Once a year, thousands of logicians gather in the desert for an event called Learning Man. It’s a week-long celebration where they share ideas, solve tough problems, and have fun. One of the highlights is the world’s most exclusive club, where a special rave for logicians takes place under the full moon. To get in, you must solve a tricky puzzle given by the Demon of Reason, who guards the entrance.
You arrive late, and 23 of your logician friends are already inside. You face the demon alone, and he presents you with a challenge. When your friends arrived, the demon put masks on their faces and forbade any communication. Each logician could see everyone else’s masks but not their own. The demon told them that he distributed the masks so that each person could eventually figure out the color of their own mask using logic. Every two minutes, he rang a bell, and anyone who could correctly identify their mask color was allowed in.
Here’s what happened: Four logicians entered at the first bell. A group wearing red masks entered at the second bell. No one entered at the third bell. Logicians wearing at least two different colors entered at the fourth bell. All 23 of your friends eventually got inside by using perfect logic. Your task is to figure out how many people entered when the fifth bell rang.
Take a moment to think about it.
At first, it seems tough to figure out your own mask color just by looking at others. But before the first bell, everyone realizes something important. If a logician has a silver mask, they would see various colors but no silver. So, they can’t assume silver is an option, meaning there must be at least two masks of each color.
Now, imagine exactly two people have the same color mask. Each sees only one mask of that color. Knowing there must be more than one, they can immediately deduce their own mask color. This likely happened before the first bell, with two pairs of logicians figuring out their mask colors by spotting a unique color in the room.
What if there are three people with the same color? Each sees two others with that color. If A sees B and C, they expect B and C to leave at the first bell, like the previous pairs. When that doesn’t happen, A realizes they must also have that color, leading all three to leave at the next bell. This is what happened with the logicians in red masks—there must have been three of them.
This sets up a pattern using inductive reasoning. Induction helps us solve the simplest case and find a pattern for larger groups. The pattern is that everyone will know their group as soon as the previous group size has the chance to leave. After the second bell, 16 people remained. No one left at the third bell, indicating there weren’t any groups of four. Multiple groups, likely of five, left at the fourth bell. Since three groups would leave only one mask wearer, which isn’t possible, it must have been two groups. This leaves six logicians outside when the fifth bell rings—the answer to the demon’s riddle.
With the riddle solved, you can now join your friends and enjoy the festivities!
Gather in small groups and simulate the mask deduction scenario. Each student will wear a colored card on their forehead, visible to others but not to themselves. Use the same rules as the riddle, and see who can deduce their card color first. Reflect on the logic used and discuss the strategies that led to the correct deductions.
Engage in a workshop where you explore inductive reasoning through various puzzles and problems. Start with simple cases and gradually increase complexity, identifying patterns and making predictions. Discuss how these skills apply to real-world scenarios and the importance of logical reasoning.
In pairs, create a riddle similar to the Demon Dance Party, focusing on logical deduction and reasoning. Exchange riddles with another pair and attempt to solve them. Share your solutions and discuss the thought processes involved in creating and solving these puzzles.
Read a short story or excerpt that involves a logical puzzle or mystery. Analyze the characters’ reasoning and decision-making processes. Discuss how logic is used to advance the plot and resolve conflicts, drawing parallels to the riddle-solving process.
Participate in a group discussion about common logical fallacies and how they differ from sound reasoning. Identify examples of fallacies in media or everyday situations. Reflect on how understanding these can improve your problem-solving skills and decision-making abilities.
Once each year, thousands of logicians gather in the desert for Learning Man, a week-long event where they share ideas, tackle tough problems, and enjoy festivities. At the heart of this gathering is the world’s most exclusive club, where under the full moon, the annual logician’s rave takes place. The entry is guarded by the Demon of Reason, and the only way to gain access is to solve one of his challenging puzzles.
You arrive late with 23 of your closest logician friends, who are already inside. You must face the demon alone. He presents you with the following scenario: When your friends arrived, the demon placed masks on their faces and prohibited any form of communication. Each logician could see everyone else’s masks but could not see their own. The demon informed them that he distributed the masks in such a way that each person would eventually deduce the color of their own mask using logic alone. Every two minutes, he rang a bell, and anyone who could correctly identify the color of their mask would be admitted.
Here’s what transpired: Four logicians entered at the first bell. A group of logicians wearing red masks entered at the second bell. No one gained entry at the third bell. Logicians wearing at least two different colors entered at the fourth bell. All 23 of your friends played the game perfectly logically and eventually got inside. Your challenge is to determine how many people gained entry when the fifth bell rang.
Pause here to figure it out yourself.
It may seem challenging to deduce one’s own mask color using only logic and the colors visible on others’ masks. However, even before the first bell, everyone realizes something crucial. If a logician has a silver mask, they would see multiple colors but no silver. Therefore, they cannot conclude that silver is an option, making it impossible for them to deduce their own mask color. This implies that there must be at least two masks of each color.
Now, consider the scenario where exactly two people wear the same color mask. Each of them sees only one mask of that color. Since they know there must be more than one, they can immediately deduce their own mask color. This likely occurred before the first bell, with two pairs of logicians realizing their mask colors upon seeing a unique color in the room.
What if there are three people wearing the same color? Each of them sees two others with that color. If A sees B and C, they would expect B and C to behave like the previous pairs and leave at the first bell. When that doesn’t happen, A realizes they must also be wearing that color, leading all three to leave at the next bell. This is what happened with the logicians in red masks—there must have been three of them.
This establishes a basis for inductive reasoning. Induction allows us to solve the simplest case and identify a pattern that applies to larger sets. The pattern here is that everyone will know their group as soon as the previously sized group has the opportunity to leave. After the second bell, there were 16 people remaining. No one left at the third bell, indicating there weren’t any groups of four. Multiple groups, likely of five, left at the fourth bell. Since three groups would leave only one mask wearer, which isn’t possible, it must have been two groups. This leaves six logicians outside when the fifth bell rings—the answer to the demon’s riddle.
With that solved, you can now join your friends and enjoy the festivities!
Logic – The systematic study of the principles of valid inference and correct reasoning. – In order to solve the complex problem, she applied logic to evaluate each possible solution.
Reasoning – The action of thinking about something in a logical, sensible way. – His reasoning was sound, leading him to the conclusion that the hypothesis was incorrect.
Puzzle – A problem designed to test ingenuity or knowledge. – The logic puzzle required careful analysis and critical thinking to solve.
Masks – In logic, a metaphor for the different perspectives or assumptions that can obscure clear thinking. – The philosopher argued that societal masks often prevent individuals from seeing the truth.
Colors – In critical thinking, a metaphor for the various biases or perspectives that can influence reasoning. – She realized that her argument was colored by personal bias, affecting her objectivity.
Deduction – The process of reasoning from one or more statements to reach a logically certain conclusion. – Through deduction, he concluded that if all humans are mortal and Socrates is a human, then Socrates is mortal.
Induction – A method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion. – By observing numerous instances of the phenomenon, she used induction to formulate a general theory.
Group – A collection of individuals or entities considered together for analysis or discussion in logic and critical thinking. – The study group collaborated to tackle the challenging logic problems assigned by their teacher.
Challenge – A task or problem that tests a person’s abilities in logic and critical thinking. – The debate posed a significant challenge, requiring participants to think critically and argue effectively.
Riddle – A question or statement intentionally phrased to require ingenuity in ascertaining its answer or meaning. – Solving the riddle demanded not only logic but also creative thinking to uncover the hidden answer.
