thirsty, I get smaller.

  • Hint:
    • Consider natural elements.
  • Answer:
    • Fire.

8.4 Forced Connections

📖 Deliberately combining unrelated ideas or concepts to generate novel and unconventional solutions.

8.4.1 Problem

You have a match and you enter a dark room. Inside are an oil lamp, a kerosene lamp, and a candle. You only have one match. Which do you light first?

  • Hint:
    • Think about the order in which you would need to use the items.
  • Answer:
    • The match.

8.4.2 Problem

A man walks into a bar and asks for a glass of water. The bartender pulls out a gun and points it at him. The man says, ‘Thank you’ and walks out. Why?

  • Hint:
    • Consider the man’s physical condition.
  • Answer:
    • The man had the hiccups and the gun scared him, curing his hiccups.

8.4.3 Problem

What has roots as nobody sees, is taller than trees, up, up it goes, and yet never grows?

  • Hint:
    • Think about something that is always present but often overlooked.
  • Answer:
    • A mountain.

8.4.4 Problem

What gets wet when it dries?

  • Hint:
    • Consider something that changes state when it interacts with water.
  • Answer:
    • A towel.

8.4.5 Problem

A farmer has 12 sheep. All but 9 die. How many sheep does the farmer have left?

  • Hint:
    • Be precise in your interpretation of the question.
  • Answer:
    • 9 sheep.

8.5 Mind Mapping

📖 Creating a visual representation of thoughts and ideas to connect them, identify patterns, and generate new insights.

8.5.1 Problem

A newspaper has just published a crossword puzzle. The clues for 5 and 6 across are as follows: 5 Across: begins with an “E” and ends with a “G” 6 Across: begins with a “K” and ends with an “G”

  • Hint:
    • Think outside the box and consider the context of the puzzle.
  • Answer:
    • 5 Across: Evening; 6 Across: King

8.5.2 Problem

You are in charge of organizing the seating for a dinner party. You have a list of guest names, but no information about who knows who. How can you arrange the seating so that everyone is sitting next to at least one person they know?

  • Hint:
    • Consider a simple way to represent the constraints of the problem and apply a mathematical concept.
  • Answer:
    • Draw a graph with the guests as nodes and draw an edge between two nodes if the corresponding guests know each other. Find a Hamiltonian cycle in the graph, which is a path that visits each node exactly once and returns to the starting node.

8.5.3 Problem

You have a collection of coins, all of which are either heads or tails. You have a balance scale, but it can only be used once. How can you determine the odd coin out (heavier or lighter than the rest)?

  • Hint:
    • Think about how many groups of coins you can create based on their weight.
  • Answer:
    • Divide the coins into three equal piles. Weigh two of the piles. If they are equal, the odd coin is in the third pile. If they are not equal, the odd coin is in the heavier pile. Now you have two piles, one with the odd coin and the other with two normal coins. Weigh any two coins from the pile with the odd coin, and you will find the odd one out.

8.5.4 Problem

You have a square piece of paper. How can you fold it in half exactly twice?

  • Hint:
    • Think about the different ways you can fold the paper in half.
  • Answer:
    • Fold the paper in half horizontally, then unfold it. Then fold the paper in half vertically, then unfold it. Finally, fold the paper diagonally from one corner to the opposite corner.

8.5.5 Problem

You have a 10x10 grid of squares. You can only move one square at a time. How can you move the bottom right square to the top left square in the fewest moves?

  • Hint:
    • Think about the different ways you can move the squares.
  • Answer:
    • Move the square to the right, then up, then left, then up, then left, then up, then left, then up, then left.