Ckriman/General365_Public huggingface dataset:
Question: Tom is trapped in a letter maze. He is currently standing on the letter T. He can move to an adjacent letter position at a time in any direction. Each position can be visited only once. He is allowed to make one jump (to any unvisited position) exactly once.
 What is the most likely final password?
T  H  E  P  A
R  O  W  S  S
D  L  I  S  L
J  A  Z  Z  O
B  L  U  K  C

A. BLUE
B. JAZZ
C. LOCK
D. PASS
E. ZERO
Answer: C
Question: Will has accidentally wandered into a letter grid. He starts on the letter T. On each move, he can step to an adjacent letter in any direction. Each position may be visited only once. At one point during the path, he may make a single jump to any position he has not visited at all before.
What is the most likely password formed by the sequence of letters he visits?
T  R  O  W  S  K
H  E  P  A  S  S
A  K  D  R  O  W 
I  S  S  O  N  G
S  A  N  D  U
A, SONG
B, WORD
C, ROWS
D, SAND
E, SING
Answer: A
Question: The teacher wrote a sequence of characters on the blackboard:
8B, 96P, DO, _______?

Which option should fill in the blank to fit the pattern?

Alex thinks it has to do with the number of "enclosed regions"(closed loops) in the characters.
Brooke thinks it is related to whether the strokes in the characters are straight or curved.
The teacher says, "You're both right."

A. A
B. Q
C. 3CU
D. B
Answer: B
Question: Archaeologists discovered a sequence of mysterious symbols on a stone tablet:
⨂⨁⨂,⨁⨁⨀⨀,⨂⨀⨀⨀⨀,_______?
Which of the following symbol sets should fill in the blank to conform to the pattern?
Assistant A noticed the count of enclosed areas for each symbol.
Assistant B focused on the number of line intersections per symbol.
The professor concluded: "Add your two counts together, and the pattern emerges."
A. ⨁⨀
B. ⨂⨂
C. ⨀⨀⨀⨀⨀
D. ⨁⨂
Answer: A
Question: A programmer found a special character sequence in garbled text:
A66, A86, A88, _______?
Which character combination from the options below should fill the blank to follow the pattern?

Alex believes the pattern relates to the number of enclosed regions (closed loops) in the characters.
Brooke believes it relates to the stroke count of the characters.
The team leader says: "Both of these factors are relevant to the pattern."

A. BB6
B. B88
C. BB8
D. 888
Answer: C
Question: In a wizard duel, five representatives (A, B, C, D, E) from the Fire Empire, Ice Duchy, Storm Kingdom, Earth Federation and Holy Light Temple stand in a row from left to right, but their exact order is unknown. The following clues are provided:
1.Representative C's familiar is a griffin.
2.Representative E wears mithril armor.
3.Representative B replenishes energy by drinking elven mead.
4.Representative D is from the Earth Federation.
5.The representative who travels via portal replenishes energy by drinking magic spring water.
6.The representative who travels via portal stands immediately to the left of the representative who rides a nightmare.
7.The representative from the Storm Kingdom wears a golden mage robe.
8.The representative who commands a giant dragon is from the Fire Empire.
9.The representative standing in the middle replenishes energy by drinking the Spring of Life.
10.The representative from the Holy Light Temple replenishes energy by drinking moonwell water.
11.Representative A stands at the far left and is adjacent to the representative who rides a unicorn.
12.The representative from the Ice Duchy is adjacent to the representative who wears a silver formal gown.
13.The representative who wears bronze battle armor is adjacent to the representative from the Fire Empire.
14.The representative from the Ice Duchy is adjacent to the representative who draws power from the mana weave.
Question: How do each of the five representatives replenish their energy?(Please answer in sequence following the format in the quotation marks: "Elven Mead, Magic Spring Water, Spring of Life, Moonwell Water, Mana Weave Power")
Answer: Mana Weave Power, Elven Mead, Spring of Life, Magic Spring Water, Moonwell Water
Question: To celebrate the upcoming Food Festival, five new specialty restaurants have opened along the street, lined up from left to right as Restaurant A, Restaurant B, Restaurant C, Restaurant D, and Restaurant E. These five restaurants each feature a different signature cuisine (Sichuan, Cantonese, Shandong, Hunan, Huaiyang). In addition, each has a unique sign style, employee uniform color, and complimentary drink offered upon entry.

The following clues are known:  
1. Restaurant C has a neon sign.  
2. Restaurant E's employees wear gray uniforms.  
3. Restaurant B offers plum juice.  
4. Restaurant D specializes in Hunan cuisine.  
5. The restaurant with a flag sign offers lemon water.  
6. The restaurant with a flag sign is immediately to the left of the restaurant with a wooden plaque sign.  
7. The restaurant specializing in Shandong cuisine has employees in yellow uniforms.  
8. The restaurant with an electronic screen sign specializes in Sichuan cuisine.  
9. The restaurant in the very middle offers soy milk.  
10. The restaurant specializing in Huaiyang cuisine offers cola.  
11. Restaurant A is at the far left and is adjacent to the restaurant with a lantern sign.  
12. The restaurant specializing in Cantonese cuisine is adjacent to the restaurant whose employees wear white uniforms.  
13. The restaurant whose employees wear red uniforms is adjacent to the restaurant specializing in Sichuan cuisine.  
14. The restaurant specializing in Cantonese cuisine is adjacent to the restaurant that offers barley tea.

What complimentary drink does each of the five restaurants A, B, C, D, and E offer, in that order? (Answer in the format: "soy milk, cola, plum juice, barley tea, lemon water")
Answer: barley tea, plum juice, soy milk, lemon water, cola
Question: Five secret agents codenamed Alpha, Bravo, Charlie, Delta and Echo meet at a safe house. They are seated from left to right in an unknown order according to their seniority. The following information is known:
1.Agent Charlie's cover identity is a tourist.
2.Agent Echo's signature equipment is an EMP device.
3.Agent Bravo's extraction method is by helicopter.
4.Agent Delta's mission target city is Lisbon.
5.The agent with the cover identity of a"businessman" is extracted by train.
6.The agent with the cover identity of a "businessman" sits immediately to the left of the agent with the cover identity of an "artist".
7.The agent whose mission target city is Vienna carries a signature explosive pen.
8.The agent with the cover identity of a "diplomat" has Berlin as their mission target city.
9.The agent sitting in the middle is extracted by submarine.
10.The agent with the cover identity of an "artist" is extracted by parachute.
11.Agent Alpha sits on the far left and is adjacent to the agent with the cover identity of a "journalist".
12.The agent whose mission target city is Cairo is adjacent to the agent equipped with a laser watch.
13.The agent equipped with a grappling hook gun is adjacent to the agent whose mission target city is Berlin.
14.The agent whose mission target city is Cairo is adjacent to the agent extracted by sports car.
Question: What are the extraction methods of the five agents respectively?(Please answer in sequence following the format in quotation marks: "helicopter, parachute, train, submarine, sports car")
Answer: sports car, helicopter, submarine, train, parachute
Question: On a scorching summer day in Jingdezhen, a valuable porcelain display at a museum was vandalized. Although the glass case remained intact, the porcelain inside was shattered. Police concluded that the perpetrator had dropped a heavy object from above the case to crush the artifacts.
The curator testified: "To preserve the artifacts, the gallery is maintained in a cool, dry environment. Unfortunately, the security system was not working, and no footage was recorded." Upon hearing the noise, the curator immediately called the police, who arrived within minutes. However, only porcelain shards were found inside the display case. The perpetrator neither cleaned the scene nor took the tool used.
What was the most likely object used to shatter the porcelain?
A. A large ice block
B. A pebble
C. A ceramic chunk
D. A lead ball
E. A wooden block
F. A hammer
G. A glass block
Answer: C
Question: A case of property damage occurred in the coal-conveying workshop of a large coal-fired power plant in Northern China. The protective glass of a surveillance camera was shattered by an external force, causing an emergency shutdown of the production line. Investigators determined that the perpetrator stood beside the conveyor belt and smashed the glass with a heavy object in hand. Upon arrival, the police inspected the conveyor and surrounding floor, and found only glass shards mixed with a thick layer of coal dust and slag. The perpetrator neither cleaned the scene nor took the tool used. What was the most likely object used to shatter the glass?
A. An ice block
B. An iron hammer
C. A coal lump
D. A wooden stick
E. An iron block
F. A firebrick
G. A rubber rod
Answer: C
Question: At a chemical plant in southern China, a sabotage incident occurred in the raw materials warehouse, where a skylight on the roof was shattered. The police determined that the perpetrator smashed the skylight by dropping a heavy object from the roof. After investigation, the warehouse manager explained: "This area stores large quantities of quicklime, and the floor is covered with white lime powder and fragments." Upon inspection, the police found only glass shards in the lime pile directly below the skylight, and the pile itself appeared completely undisturbed. The perpetrator neither cleaned the scene nor took the tool used. What is the most likely object used to smash the glass?
A. A large ice block
B. An iron block
C. A lime block
D. Dry ice
E. A frozen fish
F. A ball filled with water
G. A brick
Answer: C
Question: On a Monday morning, Mr. Zhang and five colleagues-Ms. Wang, Mr. Chen, Mr. Liu, Mr. Zhao, and Mr. Li-held a short meeting in a conference room. Each is in charge of a different department, brought one specific office item, and has a bottle of drink in front of them. The six participants are seated in two rows, North and South, with three people per row, facing each other across a long table.
The following conditions are known:
1. The person who brought a laptop is drinking black tea.
2. Mr. Zhang is in charge of the Frontend department.
3. The person drinking green tea sits directly opposite Mr. Liu.
4. The Backend manager sits directly opposite the person who brought a tablet.
5. The person who brought the laptop sits in the middle seat of their row.
6. The Testing manager sits directly opposite Ms. Wang.
7. The person drinking bottled water and the person drinking coffee are seated next to each other.
8. Mr. Chen brought the projector.
9. The person who brought the folder sits directly opposite Mr. Zhang.
10. The person who brought the calculator is not the Product manager.
11. The Product manager is drinking orange juice.
12. The person to Mr. Li's immediate right brought the tablet.
13. The person with the calculator sits to the immediate right of the Operations manager.
14. Mr. Chen and Ms. Wang are not seated next to each other.
15. Ms. Wang is drinking bottled water.
16. To Mr. Zhang's immediate left is the Testing manager.
17. Mr. Zhao did not bring the folder.
Question: Who is drinking orange juice, and who is in charge of the Design department? (Please answer in the format: "Mr. Zhang, Mr. Li")
Answer: Mr.Chen, Mr.Zhao
Question: On a winter afternoon, Professor Li and five other scholars held an academic seminar in a study. Each wears a different colored overcoat, has brought a book from their respective field, and has a cup of warm tea. The six participants are seated in two rows of three, facing each other across a mahogany long table. The following conditions are given:
The person who brought the Astronomy book is drinking Black tea.
Professor Li is wearing a brown overcoat.
The person drinking Pu'er tea sits directly opposite Professor Wang.
The person in the gray overcoat sits directly opposite the person who brought the Physics book.
The person who brought the Astronomy book occupies the middle seat of their row.
The person in the navy blue overcoat sits directly opposite Professor Zhang.
The person drinking Longjing tea and the person drinking Biluochun tea are seated next to each other.
Professor Zhao brought the Philosophy book.
The person who brought the History book sits directly opposite Professor Li.
The person who brought the Chemistry book is not wearing a white overcoat.
The person drinking Tieguanyin tea is wearing a white overcoat.
The person to the immediate right of Professor Qian brought the Physics book.
The person with the Chemistry book sits to the immediate right of the person wearing a beige overcoat.
Professor Zhao and Professor Zhang are not seated next to each other.
Professor Zhang is drinking Longjing tea.
To Professor Li's immediate left is the person in the navy blue overcoat.
Professor Sun did not bring the History book.
Question: Who is drinking Tieguanyin tea, and who is wearing a black overcoat? (Answer format: "Professor Li, Professor Zhao")
Answer: Professor Zhao, Professor Sun
Question: On Monday morning, Alice and five colleagues are working in a temporary office area. These six colleagues are from different departments (indicated by different colored badges), each using a unique piece of office equipment, and each processing a specific type of document. They are seated in two rows of three, facing each other across a partition. The following conditions are known:
The person using a tablet is reviewing the budget sheet.
Alice is wearing a red badge.
The person writing the proposal sits directly opposite Bob.
The person wearing a yellow badge sits directly opposite the person wearing noise-canceling headphones.
The person using the tablet occupies the middle seat of their row.
The person wearing a blue badge sits directly opposite Carol.
The person performing code review and the person screening resumes are seated next to each other.
David is using a mechanical keyboard.
The person using a calculator sits directly opposite Alice.
The person using dual monitors is not wearing a white badge.
The person reading the sales report is wearing a white badge.
The person to Eva's immediate right is wearing noise-canceling headphones.
The person using dual monitors sits to the immediate right of the person wearing a purple badge.
David and Carol are not seated next to each other.
Carol is performing code review.
To Alice's immediate left is the person wearing a blue badge.
Frank is not the one using the calculator.
Question: Who is reading the sales report, and who is wearing the orange badge? (Answer format: "Alice, Carol")
Answer: David,Frank
Question: On the battlefield, a general encounters three knights wearing cloaks of gold, silver, and bronze. Two of them are sworn brothers, and one is a traitor. The elder brother tells the truth by day and lies by night, while the younger brother behaves oppositely. The traitor may tell the truth or lie at any time. The general records the following dialogue after asking, "Who among you is the elder brother, and is it day or night?" Gold cloak says, "I am the sworn elder brother or the bronze cloak is the traitor." Silver cloak says, "He is not the elder brother." Bronze cloak says, "I am not the elder brother." Please list all possible situations. (Answer in the format: "Time: day; Gold cloak: elder brother; Silver cloak: younger brother; Bronze cloak: traitor")
Answer: Situation 1: Time: day; Gold cloak: elder brother; Silver cloak: younger brother; Bronze cloak: traitor.
Question: A scholar accidentally wanders into a magic tower and finds three mages wearing robes of different colors: fiery red, icy blue, and earthy brown. Two of them share a master-apprentice relationship, while the third is an intruder. The following is known: When the spell is active, the master tells the truth; when the spell is inactive, the master lies. The apprentice behaves oppositely. The intruder may tell the truth or lie at any time. The scholar records the following dialogue after asking, "Who among you is the master, and is the spell active?" Fiery Red Robe says, "Either I am the master, or the Earthy Brown Robe is the intruder." Icy Blue Robe says, "He is not the master at all." Earthy Brown Robe says, "I am not the master." Please list all possible scenarios. (Answer in sequence using the format in quotation marks: "Spell: Active; Fiery Red Robe: Master; Icy Blue Robe: Apprentice; Earthy Brown Robe: Intruder")
Answer: Scenario 1: Spell: Active; Fiery Red Robe: Master; Icy Blue Robe: Apprentice; Earthy Brown Robe: Intruder
Question: A caravan leader in a foreign city is looking for a guide and encounters three locals wearing different masks: Sun, Moon, and Star. Two of them are local partners, and one is a spy. The following is known: 1. Partner A tells the truth during high tide and lies during low tide; Partner B behaves oppositely. 2. The spy may tell the truth or lie at any time. The leader records the following dialogue after asking, "Who among you is Partner A, and is it high tide or low tide?" Sun mask says, "I am Partner A or the Star mask is the spy." Moon mask says, "He is not Partner A." Star mask says, "I am not Partner A." Please list all possible situations. (Answer in sequence using the format in quotation marks: "Tide: high tide; Sun mask: A; Moon mask: B; Star mask: spy")
Answer: Situation 1:Tide: high tide; Sun mask: A; Moon mask: B; Star mask: spy.
Question: Six knights-Arthur, Lancelot, Gawain, Bedivere, Percival, and Galahad-each obtained exactly one of the following holy relics: the Holy Grail, the Spear, the Sword, the Round Table, the Shield, and the Horn.

Each knight made two statements. Exactly one knight's two statements are both true, exactly one knight's two statements are both false, and each of the remaining four knights made one true statement and one false statement.

Determine how many possible assignments of relics satisfy all the statements below.

Statements:
Arthur: Lancelot obtained the Holy Grail; Bedivere did not obtain the Spear.
Lancelot: Gawain obtained the Sword; Percival did not obtain the Round Table.
Gawain: Bedivere obtained the Spear; Arthur did not obtain the Shield.
Bedivere: Percival obtained the Round Table; Galahad did not obtain the Horn.
Percival: Galahad obtained the Horn; Gawain did not obtain the Sword.
Galahad: Arthur obtained the Shield; Lancelot did not obtain the Holy Grail.
Answer: \boxed{324}
Question: Six departments-Marketing, R&D, Sales, HR, Finance, and Administration-are each in charge of exactly one project: Project A, Project B, Project C, Project D, Project E, and Project F.

Each department's representative made two statements. Exactly one representative made two true statements, exactly one made two false statements, and each of the other four made one true and one false statement.

Statements:
Marketing: R&D is in charge of Project A; HR is not in charge of Project B.
R&D: Sales is in charge of Project C; Finance is not in charge of Project D.
Sales: HR is in charge of Project B; Marketing is not in charge of Project E.
HR: Finance is in charge of Project D; Administration is not in charge of Project F.
Finance: Administration is in charge of Project F; Sales is not in charge of Project C.
Administration: Marketing is in charge of Project E; R&D is not in charge of Project A.

Question: How many possible assignments satisfy all the conditions?
Answer: \boxed{324}
Question: Six students-Alex, Brooke, Casey, Drew, Evan, and Finn-each borrowed exactly one book: history, geography, physics, chemistry, biology, or politics.

Each student made two statements. Exactly one studen's two statements are both true, exactly one student's two statements are both false, and each of the remaining four students made one true statement and one false statement.

Statements:
Alex: Brooke borrowed history; Drew did not borrow geography.
Brooke: Casey borrowed physics; Evan did not borrow chemistry.
Casey: Drew borrowed geography; Alex did not borrow biology.
Drew: Evan borrowed chemistry; Finn did not borrow politics.
Evan: Finn borrowed politics; Casey did not borrow physics.
Finn: Alex borrowed biology; Brooke did not borrow history.

How many possible assignments satisfy all the conditions?
Answer: \boxed{324}
Question: On a bus, it is known that:

Exactly four people are involved in a grandfather–grandchild relationship.
Exactly four people are involved in a grandmother–grandchild relationship.
Exactly four people are full siblings (they share both parents).

If there is only one grandfather on the bus, what is the minimum possible number of people on the bus?

(Note: Assume no marriages between close relatives, and count each person only once.)
Answer: \boxed{7}
Question: In a laboratory, it is known that there are 5 people who are either professors or students, 5 people who are either researchers or students, and 6 alumni. 

Given that there is exactly one professor, what is the minimum number of people in the laboratory?
Answer: \boxed{6}
Question: At a banquet, it is known that:
There are 6 people in the male host-guest group (including the male host).
There are 6 people in the female host-guest group (including the female host).
There are 8 private guests at the banquet (invited by only one host).
There is only one male host present.
What is the minimum total number of people at the banquet?
Answer: \boxed{11}
Question: At an artificial intelligence networking seminar, direct connections are established between some pairs of AI programs, while others have none. At the end of the conference, it is observed that for any two AI programs, there exists at least one other AI program that has established direct connections with both of them.
Among these 77 AI programs, what is the minimum number of direct connections that must have been established?
Answer: \boxed{114}
Question: At the annual wizards' convention, some wizards spar with one another, while others do not. By the end of the convention, it is observed that for any two wizards, there is at least one other wizard who has sparred with both of them. For the 101 wizards, what is the minimum number of magical spars that must exist?
Answer: \boxed{150}
Question: In the "City of Knowledge" in a fantasy world, some librarians recommend books to each other, while others do not. By the end-of-year review, it is observed that for any two librarians, there is at least one other librarian who has recommended books to both of them.
For the 1001 librarians, what is the minimum number of mutual recommendations that must exist?
Answer: \boxed{1500}
Question: A invented a board game where players win by arranging pieces into specific patterns on the intersections of a grid with 17 horizontal lines and 17 vertical lines. The game became a nationwide sensation, and the inventor was even granted an audience with the king. When the king asked what reward he desired, he replied, "I only ask for enough rice to fill the squares of this board: 1 grain in the first square, 2 grains in the second, 4 grains in the third, 8 grains in the fourth, and so on, doubling the amount for each subsequent square until the last one."Following this rule, the king would lose at least 2^n-1 grains of rice. What is the value of n?
Answer: \boxed{256}
Question: While playing Gomoku, B stared at the 15 × 15 board and pondered: if 1 grain of sand is placed on the first position, 3 grains on the second, 9 grains on the third, 27 grains on the fourth, and so on, following this pattern until the last position, the total number of grains would be (3^n − 1)/2. What is the value of n?
Answer: \boxed{196}
Question: In C's hometown, there is a local board game played on the intersections of a grid with 10 horizontal lines and 8 vertical lines. If rice grains are placed on the squares of this board-1 grain in the first, 2 grains in the second, 4 grains in the third, 8 grains in the fourth, and so on, doubling the amount for each subsequent position until the last one-the total number of grains on the board would be 2^n − 1. What is the value of n?
Answer: \boxed{63}
Question: A software development team has four new members: Alex, Ben, Chris, and Dana. Exactly two are front-end engineers and the other two are back-end engineers. Their roles have been assigned but not yet publicly announced.
Privately, the project manager reveals the following information:
Alex is told whether Ben and Chris are front-end or back-end.
Ben is told whether Dana is front-end or back-end.
Dana is told whether Chris is front-end or back-end.
After hearing this, Alex says, "I still cannot determine my own role."

Let a be the number of people who can now determine their own assigned roles (possibly by logical deduction). What is the value of a?
Answer: \boxed{0}
Question: Four philosophers-Socrates, Plato, Aristotle, and Diogenes-are participating in a debate. The positions have been assigned, with two arguing for the motion and two arguing against it, but the assignments are not fully disclosed to everyone.

The moderator privately tells Socrates which side Plato and Aristotle are on, tells Plato which side Diogenes is on, and tells Diogenes which side Aristotle is on. Everyone knows the rule that two people are on each side, and each person only has access to the information they are told.

After hearing this, Socrates says: "I do not know which side I am on." If the number of people who can determine their own side is a, what is the value of a?
Answer: \boxed{0}
Question: There are four boxes, owned by A, B, C, and D. Exactly two boxes contain gold, and the other two contain silver.
They are allowed to look into only the following boxes:
A may see the contents of B's and C's boxes.
B may see the contents of D's box.
D may see the contents of C's box.
After checking, A announces, "I still cannot determine what is in my own box."

Let a be the number of people who can now determine the contents of their own boxes (possibly by logical deduction). What is a?
Answer: \boxed{0}
Question: A famous painting was stolen from an art museum. Seven witnesses each made two separate assertions about the thief. It is known that for each witness, exactly one of the two assertions is true. Based on the testimonies below, determine the thief's true characteristics:
1. The thief wore a black trench coat. The thief escaped in a sedan.
2. The thief was bald. The thief wore dress trousers.
3. The thief wore jeans. The thief fled west.
4. The thief wore a black trench coat. The thief had long hair.
5. The thief escaped on a motorcycle. The thief carried a suitcase.
6. The thief wore a gray jacket. The thief fled east.
7. The thief carried a backpack. The thief had long hair.
Among these six categories-coat, pants, item carried, hairstyle, means of transportation, and escape direction-how many can be determined with certainty?
Answer: \boxed{0}
Question: A company's server was hacked. Seven cybersecurity experts analyzed the logs, each offering a pair of claims, with exactly one claim being true in each pair.

Based on the information below, infer the hacker's actual behavior. (Each numbered item corresponds to one expert's pair of claims; within that item, exactly one of the two claims is true.)

1. The login location was Asia; the attack took place in the evening.
2. The attack method was a phishing email; the target was financial data.
3. The operating system was Windows; the logs were wiped.
4. The login location was Asia; the operating system was Windows.
5. The attack took place in the early hours of the morning; a backdoor was left behind.
6. The target was user data; the login location was Europe.
7. A Linux system was used; the attack method was a brute-force attack.

Among the following aspects-login location, operating system, attack method, attack time, target data, and traces left behind-how many can be determined with certainty?
Answer: \boxed{0}
Question: A hit-and-run accident occurred at an intersection. Seven eyewitnesses provided the following descriptions of the vehicle and the driver. Each eyewitness made two separate assertions, and for each eyewitness, exactly one of the two assertions is true. Based on the testimonies, determine what must be true:
1. The vehicle is an SUV, and the driver is female.
2. The car is red, and the driver is wearing sunglasses.
3. The license plate is from out-of-province, and the incident occurred in the afternoon.
4. The vehicle is an SUV, and the driver is wearing a hat.
5. The driver is male, and the vehicle is a sports car.
6. The license plate is from in-province, and the incident occurred in the morning.
7. The car is silver, and the driver is female.
Among the following six categories-vehicle type, color, license plate origin, driver's gender, driver's features (accessories), and time of the incident-how many can be determined with certainty?
Answer: \boxed{0}
Question: In an ancient kingdom, there are 99 valiant knights. The king assigns missions, and each mission is carried out by either 1 knight or 2 knights.

For each knight, consider how many missions they participated in. The number of missions assigned to each knight is between 0 and 99, inclusive. Each knight can be assigned at most one solo mission, and no two missions involve exactly the same combination of knights.

What is the minimum number of knights who must have carried out at least one mission alone?
Answer: \boxed{50}
Question: A magic school has 5000 students. Each graduation project is completed by exactly one student or exactly two students working together.

The following conditions hold:
Every student participates in at least one project.
Every student participates in a distinct number of projects, with the total number being an integer between 0 and 5000 inclusive.
No student completes more than one solo project.
No two projects have exactly the same set of participants.

What is the minimum possible number of students who have completed a project alone?
Answer: \boxed{2500}
Question: An Olympic delegation has 10,000 athletes who take part in training sessions. Each session is either a solo session involving exactly one athlete or a pair session involving exactly two athletes.
Over one training cycle, every athlete participates in the sessions, and no two athletes take part in the same total number of sessions. Each athlete's total number of sessions is between 0 and 10,000 inclusive. Each athlete performs at most one solo session. Moreover, no two sessions have exactly the same set of participants.
What is the minimum possible number of athletes who have performed a solo session?
Answer: \boxed{5000}
Question: Atlantic Ocean : Ocean. Considering both the type of relationship and the specific characteristics of the Atlantic Ocean, which of the following is the most appropriate match?
A. Nile River : River 
B. New Guinea : Island 
C. Sahara : Africa 
D. Greenland : Island 
E. Russia : Country
Answer: B
Question: Nile : River relationship
Which of the following is the most appropriate analogy, considering the relationship and characteristics of the Nile?

A. Tonga Trench : Trench
B. Mount Everest : Himalayas
C. Yangtze River : Drainage Basin
D. Venus : Planet
E. Greenland : Island
Answer: E
Question: Jupiter : Planet

Considering both the type of relationship and the specific characteristics of Jupiter, which of the following options best fits the analogy?

A. Earth : Solar System 
B. Pluto : Planet 
C. Lake Superior : Lake 
D. Pacific Ocean : Ocean 
E. Star : Celestial Body 
F. Himalayas : Tibet
Answer: D
Question: There is a Pandora's Box containing a treasure map, but the box is locked and can only be opened by cracking the code. The code consists of 6 digits from 0 to 9, with no repetitions. Three clues are given:
1. In the sequence 089476, there are 4 correct digits in total, 2 of which are also in the correct positions.
2. In the sequence 734052, there are 3 correct digits, all of which are in the correct positions.
3. In the sequence 831456, there are 4 incorrect digits.
Question: What is the code to open the Pandora's Box?
Answer: \boxed{789012}
Question: The password is a 6-digit code made of distinct digits from 0 to 9. Use these clues:
384716: Exactly 4 digits appear in the password, and exactly 3 of those 4 are in the correct positions.
320175: Exactly 3 digits appear in the password, and all 3 are in the correct positions.
270816: Exactly 4 digits do not appear anywhere in the password.

What is the password?
Answer: \boxed{384195}
Question: The code consists of six distinct digits chosen from 0–9.
Clues:

852716 - Exactly four digits appear in the code, and exactly three of those are in the correct positions (and one correct digit is in the wrong position).

431079 - Exactly three digits appear in the code, and all three are in the correct positions.

528391 - Exactly four digits are incorrect, and two digits are correct.

Find the 6-digit code.
Answer: \boxed{452076}
Question: Mike recently learned this famous scenario: a single bacterium in a bottle doubles every minute (1 → 2 → 4 → …), and the bottle becomes full after 60 minutes. Inspired by that idea, he created the following pattern puzzle.
(50,2),0,0,5,2
(60,2),0,0,6,3
(70,2),0,0,9,4
(2,12),6,?,0,4

Each row follows the same rule. What number should replace the question mark?
Answer: \boxed{9}
Question: Mike recently learned this famous scenario: a single bacterium in a bottle doubles every minute (1 → 2 → 4 → …), and the bottle becomes full after 60 minutes. Inspired by that idea, he created the following pattern puzzle.
(14,3),4,4,7,2
(15,3),5,7,3,3
(2,11),8,4,0,2
(7,4),1,0,?,2

Each row follows the same rule. What number should replace the question mark?
Answer: \boxed{4}
Question: Mike just learned this: "A single bacterium is placed in a bottle. It undergoes binary fission (i.e., splits into two) every minute: one becomes two, two become four, and the bottle is completely full of bacteria after 60 minutes." Astonished by this, he drew inspiration from it to create a number pattern problem:
(3,8),1,6,5,6;
(4,5),4,2,0,1;
(5,5),5,2,1,3;
(3,7),7,8,1,?;
Each row follows the same rule. What number should replace the question mark?
Answer: \boxed{2}
Question: 0, -1, 5, -14, 30, ?
What number should replace the question mark? The pattern is generated by applying the same rule only to adjacent terms, and the sequence can be viewed as two interleaved subsequences.
Answer: \boxed{-55}
Question: Consider the sequence:
-2, 3, -6, 15, -42, ?

This is an alternating sequence generated by applying the same operation to each pair of adjacent terms. What number should replace the question mark?
Answer: \boxed{123}
Question: 10, 12, 9, 13, 8, ?
What number should replace the question mark? The pattern is generated by applying the same rule only to adjacent terms, and the sequence can be viewed as two interleaved subsequences.
Answer: \boxed{14}
Question: In class, the teacher gave a question:
1.^ 2. + 3./ 4. - 5. = 6. $
Which of the following is the correct grouping?
A, 146,235
B, 123,456
C, 134,256
D, 124,356
After copying the symbols down once, Alex immediately noticed the pattern and answered correctly. Which option is the correct classification?
Answer: C
Question: 1.@ 2.⊗ 3.≠ 4.∞ 5.≥ 6^

Which of the following groupings is correct? 
A. 126, 345
B. 156, 234
C. 146, 235
D. 145, 236

After copying the question once, Person A immediately spotted the pattern and answered correctly. Which option gives the correct grouping?
Answer: C
Question: 1.∝ 2.‰ 3.√4.∼ 5.※ 6!
Which of the following groupings is correct?
A, 126,345
B, 156,234
C, 146,235
D, 134,256
After copying the symbols down once, Alex immediately noticed the pattern and answered correctly. Which option is the correct classification?
Answer: D
Question: In a busy railway marshalling yard, there is a freight train consisting of 6 cars numbered 1 to 6. To depart smoothly, the train must be connected in strict numerical order (1, 2, 3, 4, 5, 6).
Due to a scheduling error, the current order of the cars is disrupted: (2, 3, 1, 6, 5, 4) (with the front of the train on the left).
The dispatcher can only control two automated tracks for adjustments, with the following rules:
Operation A (cycle): Move the first car at the front of the train to the rear; the remaining cars shift forward one position.
Example: (1, 2, 3, 4, 5, 6) → after operation becomes (2, 3, 4, 5, 6, 1).
Operation B (interleave): Split the train into front and rear halves (3 cars each), then insert the rear half's cars before the corresponding cars in the front half.
Example: (1, 2, 3, 4, 5, 6) → after operation becomes (4, 1, 5, 2, 6, 3).
What is the minimum number of operations the dispatcher needs to perform to restore the initial sequence (2, 3, 1, 6, 5, 4) to the standard order (1, 2, 3, 4, 5, 6)?
Answer: \boxed{8}
Question: The librarian of the Royal Library is organizing a set of precious encyclopedias. Instead of being numbered, the volumes are marked with letters A, B, C, D, E, and F.

To meet archiving requirements, the set must be arranged in strict alphabetical order (A, B, C, D, E, F) from left to right. The current sequence is disorganized: (B, C, A, F, E, D).

The librarian can use two types of mechanical devices to adjust the order: Device A (Shift Left): Remove the leftmost book and place it at the far right of the row. Example: (A, B, C, D, E, F) → (B, C, D, E, F, A).

Device B (Merge): Split the row into a left group (the first 3 books) and a right group (the last 3 books). Each book from the right group is inserted to the left of its corresponding book in the left group (i.e., the 1st book of the right group is placed to the left of the 1st book of the left group, the 2nd to the left of the 2nd, and so on). Example: (A, B, C, D, E, F) → (D, A, E, B, F, C).

What is the minimum number of operations (using either device) required to restore the initial sequence (B, C, A, F, E, D) to the standard order (A, B, C, D, E, F)?
Answer: \boxed{8}
Question: There are 6 bottles of magic potions with different colors on the alchemist's table. According to an ancient recipe, they must be arranged in rainbow spectrum order from left to right: red, orange, yellow, green, blue, purple.
The apprentice accidentally mixed them up, so the current order is: (orange, yellow, red, purple, blue, green).
The alchemy table has two magic circles for adjusting the potion positions:
Magic Circle A (Cycle): Instantly teleport the leftmost potion to the far right, with the remaining potions shifting left by one position.
Example: (red, orange, yellow, green, blue, purple) → (orange, yellow, green, blue, purple, red)
Magic Circle B (Interleave): Split the potions into two halves (3 bottles each), then insert the right half's potions one by one in front of the corresponding potions in the left half.
Example: (red, orange, yellow, green, blue, purple) → (green, red, blue, orange, purple, yellow)
What is the minimum number of operations required to restore the sequence (orange, yellow, red, purple, blue, green) to the standard order (red, orange, yellow, green, blue, purple)?
Answer: \boxed{8}
Question: One morning, Zhang woke up to find that his watch had stopped-the hour and minute hands were frozen in place. He quickly replaced the battery. After confirming the hands were moving again, he went to work without resetting the time because he was in a rush. At that moment, when he first checked the watch, it showed 10:00.

On the way, he passed a large clock in the street showing that it was already 7:00. He arrived at the office as usual, without being late. After a busy morning, he checked his watch and it read 4:00. Feeling puzzled, he remembered that he had never reset the time, and he had no other way to check the time nearby, so he gave up.

After work, he walked home along the same route at his usual pace. He worked late today, but he was not in a hurry. When he passed the public clock again, it was already 8:30 p.m. When he got home, his watch happened to show 1:00.

At that time, what was the actual time in 24-hour format?
Answer: 21:15:00
Question: One morning, Jordan notices that his wristwatch has stopped-the hour and minute hands are frozen. He replaces the battery. The watch starts running normally again, but because he is in a rush, he does not reset it. At that moment, the watch reads 11:30. On his way to work, he passes a large public clock that shows 6:50. He arrives at the office and is not late. After a busy morning, he checks his watch and it reads 7:30. He then remembers he never reset it, and he has no other way to check the time at the office, so he gives up trying to correct it. After work, he walks home along the same route. He worked overtime and left later than usual, but he does not hurry and keeps his usual walking speed. When he passes the same public clock again, it shows 9:10 p.m. When he arrives home, his watch reads exactly 3:30.
What is the actual time at that moment, in 24-hour format?
Answer: 22:00:00
Question: One morning, Ethan woke up and found that his watch had stopped-the hour and minute hands were frozen in place. He quickly replaced the battery. Because he was busy, he only confirmed that the hands were moving properly again and went to work without resetting the time. At that moment, his watch showed 12:00.

On his way to work, he passed a large public clock showing 9:00. He got to work on time. After a busy morning, he checked his watch and saw it displaying 5:00. Feeling puzzled, he then remembered that he had forgotten to set the correct time, and he had no other timekeeping device with him, so he gave up.

After work, he took the same route home. Since he got off work on time that day, he walked at his usual pace. When he passed the public clock on the way back, it was 6:00 p.m. When he arrived home, his watch showed exactly 9:20.

What was the actual standard time (in 24-hour format) at that moment?
Answer: 18:10:00
Question: Assume a new regulation: The Earth's east-west orientation is reversed, such that the Sun rises in the west and sets in the east every day.

Prior to this regulation, Rome was located on the central meridian of its time zone at a longitude of 10° E. Under this new system, if the time difference between New Delhi and Rome is 5 hours, and the time difference between Bangkok and Rome is 7 hours, what are the longitudes of the central meridians for the time zones where New Delhi and Bangkok are located?
Answer: 65°W,95°W
Question: Rule: The east-west direction on Earth is reversed, and the Sun rises in the west and sets in the east every day.
Prior to this change, Berlin was located on the central meridian of a certain time zone at longitude 40° E. Istanbul is 2 hours ahead of Berlin, and Tehran is 4 hours ahead of Berlin.
What are the central meridian degrees of Istanbul and Tehran's time zones?
Answer: 10°E,20°W
Question: It is now stipulated that the directions of East and West on Earth are reversed, meaning the sun rises in the West and sets in the East. Prior to this change, Madrid was situated on the central meridian of its time zone at $5^{\circ} \text{E}$. If the time difference between Singapore and Madrid is 8 hours, and the difference between Tokyo and Madrid is 9 hours, what are the longitudes of the central meridians for the time zones of Singapore and Tokyo under the new stipulation?
Answer: 115°W,130°W
Question: Wright and Johnson are chefs working in the same restaurant. For a 5‑day "Gourmet Week," the restaurant presents 5 signature dishes in total. Each chef is required to feature one signature dish each day.

Wright features one different dish each day.
Johnson features 4 distinct dishes over the 5 days, repeating exactly one of them on the remaining day.

Question: What is the probability that they featured the same signature dish on exactly 4 out of the 5 days?
Answer: \boxed{\frac{1}{60}}
Question: Emma and Sophia are members of the same gym, which offers five popular group classes: Yoga, Spin, Kickboxing, Barbell, and Pilates. They both plan to attend one class per day for five consecutive days. Over the course of the week, Emma attends five different classes, while Sophia attends four different types of classes, repeating one of them on a second day. What is the probability that their schedules match (i.e., they attend the same class) on exactly four out of the five days?
Answer: \boxed{\frac{1}{60}}
Question: Mike and Gary are students at the same art studio, both participating in a four-day painting competition. Each day, they must select one of four designated themes: Landscape, Portrait, Still Life, and Abstract. During the competition, Mike chooses a different theme for each of the four days. Gary chooses three distinct themes over the four days, repeating one of them on a second day. 

What is the probability that they choose the same theme on exactly three out of the four days?
Answer: \boxed{\frac{1}{12}}
Question: Five "logically perfect" knights are seated around a round table. Each knight's shield bears either a lion emblem or an eagle emblem. Each knight can see the other four shields but not his own.

In front of all the knights, the king announces:
"Every shield bears either a lion or an eagle. At least one shield has a lion, and the number of lion shields is strictly less than the number of eagle shields.
I will now begin counting the lion shields, starting from 1 and counting slowly, saying each number aloud. After each number, each of you will have one chance to raise your hand. I will stop counting as soon as someone raises a hand.
Raise your hand only if you are certain of what's on your own shield."

After the king stops counting, how many knights raise their hands?
Answer: \boxed{5}
Question: There are n (n>4) "perfectly rational" robots standing in a circle. Each robot has either a green light or a yellow light on its chest. Each robot can see the light colors of the other robots but cannot see its own.
An engineer announces to all robots: "Each of you has either a green or a yellow light. There is at least one green light, and there are fewer green lights than yellow lights. I will start counting upward: 1, 2, 3, … as the possible total number of green lights. After each number I call out, you will all have one chance to send a signal. I will stop counting as soon as at least one robot signals. You should signal only when you know your own light color with certainty."
Question: When the counting stops, how many robots will have signaled?
Answer: \boxed{n}
Question: Twenty-one "perfectly rational" students are participating in an experiment. Each student has a card attached to their forehead labeled with either an odd or an even number. Each student can see the cards of the other 20 students but cannot see their own.
The professor announces to the group: "Each of you has a card with either an odd or an even number. At least one card is odd, and there are fewer odd cards than even cards. I will start counting upward: 1, 2, 3, …, as the possible total number of odd cards. After each number I call out, you will all have an opportunity to raise your hand. If anyone raises their hand, I will stop counting. You should only raise your hand if you have deduced with certainty whether the number on your own card is odd or even."
Question: When the professor stops counting, how many students will have raised their hands?
Answer: \boxed{21}
Question: A garden is divided into a 3×3 grid of connected cells. Eight cells contain items and one cell is empty (Row 3, Column 2).

Row 1: Garden table | Bench            | Flower stand
Row 2: Hammock      | Tool cabinet  | Landscape light
Row 3: Fountain         | [Empty]         | Storage box

The owner loves flowers and wants the garden table to end up adjacent to the flower stand (adjacent means sharing an edge; diagonal contact does not count). The flower stand must remain in its original cell.
The desired final state is:
The garden table ends up in the landscape light's original cell.
The flower stand, the empty cell, the fountain, and the hammock all remain in their original cells.
The remaining items may end up in any cells.

Movement rules:
- A cell can hold only one item at a time.
- An item may be moved only into an orthogonally adjacent empty cell (up, down, left, or right).

What is the minimum number of moves required to reach the desired final state?
Answer: \boxed{12}