List 60 logic prompts. Resolve each logically and explain your logic.
🏛️ Deductive Reasoning Puzzles
These puzzles have a single, verifiable solution derived from the premises.
1. The Two Guards
Prompt: You are at a fork in the road. One path leads to freedom, the other to doom. Two guards stand here. One always tells the truth (the Knight), and one always lies (the Knave). You can ask one guard one question. What question do you ask to find the path to freedom?
Resolution: You point to one of the paths (e.g., Path A) and ask either guard, "If I were to ask the other guard which path leads to freedom, what would he say?"
Logic:
If you ask the Knight: The Knight knows the Knave would lie and point to the wrong path (Path B). So, the Knight will tell you "He would say Path B."
If you ask the Knave: The Knave knows the Knight would truthfully point to the right path (Path A). The Knave must lie about this, so he will also tell you "He would say Path B."
In both cases, you are told the path to doom. You must take the opposite path.
2. The Three Switches
Prompt: A lightbulb is in a closed room. Outside the room are three light switches. You know one of them controls the bulb. You can flip the switches as much as you want while the door is closed, but you may only open the door and enter the room once. How do you determine which switch controls the light?
Resolution:
Turn Switch 1 ON for five minutes.
Turn Switch 1 OFF.
Turn Switch 2 ON.
Enter the room.
Logic:
If the light is ON, it's Switch 2.
If the light is OFF but the bulb is WARM, it's Switch 1.
If the light is OFF and the bulb is COLD, it's Switch 3.
3. Syllogism: All Men are Mortal
Prompt: Given these premises, is the conclusion valid?
All men are mortal.
Socrates is a man.
Conclusion: Therefore, Socrates is mortal.
Resolution: Yes, the conclusion is valid.
Logic: This is a classic example of a valid deductive syllogism. The conclusion necessarily follows from the premises. If the group "men" is entirely contained within the group "mortal," and Socrates is a member of the group "men," he must also be a member of the group "mortal."
4. Syllogism: Some Cats are Black
Prompt: Given these premises, is the conclusion valid?
Some cats are black.
Mittens is a cat.
Conclusion: Therefore, Mittens is black.
Resolution: No, the conclusion is invalid.
Logic: The first premise only states that some (not all) members of the "cats" group are also in the "black" group. Mittens is a cat, but she could be in the part of the "cats" group that is not black.
5. Syllogism: The Politician
Prompt: Given these premises, is the conclusion valid?
No honest people are politicians.
Sarah is honest.
Conclusion: Therefore, Sarah is not a politician.
Resolution: Yes, the conclusion is valid.
Logic: The first premise states that the set of "honest people" and the set of "politicians" are mutually exclusive (they have no members in common). Since Sarah is in the "honest people" set, she cannot be in the "politicians" set.
6. The Farmer, Wolf, Goat, and Cabbage
Prompt: A farmer must cross a river with a wolf, a goat, and a cabbage. His boat can only carry himself plus one other item. If left alone, the wolf will eat the goat, and the goat will eat the cabbage. How does he get all three across safely?
Resolution:
Farmer takes the Goat across. (Wolf and Cabbage are safe)
Farmer returns alone.
Farmer takes the Wolf across.
Farmer returns with the Goat. (Leaves Wolf on the far side)
Farmer takes the Cabbage across. (Leaves Goat on the start side)
Farmer returns alone.
Farmer takes the Goat across.
Logic: The goat is the key "problem" item, as it cannot be left with either the wolf or the cabbage. The solution requires a "shuttle" move, bringing the goat back to the original side temporarily.
7. The Sock Drawer
Prompt: You have 10 black socks and 10 white socks in a drawer. The room is completely dark. How many socks must you pull out to be absolutely certain you have a matching pair?
Resolution: Three.
Logic: This is the Pigeonhole Principle. There are only two "categories" (colors) of socks.
Your first sock is either black or white.
Your second sock is either black or white. If it matches the first, you have a pair.
If it doesn't match (e.g., you have one black, one white), the third sock must be either black or white, guaranteeing a match with one of the two you are already holding.
8. Married or Unmarried?
Prompt: Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?
Resolution: Yes.
Logic: We don't know if Anne is married or not, so we must check both possibilities.
Case 1: Anne is married. She is looking at George, who is unmarried. So, a married person (Anne) is looking at an unmarried person (George).
Case 2: Anne is unmarried. Jack, who is married, is looking at her. So, a married person (Jack) is looking at an unmarried person (Anne).
In either case, the statement is true.
9. The Three Children
Prompt: A woman has three children. The first child was born on a Monday. The second child was born on a Tuesday. Her third child was named "Wednesday." Why?
Resolution: "Wednesday" is the child's actual name.
Logic: This is a trick of assumption. The prompt misdirects you into thinking about the day of the week the child was born, but it's just a name.
10. Albert, Bernard, and Cheryl's Birthday
Prompt: Albert and Bernard just met Cheryl. "When's your birthday?" Albert asked. Cheryl said, "I won't tell you, but I'll give you clues." She writes down 10 dates:
May 15, May 16, May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17 She tells Albert the month and Bernard the day.
Albert: "I don't know when her birthday is, but I know that Bernard doesn't know either."
Bernard: "At first I didn't know, but now I know."
Albert: "Then I also know." When is Cheryl's birthday?
Resolution: July 16.
Logic:
Albert's first statement: Albert knows the month. For him to know that Bernard doesn't know, his month cannot contain a unique day. The unique days are 18 (June) and 19 (May). If Cheryl had told Albert "May" or "June," he couldn't be sure Bernard didn't know (Bernard might have 18 or 19). Therefore, Albert must have been told July or August.
Bernard's statement: Bernard hears this and eliminates May and June. He now only considers dates in July and August. He says he now knows the birthday. This means the day he was told is unique among the remaining options (July 14, July 16, Aug 14, Aug 15, Aug 17). The day 14 appears twice, but 16, 15, and 17 are now unique. If he had 14, he wouldn't know. So he must have 15, 16, or 17.
Albert's final statement: Albert hears that Bernard now knows. Albert (who knows the month is July or August) can now figure it out.
If Albert had August, Bernard could have 15 or 17. Since Bernard knew, Albert still wouldn't know if it was Aug 15 or Aug 17.
If Albert had July, Bernard could have 16. Since Bernard knew, Albert knows it must be July 16.
Since Albert also knows, the month must be July.
🌀 Paradoxes (Contradictions in Logic)
These prompts present scenarios where valid reasoning leads to a self-contradictory or logically impossible conclusion.
11. The Liar Paradox
Prompt: A man says, "This statement is false." Is the statement true or false?
Resolution: This is a paradox.
Logic:
If the statement is TRUE, then what it says ("This statement is false") must be true. This is a contradiction.
If the statement is FALSE, then what it says ("This statement is false") must be false. This means the statement is not false, which means it is true. This is also a contradiction.
The statement is unresolvable because it is self-referential and negative.
12. The Barber Paradox
Prompt: In a village, the barber (a man) shaves all men who do not shave themselves, and only those men. Who shaves the barber?
Resolution: This is a paradox; the barber cannot exist under these rules.
Logic:
If the barber shaves himself: The rule says he only shaves men who do not shave themselves. By shaving himself, he violates the rule.
If the barber does not shave himself: The rule says he must shave all men who do not shave themselves. By not shaving himself, he violates the rule.
The setup describes an impossible set of conditions.
13. The Ship of Theseus
Prompt: A famous ship is kept in a museum. Over 100 years, every single wooden plank, sail, and rope is replaced due to decay. Is it still the same Ship of Theseus?
Follow-up: What if someone collected all the original, decayed pieces and rebuilt the ship? Which one is the real Ship of Theseus?
Resolution: This is a philosophical paradox about identity. There is no single logical "right" answer.
Logic: It forces us to question what "identity" means.
Argument 1 (Identity is continuity): The ship in the museum is the real one, as it has a continuous historical existence, even if its parts changed.
Argument 2 (Identity is material): The rebuilt ship is the real one, as it is made of the original "stuff."
The paradox reveals that our concept of "sameness" is ambiguous.
14. Zeno's Dichotomy Paradox
Prompt: To walk to a wall, you must first walk halfway there. To cover the remaining distance, you must walk halfway again (1/4 total). Then you must walk halfway again (1/8 total), and so on. Since you must complete an infinite number of "halfway" tasks, how can you ever reach the wall?
Resolution: The paradox confuses a conceptual (infinite divisions) with a physical (finite distance).
Logic: While you can conceptually divide a finite distance an infinite number of times, the time it takes to cross these divisions also gets infinitely smaller. The sum of this infinite series of time intervals is a finite number. In calculus, the sum of converges to a finite limit (1). Motion is possible because a finite distance can be crossed in a finite time.
15. The Grandfather Paradox
Prompt: You build a time machine and go back in time to when your grandfather was a young, childless man. You kill him. If he dies, he never has your parent, and you are never born. If you are never born, you can't go back in time to kill him. So he lives... which means you are born and can go back and kill him.
Resolution: This is a paradox of time travel causality.
Logic: It highlights a logical contradiction in the idea of changing the past. Possible (hypothetical) resolutions include:
Fixed Timeline: You cannot change the past. The universe would somehow prevent you. Your attempt to kill him would fail (e.g., your gun jams), because you are there as living proof of his survival.
Multiverse: Your action creates a new, alternate timeline. You have killed the grandfather in Timeline B, but you originated from Timeline A, where he lived. You can never return to your original timeline.
16. The Irresistible Force Paradox
Prompt: What happens when an unstoppable force (an object that cannot be stopped) meets an immovable object (an object that cannot be moved)?
Resolution: The premises are contradictory. Such a scenario is impossible.
Logic:
If an unstoppable force exists, then by definition, an immovable object cannot exist (because the force would move it).
If an immovable object exists, then by definition, an unstoppable force cannot exist (because the object would stop it).
It's a logical contradiction, not a physics problem. You cannot have both in the same universe.
17. The Unexpected Hanging
Prompt: A prisoner is told he will be hanged at noon on a weekday next week (Mon-Fri). He is also told, "The exact day will be a surprise." The prisoner thinks:
"It can't be Friday, because if I'm not hanged by Thursday, I'll know it's Friday, so it's not a surprise."
"Since Friday is out, it can't be Thursday (if I'm not hanged by Wednesday, I'll know it's Thursday)."
He reasons this way back to Monday, concluding he cannot be hanged at all.
He is hanged on Wednesday. He was completely surprised. What went wrong with his logic?
Resolution: The prisoner's logic fails because his initial premise ("I can know it's not a surprise") is flawed.
Logic: The paradox arises from the self-referential nature of "surprise." The prisoner's error is assuming he can know the future. He can only "know" it's not a surprise after the event (or lack of event) occurs.
On Wednesday, he cannot be certain he won't be hanged on Thursday or Friday. Therefore, the hanging on Wednesday is genuinely a surprise.
His ability to "rule out" Friday is itself based on a set of conditions (making it to Thursday night) that haven't happened yet. The sentence "The day will be a surprise" is a statement about the judge's knowledge vs. the prisoner's, and it cannot be perfectly mapped into the prisoner's own logical deductions about the future.
18. The Lottery Paradox
Prompt: It is rational to believe that any single ticket in a 10-million-ticket lottery will not win (the odds are 9,999,999 to 1 against). If it's rational to believe Ticket 1 won't win, and rational to believe Ticket 2 won't win, etc... then it is rational to believe that no ticket will win. But we know one ticket must win.
Resolution: This paradox shows a conflict between "rational to believe" (inductive) and "certain to be true" (deductive).
Logic: It is a mistake to combine many highly probable beliefs (Ticket X won't win) and conclude that the conjunction of all those beliefs is also highly probable. In fact, the conjunction (that no ticket will win) is 100% false. Logic dictates that "Some ticket will win" is a certainty, even if "This specific ticket will win" is a near impossibility.
19. The Card Paradox
Prompt: You are holding a card.
The front side says: "The statement on the other side of this card is TRUE."
The back side says: "The statement on the other side of this card is FALSE."
Resolution: This is another version of the Liar Paradox.
Logic:
If the Front is TRUE, then the Back must be TRUE. But the Back says the Front is FALSE. Contradiction.
If the Front is FALSE, then the Back must be FALSE. But the Back says the Front is FALSE, which would make the Back statement TRUE. Contradiction.
It's an unresolvable loop of self-reference.
20. The Sorites Paradox (Paradox of the Heap)
Prompt: A 1,000,000-grain pile of sand is a "heap." If you remove one grain, it is still a heap. If you remove another, it's still a heap. If "1,000,000 grains is a heap" and "a heap minus one grain is still a heap" are both true, then you must conclude that 1 grain of sand (or 0 grains) is also a heap. This is false.
Resolution: The paradox exposes the problem of vague terms.
Logic: The word "heap" is not a precise, mathematically defined term. It is a vague concept. The error is applying precise, step-by-step mathematical induction (if P(n) is true, then P(n-1) is true) to a concept that has no clear boundary. There is no specific grain of sand that "breaks" the heap, but the term "heap" still ceases to apply at some point.
🧐 Logical Fallacies (Flawed Arguments)
These prompts present an argument. The task is to identify why the argument is logically invalid.
21. Ad Hominem ("To the Man")
Prompt: "You can't trust Dr. Smith's research on climate change. I heard he's a bad tipper and is rude to his wife."
Resolution: This is an Ad Hominem fallacy.
Logic: The argument attacks Dr. Smith's personal character, which is irrelevant to the scientific validity of his research. It fails to address the argument or data itself.
22. Straw Man
Prompt:
Person A: "I think we should spend more on education and healthcare."
Person B: "So you're saying you hate our country, want to bankrupt us, and leave us defenseless by cutting all military spending?"
Resolution: This is a Straw Man fallacy.
Logic: Person B has ignored Person A's actual argument and replaced it with a distorted, exaggerated, and easy-to-attack "straw man" version (that A never made).
23. Slippery Slope
Prompt: "If we allow kids to choose their own bedtime, next they'll be choosing their own meals, then they'll be skipping school, and before you know it, they'll be living in a van down by the river. We can't let them choose their bedtime."
Resolution: This is a Slippery Slope fallacy.
Logic: The argument claims that a single, minor action (choosing bedtime) will necessarily lead to a chain of extreme, negative consequences, without providing any evidence that this causal chain is true or likely.
24. False Cause (Post Hoc Ergo Propter Hoc)
Prompt: "Ever since we hired the new CEO, sales have gone up. He is a fantastic leader."
Resolution: This is a False Cause (or Post Hoc) fallacy.
Logic: The argument assumes that because Event A (hiring CEO) happened before Event B (sales up), Event A caused Event B. This ignores other potential causes (e.S., a new product, a competitor failing, seasonal trends). Correlation does not equal causation.
25. False Dilemma (Either/Or)
Prompt: "In this city, you're either with us, or you're against us. Which is it?"
Resolution: This is a False Dilemma (or False Dichotomy).
Logic: The argument presents only two extreme options as if they are the only possibilities, when in reality, a spectrum of other options exists (e.g., being neutral, agreeing in part, having no opinion).
26. Appeal to Authority
Prompt: "My favorite actor, a 4-time Oscar winner, said this brand of vitamin water is the key to good health. It must be true."
Resolution: This is an Appeal to (False) Authority.
Logic: While an authority's opinion can be valid evidence (e.g., a doctor on medicine), this argument relies on an authority figure (an actor) who has no expertise in the relevant field (nutrition/health).
27. Bandwagon (Appeal to Popularity)
Prompt: "Millions of people have switched to this new social media app. It must be the best one."
Resolution: This is a Bandwagon fallacy.
Logic: The argument claims something is good or true simply because it is popular. Popularity does not guarantee quality or truth (e.g., "Millions of people used to think the Earth was flat").
28. Hasty Generalization
Prompt: "I visited New York City once and a taxi driver was rude to me. All New Yorkers are rude."
Resolution: This is a Hasty Generalization.
Logic: The argument draws a broad conclusion about an entire group based on a tiny, insufficient, and/or unrepresentative sample (one taxi driver).
29. Circular Reasoning (Begging the Question)
Prompt: "The Bible is the word of God. We know this because the Bible itself tells us it is."
Resolution: This is Circular Reasoning.
Logic: The argument's conclusion ("The Bible is the word of God") is used as its own premise ("The Bible... tells us it is"). It assumes the very thing it is trying to prove.
30. Appeal to Ignorance
Prompt: "No one has ever proven that ghosts don't exist. Therefore, they must exist."
Resolution: This is an Appeal to Ignorance.
Logic: The argument claims a proposition is true simply because it has not been proven false (or vice-versa). The absence of evidence is not evidence of absence.
31. The Gambler's Fallacy
Prompt: "That roulette wheel has landed on 'Red' five times in a row. It is due for 'Black' next."
Resolution: This is the Gambler's Fallacy.
Logic: The argument assumes that past, independent random events influence future outcomes. In reality, each spin of a (fair) roulette wheel is an independent event; the odds () are the same every single time.
32. The "No True Scotsman" Fallacy
Prompt:
Angus: "No Scotsman puts sugar on his porridge."
Bill: "My uncle is a Scotsman, and he puts sugar on his porridge."
Angus: "Ah, but no true Scotsman puts sugar on his porridge."
Resolution: This is the No True Scotsman fallacy.
Logic: Instead of accepting evidence that refutes his generalization, Angus is modifying his claim after the fact to exclude the counter-example. He is protecting his generalization by retroactively changing the definition of "Scotsman" to "people who don't use sugar."
33. Appeal to Nature
Prompt: "This herbal supplement is 100% natural, so it must be safe and effective. It's better than those artificial, lab-made medicines."
Resolution: This is an Appeal to Nature fallacy.
Logic: The argument assumes that "natural" is inherently good and "artificial" is inherently bad. This is flawed; many natural things are deadly (e.g., cyanide, arsenic, hemlock), and many artificial things are life-saving (e.g., antibiotics, vaccines).
34. The Texas Sharpshooter
Prompt: A researcher analyzes data from 100 counties and finds one county where the cancer rate is significantly lower. He then searches that one county for unique environmental factors and finds it uses a specific well-water source. He proclaims this well-water protects against cancer.
Resolution: This is the Texas Sharpshooter fallacy.
Logic: The argument is named after a Texan who fires 100 shots at a barn wall, then paints a target around the closest cluster of bullet holes and claims to be a sharpshooter. The researcher is finding a random cluster (a statistical anomaly) first and then defining the "target" (the well-water) after the fact, ignoring all the "misses" (the 99 other counties).
35. Sunk Cost Fallacy
Prompt: "I've already spent three years and $50,00.00 on this degree program. I hate it, but I can't quit now; I've invested too much."
Resolution: This is the Sunk Cost Fallacy.
Logic: The argument makes a decision about the future based on past, irrecoverable investments (the "sunk costs"). Logically, the decision to continue should only be based on future prospects (e.g., "Will finishing this degree be worth the additional time and money?"). The past costs are gone regardless.
36. Anecdotal Evidence
Prompt: "My grandfather smoked a pack a day and lived to be 95. Therefore, the idea that smoking is bad for you is clearly exaggerated."
Resolution: This is a fallacy of Anecdotal Evidence (a type of Hasty Generalization).
Logic: The argument uses a single personal story (an anecdote) to dismiss a large body of statistical evidence (which shows smoking is strongly correlated with early death). An anecdote is not data; it's a statistical outlier.
37. Middle Ground
Prompt: "Person A says the sky is blue. Person B says the sky is yellow. The truth must be somewhere in the middle; the sky is green."
Resolution: This is the Middle Ground fallacy.
Logic: The argument assumes that a compromise between two opposing positions is always the correct one. This is illogical when one position is factually correct and the other is factually wrong.
38. Burden of Proof
Prompt: "I claim there is an invisible, silent dragon in my garage. Since you cannot disprove my claim, I am right."
Resolution: This is Shifting the Burden of Proof.
Logic: The person making the extraordinary claim (the one with the dragon) has the burden of providing evidence for it. It is not the responsibility of others to disprove it.
39. Appeal to Emotion (Pity)
Prompt: "Professor, I know I failed all the exams, but I really need to pass this class. I've had a very hard semester, and if I fail, I'll lose my scholarship."
Resolution: This is an Appeal to Emotion (Pity).
Logic: The student is appealing to the professor's sense of pity, rather than providing any evidence that their grade (based on their work) is incorrect. The sad circumstances are not logically relevant to the academic assessment.
40. Genetic Fallacy
Prompt: "You're only a Christian because you were born in America. If you were born in India, you'd be a Hindu. Therefore, your beliefs are false."
Resolution: This is the Genetic Fallacy.
Logic: The argument attacks the origin (or genesis) of a belief, rather than the merits of the belief itself. How a person came to a belief is irrelevant to whether that belief is true or false.
📈 Inductive & Lateral Thinking Puzzles
These puzzles require you to find the most likely pattern or think "outside the box."
41. The Man in the Elevator
Prompt: A man lives on the 10th floor. Every day he takes the elevator down to the lobby. When he returns, if it's raining or if there are other people in the elevator, he goes straight to the 10th floor. Otherwise, he goes to the 7th floor and walks up the stairs. Why?
Resolution: The man is a little person (a dwarf).
Logic: He is too short to reach the "10" button.
If it's raining, he can use his umbrella to press the button.
If others are in the elevator, he can ask them to press it for him.
Otherwise, he can only reach the "7" button and must walk the rest.
42. The Man in the Bar
Prompt: A man walks into a bar and asks the bartender for a glass of water. The bartender pulls out a shotgun and points it at the man. The man says, "Thank you," and leaves. Why?
Resolution: The man had the hiccups.
Logic: The man didn't want water to drink; he wanted a cure for his hiccups. The bartender, realizing this, scared the hiccups out of him. The "Thank you" confirms the cure worked.
43. The Black Ravens
Prompt: You have observed 1,000 ravens, and all of them have been black. What is the logical conclusion?
Resolution: The most probable conclusion is that "All ravens are black."
Logic: This is Inductive Reasoning. We are moving from a large set of specific observations (1,000 black ravens) to a general rule. It is not deductively certain (a 1,001st raven could be white), but it is a very strong inductive inference.
44. What's the Next Number?
Prompt: What is the next number in this sequence: 1, 11, 21, 1211, 111221, ...
Resolution: 312211
Logic: This is a "look and say" sequence. Each number describes the previous number.
1is "one 1" ->1111is "two 1s" ->2121is "one 2, one 1" ->12111211is "one 1, one 2, two 1s" ->111221111221is "three 1s, two 2s, one 1" ->312211
45. What's the Next Letter?
Prompt: What is the next letter in this sequence: O, T, T, F, F, S, S, ...
Resolution: E
Logic: They are the first letters of the numbers: One, Two, Three, Four, Five, Six, Seven, Eight.
46. The Two Ropes
Prompt: You have two ropes, each of which takes exactly 1 hour to burn from end to end. The ropes do not burn at a uniform rate (e.g., the first half might burn in 10 minutes and the second half in 50). How can you measure exactly 45 minutes?
Resolution:
Light Rope 1 on both ends at the same time.
Simultaneously, light Rope 2 on one end.
Rope 1 will burn out completely in 30 minutes (since it's burning from both ends).
The instant Rope 1 burns out, light the other end of Rope 2.
Rope 2 (which had 30 minutes of burn time left) will now burn from both ends, taking half the remaining time: 15 minutes.
Total time = 30 mins (from Rope 1) + 15 mins (from Rope 2) = 45 mins.
Logic: The key is knowing that a rope lit on both ends always burns in half the total time (30 mins), regardless of its non-uniformity.
47. The Monty Hall Problem
Prompt: You are on a game show. There are three doors. Behind one is a car; behind the other two are goats. You pick Door #1. The host (who knows where the car is) opens one of the other doors, Door #3, to reveal a goat. He then asks you, "Do you want to switch your choice to Door #2?" Should you switch?
Resolution: Yes, you should absolutely switch.
Logic: This is a famous probability puzzle.
Initial Choice: When you picked Door #1, you had a 1/3 chance of being right and a 2/3 chance of being wrong (meaning the car is behind #2 or #3).
The Host's Action: The host opening a door is new information. He will always open a goat door.
If you initially picked the car (1/3 chance), switching makes you lose.
If you initially picked a goat (2/3 chance), the host is forced to open the other goat door, leaving the car behind the remaining door. Switching makes you win.
By switching, you are betting on your initial 2/3 chance of being wrong. Your new odds of winning by switching are 2/3, while staying gives you only a 1/3 chance.
48. The Man and the Window
Prompt: A man is found dead in a room with a closed door, a locked window, and a puddle of water. How did he die?
Resolution: He was stabbed with an icicle.
Logic: This is a classic lateral thinking puzzle. The "puddle of water" is the key clue. The icicle was used as a weapon (stabbing) and then melted, leaving no murder weapon, just water.
49. The Car Push
Prompt: A man pushes his car to a hotel and is told he is bankrupt. What happened?
Resolution: He is playing Monopoly.
Logic: The "car" is his game token. He "pushed" it, landed on a property with a "hotel," and didn't have enough money to pay the rent.
50. The Cabin in the Woods
Prompt: Five people are found dead in a remote cabin in the woods. They did not die of starvation, thirst, or violence. The cabin is intact. How did they die?
Resolution: They were in the cabin of a crashed airplane.
Logic: The "cabin" is an airplane cabin. They died in the crash.
51. Grue and Bleen (Goodman's New Riddle of Induction)
Prompt: An emerald is "grue" if it is observed to be green before midnight tonight, OR if it is blue (if observed after tonight). All emeralds we have ever seen are green.
Hypothesis 1: All emeralds are green.
Hypothesis 2: All emeralds are grue.
All our evidence supports both hypotheses equally. Why do we only accept Hypothesis 1?
Resolution: This is a deep philosophical problem about induction.
Logic: Nelson Goodman's paradox shows that our evidence doesn't logically force us to prefer "green" over "grue." We prefer "green" because it is "entrenched"—it's a simple, projectible property we have used in past successful inductions. "Grue" is a complex, time-dependent, and artificial property. The paradox suggests that good inductive reasoning relies on more than just the evidence; it also relies on which predicates we consider "natural" or "projectible."
52. The Surgeon
Prompt: A father and son are in a horrible car crash. The father dies. The son is rushed to the hospital. The chief surgeon sees the boy and says, "I cannot operate on this boy. He is my son." How is this possible?
Resolution: The surgeon is his mother.
Logic: This puzzle plays on the implicit (and outdated) gender bias that the "chief surgeon" is a man.
53. The Hospital Babies
Prompt: You are in a hospital. A new mother has a baby. What is the approximate probability that it's a boy?
Follow-up: The mother says, "I have two children. One of them is a boy." What is the probability that her other child is also a boy?
Resolution:
First question: (or, more precisely, ).
Second question: 1/3.
Logic:
The probability of a single birth is simple.
This is a conditional probability puzzle. When we know the mother has two children, there are four equally likely possibilities for (Child 1, Child 2):
(Boy, Boy)
(Boy, Girl)
(Girl, Boy)
(Girl, Girl)
The information "One of them is a boy" eliminates the (Girl, Girl) possibility. We are left with three possibilities: (Boy, Boy), (Boy, Girl), (Girl, Boy).
Only one of these three possibilities is (Boy, Boy). Therefore, the probability that the other child is a boy is 1/3.
54. The Lily Pad
Prompt: A lily pad is in a pond. It doubles in size every day. If it takes 30 days to cover the entire pond, on what day did it cover half the pond?
Resolution: Day 29.
Logic: The puzzle works backward. If the pad doubles every day, and it covers the whole pond on Day 30, it must have covered half the pond on the day before it doubled to its final size.
55. The Baseball Bat and Ball
Prompt: A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
Resolution: The ball costs $0.05 (five cents).
Logic: This is a cognitive test, not a complex math problem. The intuitive answer is $0.10, but that is wrong.
Let = Cost of Ball
Let = Cost of Bat
Substitute (B + 1.00) for T:
(Therefore, the ball is $0.05 and the bat is $1.05, for a total of $1.10)
56. The Chicken and the Egg
Prompt: Which came first, the chicken or the egg?
Resolution: The egg.
Logic: This is a biological logic prompt. At some point in evolutionary history, a non-chicken (a "proto-chicken") laid a fertilized egg. Due to a small genetic mutation, the creature that hatched from that egg was the first "chicken." Therefore, the egg (laid by a non-chicken) came before the chicken (that hatched from it).
57. The Horse Race
Prompt: A king wants his two sons to race their horses to a distant city to see who will inherit the kingdom. He declares that the son who owns the slower horse will win. The sons, confused, wander for days. They meet a wise old woman. After she gives them advice, they leap onto the horses and race as fast as they can to the city. What did she tell them?
Resolution: "Switch horses."
Logic: The rule is that the owner of the slower horse wins. By switching horses, each son is now motivated to ride the (other's) horse as fast as possible, to make his own horse (the one he's not riding) the slower of the two.
58. The Locked Room
Prompt: A man is found hanging in a locked room. The rope is around his neck, and his feet are 3 feet off the ground. The room is completely empty except for a large puddle of water on the floor directly beneath him. There is no chair or table. How did he do it?
Resolution: He stood on a large block of ice.
Logic: Similar to the icicle puzzle, the key is the puddle of water. He stood on the ice to secure the rope, and it melted away, leaving no evidence.
59. The Birthday Problem
Prompt: How many people need to be in a room for there to be a >50% probability that at least two of them share a birthday?
Resolution: 23 people.
Logic: This is a counter-intuitive probability problem. It's easier to calculate the probability of no matches.
With 1 person, there's a 365/365 chance of no match.
With 2 people, it's (365/365) * (364/365).
With 3 people, it's (365/365) * (364/365) * (363/365).
By the time you get to 23 people, the probability of no match drops below 50% (to ).
Therefore, the probability of at least one match rises above 50% (to ).
60. Wason Selection Task
Prompt: You are shown four cards on a table. Each card has a letter on one side and a number on the other. You see: [ A ] [ K ] [ 4 ] [ 7 ].
You must test this rule: "If a card has a vowel on one side, then it must have an even number on the other side."
Which card(s) must you turn over to check if the rule is being broken?
Resolution: You must turn over [ A ] and [ 7 ].
Logic:
[ A ] (a vowel): You must check this card. If its other side is odd, the rule is broken.
[ K ] (a consonant): You do not need to check this. The rule says nothing about what consonants must have.
[ 4 ] (an even number): You do not need to check this. Finding a consonant on the other side would not break the rule. The rule is not "if it has an even number, it has a vowel."
[ 7 ] (an odd number): You must check this card. This is the one most people miss. If its other side is a vowel, the rule is broken. This is checking the contrapositive (if not-even, then not-vowel).
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That's a great question, but the number 60 is not a standard classification. In logic, there aren't 60 distinct "types" of syllogisms. Instead, there are a few main categories, and one of those categories (categorical syllogisms) has 256 possible forms.
The most useful way to answer your request is to list the most important of these forms: the ones that are logically valid.
Here is a breakdown of the main syllogism types, including the 24 valid forms of categorical syllogisms and other major logical structures.
Part 1: Categorical Syllogisms
A categorical syllogism is a deductive argument with two premises and one conclusion, all of which are categorical propositions. These propositions come in four "moods":
A: Universal Affirmative (All S are P)
E: Universal Negative (No S are P)
I: Particular Affirmative (Some S are P)
O: Particular Negative (Some S are not P)
The "figure" of the syllogism (1, 2, 3, or 4) refers to the arrangement of the middle term (M). This gives 256 possible forms (e.g., AAA-1, EAE-2), but only 24 are valid.
The 15 Unconditionally Valid Forms
These are valid regardless of whether the categories they refer to have any existing members.
Figure 1 (M-P, S-M):
Barbara (AAA-1): (All M are P) + (All S are M) (All S are P). This is the most common form.
Example: All mammals are animals. All dogs are mammals. Therefore, all dogs are animals.
Celarent (EAE-1): (No M are P) + (All S are M) (No S are P).
Example: No reptiles are mammals. All snakes are reptiles. Therefore, no snakes are mammals.
Darii (AII-1): (All M are P) + (Some S are M) (Some S are P).
Example: All dogs are friendly. Some pets are dogs. Therefore, some pets are friendly.
Ferio (EIO-1): (No M are P) + (Some S are M) (Some S are not P).
Example: No homework is fun. Some assignments are homework. Therefore, some assignments are not fun.
Figure 2 (P-M, S-M): 5. Cesare (EAE-2): (No P are M) + (All S are M) (No S are P). * Example: No mammals are fish. All whales are fish. Therefore, no whales are mammals. 6. Camestres (AEE-2): (All P are M) + (No S are M) (No S are P). * Example: All fish have gills. No mammals have gills. Therefore, no mammals are fish. 7. Festino (EIO-2): (No P are M) + (Some S are M) (Some S are not P). * Example: No lazy people pass the test. Some students passed the test. Therefore, some students are not lazy. 8. Baroco (AOO-2): (All P are M) + (Some S are not M) (Some S are not P). * Example: All virtuous people are kind. Some people are not kind. Therefore, some people are not virtuous.
Figure 3 (M-P, M-S): 9. Darapti (AAI-3): (All M are P) + (All M are S) (Some S are P). * Example: All squares are rectangles. All squares are rhombuses. Therefore, some rhombuses are rectangles. 10. Disamis (IAI-3): (Some M are P) + (All M are S) (Some S are P). * Example: Some flowers are red. All flowers are plants. Therefore, some plants are red. 11. Datisi (AII-3): (All M are P) + (Some M are S) (Some S are P). * Example: All good students study. Some good students are athletes. Therefore, some athletes study. 12. Felapton (EAO-3): (No M are P) + (All M are S) (Some S are not P). * Example: No ghosts are real. All ghosts are spooky. Therefore, some spooky things are not real. 13. Bocardo (OAO-3): (Some M are not P) + (All M are S) (Some S are not P). * Example: Some mammals are not dogs. All mammals are animals. Therefore, some animals are not dogs. 14. Ferison (EIO-3): (No M are P) + (Some M are S) (Some S are not P). * Example: No books are video games. Some books are boring. Therefore, some boring things are not video games.
Figure 4 (P-M, M-S): 15. Fresison (EIO-4): (No P are M) + (Some M are S) (Some S are not P). * Example: No criminals are trustworthy. Some trustworthy people are witnesses. Therefore, some witnesses are not criminals.
The 9 Conditionally Valid Forms
These 9 forms are valid only if we assume the terms being discussed actually exist.
Barbari (AAI-1): (All M are P) + (All S are M) (Some S are P)
Celaront (EAO-1): (No M are P) + (All S are M) (Some S are not P)
Cesaro (EAO-2): (No P are M) + (All S are M) (Some S are not P)
Camestros (AEO-2): (All P are M) + (No S are M) (Some S are not P)
Bamalip (AAI-4): (All P are M) + (All M are S) (Some S are P)
Camenes (AEE-4): (All P are M) + (No M are S) (No S are P)
Dimaris (IAI-4): (Some P are M) + (All M are S) (Some S are P)
Fesapo (EAO-4): (No P are M) + (All M are S) (Some S are not P)
Calemos (AEO-4): (All P are M) + (No M are S) (Some S are not P)
Part 2: Other Major Types of Syllogisms
Beyond categorical syllogisms, there are several other important logical structures.
Hypothetical Syllogism (or Chain Argument): A valid argument made of three conditional ("if-then") statements.
Form: If P, then Q. If Q, then R. Therefore, if P, then R.
Example: If I study, I will pass. If I pass, I will graduate. Therefore, if I study, I will graduate.
Modus Ponens (Affirming the Antecedent): A valid mixed-hypothetical syllogism.
Form: If P, then Q. P is true. Therefore, Q is true.
Example: If it is raining, the ground is wet. It is raining. Therefore, the ground is wet.
Modus Tollens (Denying the Consequent): A valid mixed-hypothetical syllogism.
Form: If P, then Q. Q is false. Therefore, P is false.
Example: If it is raining, the ground is wet. The ground is not wet. Therefore, it is not raining.
Disjunctive Syllogism: A valid argument using an "either-or" premise.
Form: Either P or Q. Not P. Therefore, Q.
Example: I will have tea or coffee. I will not have tea. Therefore, I will have coffee.
Polysyllogism: A series of syllogisms where the conclusion of one becomes a premise for the next.
Sorites: A specific type of polysyllogism where premises are linked in a chain, and the final conclusion links the first subject to the last predicate.
Example: All A are B. All B are C. All C are D. Therefore, All A are D.
Enthymeme: An argument where one premise (or the conclusion) is left unstated because it is assumed to be obvious.
Example: "Socrates is mortal because he is human." (The unstated premise is "All humans are mortal.")
Epicheirema: A syllogism where a premise is supported by an additional reason or sub-argument.
Example: All men are mortal, because they are living beings. Socrates is a man. Therefore, Socrates is mortal.
Part 3: Common Syllogistic Fallacies (Invalid Forms)
It is also useful to know the "types" of syllogisms that are invalid. These are logical fallacies.
Fallacy of the Undistributed Middle: The middle term is not universal ("all" or "no") in at least one premise.
Example: All dogs are mammals. All cats are mammals. Therefore, all cats are dogs. (Invalid)
Fallacy of the Illicit Major: The "major" term (predicate of the conclusion) is universal in the conclusion but not in its premise.
Example: All dogs are mammals. No cats are dogs. Therefore, no cats are mammals. (Invalid)
Fallacy of the Illicit Minor: The "minor" term (subject of the conclusion) is universal in the conclusion but not in its premise.
Example: All tigers are predators. All tigers are mammals. Therefore, all mammals are predators. (Invalid)
Fallacy of Exclusive Premises: A syllogism with two negative premises.
Example: No reptiles are mammals. No fish are reptiles. Therefore, no fish are mammals. (Invalid)
Fallacy of Affirming the Consequent: An invalid form of a hypothetical argument.
Form: If P, then Q. Q is true. Therefore, P is true.
Example: If it is raining, the ground is wet. The ground is wet. Therefore, it is raining. (Invalid—the ground could be wet from a sprinkler).
Fallacy of Denying the Antecedent: An invalid form of a hypothetical argument.
Form: If P, then Q. P is false. Therefore, Q is false.
Example: If I am a chef, I own a hat. I am not a chef. Therefore, I do not own a hat. (Invalid—I could own a hat for other reasons).
This list provides a comprehensive overview of the most important valid and invalid forms that are studied in logic.
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