Ckriman/General365_Public huggingface dataset:
Question: A large square sheet of wrapping paper is used to wrap a cube. To create a specific grid texture, a designer follows a sequence where each cycle consists of three steps: first, folding the paper along its horizontal midline; second, folding it along its vertical midline; and finally, folding it along the horizontal midline again. These three actions together form a new rectangle. Ignoring physical limitations, if a total of 15 folding actions are performed following this pattern, into how many independent small rectangular regions will the creases divide the wrapping paper?
Answer: \boxed{32768}
Question: During a chemistry class, a student was folding a piece of circular qualitative filter paper. The process involved repeatedly folding the paper in half: first, folding the circle into a semicircle; then, folding the semicircle into a quadrant; and finally, folding that sector in half once more, resulting in an even narrower sector. If the student performed 15 consecutive folding operations on an exceptionally large piece of filter paper, how many independent small sectors would theoretically be formed by the creases?
Answer: \boxed{32768}
Question: One day, a teacher was grading homework when he turned to the other teachers in the office and said, "One of the questions was really tough - only three students got it right. We use the 26 letters of the alphabet to represent the 26 students. One letter appears in the word ZERO. One letter  stands for  a compass direction. In the alphabet, the letter that is 3 positions after the letter which is 9 positions before the third letter is exactly the second letter. The letter that is 10 positions after the first letter is exactly the second letter. Now, can you figure out what these three letters are?"
Answer: EOU
Question: One day, a teacher was grading assignments and remarked to his colleagues in the office, "One question was particularly difficult-only three students solved it correctly. We represent the 26 students using the 26 letters of the alphabet. Among the three letters in the answer, one letter is written using only straight lines; one letter is also a Roman numeral. According to alphabetical order, the letter that is two positions after the letter which is five positions before the third letter is exactly the second letter. Moreover, the letter that is seventeen positions after the first letter is exactly the second letter. What are these three letters?"
Answer: EVY
Question: One day, a teacher was grading homework when he turned to the other teachers in the office and said, "One of the questions was really tough and only three students got it right. We use the 26 letters of the alphabet to represent the 26 students. Here are the clues about the three letters corresponding to the students who solved the problem: One letter is a central symmetric figure; One letter stands for a common student grade; In the alphabet, the letter that is 2 positions after the 4th letter counting backward from the third letter is exactly the second letter. The letter that is 7 positions after the first letter is exactly the second letter." Question: What could these three letters be? List all possibilities.
Answer: AHJ,BIK,FMO
Question: In a magic library named Stardust Dome, the numbering of magic books' pages follows an ancient set of rules. A 40-page offensive spellbook is recorded as 1111; A 50-page offensive spellbook is recorded as 1212; A 30-page defensive spellbook is recorded as 132; A 35-page defensive spellbook is recorded as 203; A 60-page potion recipe book is recorded as 220; A 70-page potion recipe book is recorded as 240; A 20-page ancient magic tome is recorded as 32; A 50-page ancient magic tome is recorded as 122. Question: What should the page number be recorded as for a 40-page defensive spellbook with a large number of offensive spell illustrations?
Answer: \boxed{220}
Question: Among the mysterious and powerful dragon race, the true age of every dragon (measured in years) follows a peculiar notation system: the age of a 35-year-old adult male dragon is recorded as 1022. The age of a 40-year-old adult male dragon is recorded as 1111. The age of a 30-year-old adult female dragon is recorded as 110.
The age of a 32-year-old adult female dragon is recorded as 112. The age of an 8-year-old young dragon is recorded as 11. The age of a 10-year-old young dragon is recorded as 13. The age of a 90-year-old ancient giant dragon is recorded as 132. The age of a 100-year-old ancient giant dragon is recorded as 144. Question: What should the age be recorded as for a 121-year-old ancient giant female dragon pregnant with a male young dragon?
Answer: \boxed{171}
Question: In an avant-garde art gallery, every collection is coded with a special number based on its valuation (unit: 10,000 yuan). An oil painting valued at 250,000 yuan is coded as 121.
An oil painting valued at 400,000 yuan is coded as 220. A sculpture valued at 300,000 yuan is coded as 1010. A sculpture valued at 500,000 yuan is coded as 1212. A photographic work valued at 80,000 yuan is coded as 10. A photographic work valued at 120,000 yuan is coded as 14. An installation artwork valued at 600,000 yuan is coded as 220. An installation artwork valued at 800,000 yuan is coded as 310.
Question: What should the code be for a 200,000-yuan photographic work that documents ancient classic sculptures?
Answer: \boxed{24}
Question: An explosion occurred at a chemical plant early in the morning. Four staff members on duty checked their watches immediately after the blast. The times displayed were: 4:00, 4:05, 4:10, and 4:15.
It was later confirmed that these watches were inaccurate: One watch was 10 minutes fast. One watch was 5 minutes fast.The status of the other two watches was unknown.
Question: What was the exact time of the explosion?
Answer: 03:55:00
Question: Scenario: At a small observatory, four amateur astronomers recorded the time a rare comet reached its optimal observation point. The recorded times were: 00:20, 00:15, 00:10, 00:05. It was later found that their watches were inaccurate: One watch was 10 minutes fast. One watch was 5 minutes fast. The accuracy of the remaining two watches was unknown.
Question: What was the exact time the comet reached its optimal observation point?
Answer: Midnight (00:00)
Question: Last night, a theft of a rare treasure suddenly took place at a renowned downtown art museum. When the alarm blared, four security guards  at the scene checked their wristwatches, which displayed the following times: 11:05, 11:10, 11:15, and 11:20. Subsequent investigation revealed that none of their watches were keeping accurate time. One of the wristwatches was 10 minutes faster than the standard time and another was 5 minutes faster. The security guards couldn't recall the time deviations of the other two watches clearly. Question: What was the exact time when the theft occurred?
Answer: 11:00:00
Question: In a library, there are two types of books: fiction and non‑fiction. Each book is written in one of two languages: Chinese or English. Five readers, A, B, C, D, and E, make the following statements:

A: "All fiction books are in Chinese, or all non‑fiction books are in English."
B: "All fiction books are in English, or all non‑fiction books are in Chinese."
C: "Some fiction books are in Chinese, and some non‑fiction books are in English."
D: "Some fiction books are in English, and some non‑fiction books are in Chinese."
E: "Some fiction books are in Chinese, or some non‑fiction books are in English."

It is known that exactly two of these statements are true. Who must have lied?
Answer: ACE
Question: In a company, there are two types of computers: laptops and desktops. Each computer is installed with exactly one of two operating systems: Windows or Linux. Five employees, A, B, C, D, and E, make the following statements:

A: "All laptops run Windows, or all desktops run Linux."
B: "All laptops run Linux, or all desktops run Windows."
C: "Some laptops run Windows, and some desktops run Linux."
D: "Some laptops run Linux, and some desktops run Windows."
E: "Some laptops run Windows, or some desktops run Linux."

It is known that exactly two of these statements are true. Who must have told a lie?
Answer: ACE
Question: In a soccer team there are two types of players: forwards and defenders. This season, each player can be described in terms of scoring: a player has either scored at least one goal or has not scored any goals.

Five fans, A, B, C, D, and E, make the following statements:

A: "Either every forward has scored, or every defender has not scored."
B: "Either every forward has not scored, or every defender has scored."
C: "At least one forward has scored, and at least one defender has not scored."
D: "At least one forward has not scored, and at least one defender has scored."
E: "At least one forward has scored, or at least one defender has not scored."

It is known that exactly two of these statements are true. Who must have lied?
Answer: ACE
Question: A coachman drives a stagecoach. At the first town, one passenger gets off. At the second town, three new passengers board and one passenger gets off. At the third town, two more passengers board. No one both boards and alights at the same town. When a passenger leaves, any items they are carrying are also removed from the coach.

Originally, the coach is pulled by four horses. Later, because the mountain road is difficult, the coachman adds two more horses. Each passenger who boards at the second town carries five bags; each bag contains one four‑legged lizard that is missing one leg. Each passenger who boards at the third town carries eight jars; every jar holds two eight‑legged scorpions. The coach itself has twelve windows. During the journey, it passes a pasture containing one hundred sheep.

Under these conditions, what is the minimum possible number of living legs (including those of the horses) that are on the coach?
Answer: \boxed{337}
Question: A boatman is piloting a covered wooden boat. At the first ferry crossing, 3 passengers disembark.
At the second crossing, 5 passengers board and 1 disembarks. At the third crossing, 2 passengers board. No one boards and disembarks at the same crossing, and whenever a passenger disembarks, all of the luggage they are carrying leaves the boat with them. Every passenger who boards at the second crossing carries 3 cages, each containing 1 six-legged beetle. Every passenger who boards at the third crossing carries 4 bags, each containing 1 three-legged frog. The boatman considers the current too strong and therefore hires 2 horses on shore to tow the boat. Along the way, 5 large dogs are seen, each accompanied by 10 kittens. Inside the boat there are 50 seats; the legs of the seats are not to be counted.
Question: Under these conditions, what is the minimum total number of legs of living creatures that are on the boat or towing it?
Answer: \boxed{138}
Question: A bus driver is operating a double-decker bus. At the first stop, 8 passengers get off. At the second stop, 10 passengers board and 2 passengers get off. At the third stop, 7 passengers board. No one boards and alights at the same stop, and whenever a passenger gets off the bus, any pets they are carrying also leave with them. The driver keeps a two-legged parrot as a pet in the driver's cabin. Each passenger who boards at the second stop carries 3 boxes, each box containing 2 four-legged lizards. Each passenger who boards at the third stop carries 2 cages, each cage containing 10 six-legged grasshoppers. The bus has 120 handrails; non-living objects are not to be counted.
Question: Under these conditions, what is the minimum total number of legs of living creatures on the bus?
Answer: \boxed{1118}
Question: Mr. Wu encountered a puzzle:
2, 7, 1, 9, 25, 4, 3, 6, 2, 26, 5, a, b, 8, 88, 1, 8, 5, 10, 50, 6, 2, 4, 7, 50
After consulting an expert, he was told that the puzzle should be analyzed by grouping.
If a is a multiple of 3, how many distinct possible values can a+b have?
Answer: \boxed{5}
Question: Mr.Qiang encountered a puzzle:
1,3,2,6,12,2,4,3,5,22,8,a,b,2,56,3,1,8,7,29,4,2,9,1,22,
After consulting an expert, he was told that the puzzle should be analyzed by grouping.
Given a >5, how many distinct possible values can 
a+b have?
Answer: \boxed{4}
Question: Mr. Qing encountered a puzzle:
3,4,5,6,38,1,2,8,9,25,2,a,b,6,40,4,1,7,3,19,5,5,5,5,50,
After consulting an expert, he was told that the puzzle should be analyzed by grouping.
If a+b<20, how many distinct possible values can a+b have?
Answer: \boxed{2}
Question: At a company annual lottery, there are five boxes (numbered 1 through 5), and exactly one of them contains the grand prize. Each box has a note attached to it:
Box 1: "The grand prize is in Box 2 or Box 3."
Box 2: "The grand prize is not in Box 4 and not in Box 5."
Box 3: "This box does not contain the grand prize."
Box 4: "Neither Box 1 nor Box 2 contains the grand prize."
Box 5: "The box(es) mentioned above that are telling the truth are not the box containing the grand prize."
Question: How many different possible combinations of truth-telling boxes are there?
Answer: \boxed{5}
Question: At a graduation ceremony, there are five sealed mystery gifts in envelopes labeled A, B, C, D, and E, and exactly one of them contains the Principal's Special Award. Each envelope bears a statement:
Envelope A: "The award is in Envelope B or Envelope E."
Envelope B: "The award is in Envelope C or Envelope D."
Envelope C: "This envelope does not contain the award."
Envelope D: "Neither Envelope A nor Envelope B contains the award."
Envelope E: "All envelopes that make false statements are not the envelope containing the award."
Question: How many different possible combinations of envelopes that state the truth are there?
Answer: \boxed{6}
Question: On an alien space station, there are five teleporters labeled α, β, γ, δ, and ε, and exactly one of them can send you back to Earth. Next to each teleporter is a display screen showing a statement:
Teleporter α: "The teleporter that returns to Earth is β or γ."
Teleporter β: "The teleporter that returns to Earth is δ or ε."
Teleporter γ: "This teleporter cannot return to Earth."
Teleporter δ: "Neither teleporter α nor teleporter β can return to Earth."
Teleporter ε: "The teleporter that can return to Earth has a display showing a true statement."
Question: How many distinct possible combinations of teleporters whose displays show true statements are there?
Answer: \boxed{5}
Question: Seven super servers-Alpha, Beta, Gamma, Delta, Epsilon, Zeta, and Omega-are engaged in an automated attack-and-defense exercise. The operational rules and constraints are as follows:
Each server is restricted to specific targets:
Alpha: Can only attack one of the following: Beta, Gamma, or Zeta.
Beta: Can only attack one of the following: Alpha, Gamma, or Epsilon.
Gamma: Can only attack one of the following: Alpha, Beta, or Zeta.
Delta: Can only attack one of the following: Alpha, Gamma, or Epsilon.
Epsilon: Can only attack one of the following: Zeta or Omega.
Zeta: Can only attack one of the following: Epsilon or Omega.
Omega: Holds highest privileges and can attack any one of the other six servers.
The attack order is strictly fixed as follows:
Omega → Alpha → Beta → Gamma → Delta → Epsilon → Zeta.
Once a server is successfully attacked, it is immediately neutralized and taken offline. It will no longer participate in the sequence or execute any subsequent attacks.
The servers operate based on distinct priority directives:
Alpha, Beta, Gamma, Delta: These servers prioritize their own survival above all else. They will preferentially attack any active server that poses a direct threat to them.
Epsilon, Zeta: These servers have been programmed with a special directive: their highest priority is to neutralize Omega, regardless of their own survival.
Which server must Omega attack and neutralize at the very beginning of the sequence to guarantee that it will not be neutralized by any subsequent server?
Answer: Epsilon
Question: Seven galactic representatives-Alpha, Beta, Gamma, Delta, Epsilon, Zeta, and Omega-are attending a high-stakes sanctions conference. The proceedings are governed by a strict veto and expulsion protocol:
Each representative is restricted to a specific pool of targets:
Alpha: Must veto one of: Beta, Gamma, or Zeta.
Beta: Must veto one of: Alpha, Gamma, or Epsilon.
Gamma: Must veto one of: Alpha, Beta, or Zeta.
Delta: Must veto one of: Alpha, Gamma, or Epsilon.
Epsilon: Must veto one of: Zeta or Omega.
Zeta: Must veto one of: Epsilon or Omega.
Omega: Holds supreme authority and may veto any one of the other six representatives.
The voting sequence is fixed and linear:
Omega → Alpha → Beta → Gamma → Delta → Epsilon → Zeta.
Once a representative is vetoed, they are immediately expelled from the conference and disqualified from participating in any subsequent voting rounds.
The representatives act according to the following priorities:
Alpha, Beta, Gamma, Delta: Their primary objective is to "secure their own seat." They will prioritize vetoing any active representative who has the power to veto them.
Epsilon, Zeta: Their sole strategic goal is the expulsion of Omega, regardless of their own survival.
Omega's only goal is to ensure it remains in the conference and is not expelled by any subsequent representative.
Which representative must Omega veto first to guarantee that it will not be expelled by the end of the sequence?
Answer: Epsilon
Question: Seven mages, codenamed 1 through 7, are engaged in a duel where each may cast a Silencing Spell exactly once. The targeting restrictions are as follows:
Mage 1: Must target one of: 2, 3, or 6.
Mage 2: Must target one of: 1, 3, or 5.
Mage 3: Must target one of: 1, 2, or 6.
Mage 4: Must target one of: 1, 3, or 5.
Mage 5: Must target one of: 6 or 7.
Mage 6: Must target one of: 5 or 7.
Mage 7: May target any other mage except themselves.
The casting sequence is strictly fixed:
Mage 7 → Mage 1 → Mage 2 → Mage 3 → Mage 4 → Mage 5 → Mage 6.
A mage who is successfully silenced is immediately eliminated and removed from the Tower. They lose their turn and cannot participate in any subsequent part of the sequence.
The combatants operate under specific strategic directives:
Mages 1, 2, 3, 4: These mages prioritize their own survival. They will preferentially silence the earliest active mage in the sequence who has the capability to target them.
Mages 5, 6: These mages are focused solely on the elimination of Mage 7. This objective supersedes their own survival.
Mage 7's objective is to ensure they are not eliminated by any mage later in the sequence.
Which mage must Mage 7 silence at the very beginning to guarantee that they will not be eliminated?
Answer: Mage 5
Question: Wang and his classmates are studying an encryption algorithm. They defined the following rules:
3 + 1 = 100, 3 + 2 = 101, 3 + 3 = 110, 3 + 4 = 111, 3 + 5 = 1000.
Wang notes that the first number "3" is only included to make the pattern look more complicated.
According to this algorithm, if 3 + a = 13 and 3 + 8 = b, what is the value of b − a?
Answer: \boxed{1001}
Question: Le Le and his older brother were playing a number game, and they made a rule: 7+2=100, 7+3=101, 7+4=102, 7+5=110, 7+6=111. Le Le said that the first number 7 was actually useless and just a decoy. According to this algorithm, if 7+a=16 and 7+12=b, then what is the value of a+b?
Answer: \boxed{210}
Question: Two aliens were communicating with each other, using a calculation method unfamiliar to humans: 1+6=10, 1+7=11, 1+12=16, 1+13=20, 1+14=21. One of the aliens said, "We always start counting from 1, but this number 1 itself does not participate in the core transformation." According to this calculation method, if 1+a=13 and 1+16=b, then what is the value of b-a?
Answer: \boxed{14}
Question: Our company shuttle picks up and drops off employees after work. Because they live in different neighborhoods, the bus makes several stops along the route.
The driver told me that all employees follow the rules and board or alight in an orderly manner.

At the first stop, no one boarded, and 15 people got off.
At the second stop, 8 boarded and 22 got off.
At the third stop, 30 boarded and 10 got off.
At the fourth stop, 25 boarded and 5 got off.
At the fifth stop, 10 boarded and 30 got off.

What is the minimum possible number of employees remaining on the shuttle after these five stops?
Answer: \boxed{30}
Question: A luxury cruise ship was on its Mediterranean circumnavigation route, where passengers could board and disembark freely at different port cities. For the convenience of management, each passenger was only allowed to use the embarkation and disembarkation passages once at each port. According to the voyage log, 100 new passengers boarded the ship and 250 passengers disembarked for sightseeing at the first port of call; 300 passengers boarded and 150 disembarked at the second port; 200 passengers boarded and 400 disembarked at the third port; 500 passengers boarded and 100 disembarked at the fourth port. How many passengers were there at least on the cruise ship when it departed from the fourth port?
Answer: \boxed{600}
Question: To attend an island music festival, my friends took a ferry to their destination. According to them, the ferry stopped at several islets along the way to pick up and drop off tourists. For the convenience of management, each passenger was only allowed to use the embarkation and disembarkation passages once at each dock. 50 passengers boarded and 80 passengers disembarked at the first dock; 100 passengers boarded and 90 disembarked at the second dock; 200 passengers boarded and 300 disembarked at the third dock; 250 passengers boarded and 100 disembarked at the fourth dock; 120 passengers boarded and 40 disembarked at the fifth dock. How many passengers were there at least on the ferry when it departed from the dock for the last time?
Answer: \boxed{430}
Question: A young knight set out on a quest to find the legendary sacred sword. In the guardian temple, he discovered an inscription: "Warrior, strength is not the only thing-wisdom is the key." On the temple wall, the following symbols were carved:
1 2 3
4 / /
/ / /
5 / 6
/ 7 8

The knight puzzled over it for a long time until a tiny elf fluttered in, studied the wall, and laughed. "I see-it's not about the numbers." Then it covered the numbers with a few dots, hinting that the password was a single word. The knight suddenly understood and, in the end, drew the sacred sword. What is the password?
Answer: SWORD
Question: An explorer is searching for the legendary Sun Scepter in an ancient Aztec temple. On the stone door of the main burial chamber, the following symbols are arranged:

7 / 8 9
4 5
/ / 6
1 2 3 4
/
The explorer studies the door for a long time, until sunlight passes through cracks in the temple, forming light spots that fall upon and cover the numbers. He then realizes the secret and laughs, "So the numbers themselves don't matter."

He enters a single word and the stone door opens.

Question: What is the password?
Answer: light
Question: A marine biologist explores an unknown deep‑sea ruin in a submersible. The entrance is blocked by an energy barrier displaying flowing symbols along with the message:
"Mortal, this is the Sea God's forbidden domain. Decipher the password to enter."
Below the message appears the arrangement:

4 / /
1 /
/
5
2 / 7

As the biologist is pondering, tiny plankton drift against some of the numbers, leaving traces that resemble small dots covering those digits.
He suddenly realizes that the actual values of the numbers are irrelevant, enters a single word as the password, and the barrier vanishes.

Question: What is the password?
Answer: water
Question: Detective Liu is on a sting operation at a trendy café that has become popular online. His target is a "Keyboard Operator"-a facilitator for money laundering who is waiting at this location to receive a digital instruction. The café is crowded, with most patrons occupied by laptops or remote meetings.
The suspect, codenamed "Gray Wolf," entered the café and pretended to search for a power socket. He lingered briefly behind three individuals using laptops but did not engage in any direct conversation. Moments later, Detective Liu received a high-priority intelligence update: "Instructions received; operation in progress."
Detective Liu recalled Gray Wolf's specific movements regarding the three suspects:
A young man deeply engrossed in a mobile game with noise-canceling headphones. When Gray Wolf accidentally bumped into him, the young man looked up and cursed at him in frustration.
A businessman conducting a live video conference. As Gray Wolf walked past, he tripped over and disconnected the power plug for the executive's wireless router. Despite the loss of the router's power, the businessman continued his presentation without interruption or acknowledgment of the disconnection.
A girl watching a film. When Gray Wolf leaned in to glance at her screen, she immediately slammed her laptop shut and stared him down suspiciously until he moved away.
Based on these details, who is most likely the "Keyboard Operator"?
Answer: The business executive
Question: Detective Harris is assigned to identify an informant disguised as a street performer on a bustling pedestrian street. Three performers are currently active. A contact codenamed "Vulture" blends into the crowd and successively drops an object into each performer's instrument case or hat. He does not speak to any of them.
Shortly after, the surveillance team confirms: "Identity verified."
Detective Harris reviews the recorded footage of Vulture's movements:
A woman with long hair playing the violin, seemingly lost in her music. Vulture stands and listens for a while, then applauds. The woman shows no reaction and continues to play without interruption.
A bald man strumming a guitar with his eyes closed in concentration. Vulture takes out a banknote and gently places it into his hat. The guitarist immediately opens his eyes and says, "Thank you."
A man appearing to be blind, playing the erhu while wearing dark sunglasses. Vulture pulls a coin from his pocket and tosses it into the instrument case. The coin hits several other coins already inside with a distinct metallic clink. The "blind" man acknowledges this with a slight nod.
Based on these observations, who is most likely the informant?
Answer: Bald man
Question: Secret Agent 007 infiltrated a massive shipyard workshop to intercept a mole engaged in sabotage. The environment was hazardous, filled with flying sparks and several workers performing high-intensity electric welding.
A contact codenamed "Sledgehammer" entered the workshop, circled near several welders who were actively working, and then departed. Intelligence later confirmed that the contact was successfully established. 007 recalled the following details:
The first welder was joining ship plates. When Sledgehammer walked over and shouted, "What time is it?" above the din, the welder ignored him and continued working without pause.
The second welder was squatting on the ground, actively welding while wearing a heavy, dark-tinted welding mask. Sledgehammer walked to a spot approximately one meter directly in front of him and simply raised his wrist to check his watch. The welder immediately extinguished his welding arc, pushed up his mask, and glanced at Sledgehammer.
The third welder had just completed a section and was tapping the weld with a hammer to inspect the seam. Sledgehammer walked over and patted him on the shoulder; the welder turned around and greeted him.
Based on these observations, who is most likely the mole?
Answer: The second welder
Question: In a company, you are the CEO. Your direct reports include a 50‑year‑old director, a 40‑year‑old manager, and a 30‑year‑old specialist.
Can you determine the CEO's current age?
Answer: Yes
Question: In a family, you are the mother. Your eldest son is 12 years old, your daughter is 8 years old, and your youngest son is 5 years old. So may I ask: do you know the mother's current age?
Answer: Yes
Question: In a class at school, you are the head teacher. The monitor is 15 years old, the academic representative is 15 years old, and the PE representative is 16 years old. So may I ask: can you guess the head teacher's current age?
Answer: Yes
Question: Dad has two watches with fixed rotation speeds. Watch A shows the correct time only once a year, while Watch B shows the correct time twice a day. Dad wanted to test Ming and asked him which watch would have a relatively smaller error for telling time. So which one should he choose?
Answer: A
Question: I have two watches, each running at a constant rate.
Watch A shows the correct time only once every 3 years.Watch B shows the correct time three times a day.
To obtain the most accurate time possible, which watch should I choose?
Answer: A
Question: A manager has two clocks, each running at a constant rate.
Clock A shows the correct time twice a day.
Clock B shows the correct time only once a month.

If you are asked to choose one to hang in the office for time reference, which one should you select?
Answer: B
Question: A merchant has 400 liters of special coolant and intends to transport it to a research station deep in the desert to make a profit. Each trip, he can carry a maximum of 50 liters of coolant, and 1 liter of coolant is consumed per kilometer traveled (consumed evenly). Suppose the price of coolant is 0 yuan per liter at the departure point and is directly proportional to the transportation distance (i.e., 10 yuan per liter at 10 kilometers, 20 yuan per liter at 20 kilometers, and so on). Once he stops, he must sell all the remaining coolant except the amount needed to ensure a safe return trip. Given that he has to return safely, what is the maximum profit he can make?
Answer: \boxed{2500}
Question: An explorer has 300 kg of high‑energy nutrient solution to transport to a mountain camp for sale.
He can carry at most 60 kg per trip, and each kilometer traveled consumes 0.5 kg of the solution uniformly. Assume the price of the nutrient solution is 0 at the departure point, and the price per kilogram is proportional to the distance from the start. (i.e., 10 yuan per kg at 10 kilometers, 20 yuan per kg at 20 kilometers, and so on.)
Once he stops, apart from the nutrient solution reserved to ensure a safe return, all remaining solution must be sold out. It is also assumed that he must return safely.
What is the maximum revenue he can obtain?
Answer: \boxed{4500}
Question: A pharmacist has 200 boxes of anti‑radiation medicine to transport to a wasteland to trade.
He can carry at most 50 boxes per trip, and each kilometer traveled consumes 1 box to prevent zombification due to radiation.
Suppose the price of medicine is 0 yuan per box at the departure point and is directly proportional to the transportation distance (i.e., 20 yuan per box at 10 kilometers, 40 yuan per box at 20 kilometers, and so on).
Once he stops, apart from the medicine reserved to ensure a safe return, all remaining medicine must be sold out. It is also assumed that he must return safely.
What is the maximum revenue he can obtain?
Answer: \boxed{2500}
Question: Four chess masters-Alex, Ben, Chris, and Dave-each possess exactly one unique signature skill: A, B, C, or D. A reporter interviews them to determine which skill belongs to whom.
Alex: "Ben's signature skill is not A."
Ben: "Chris's signature skill is not B."
Chris: "Dave's signature skill is not C."
Dave: "Among the other three (Alex, Ben, and Chris), only the one who possesses skill D told the truth."
Exactly two of the four statements above are true.
Based on these conditions, how many possible valid assignments of skills (A, B, C, D) to the four masters exist?
Answer: \boxed{9}
Question: Four spaceships-P, Q, R, and S-are each traveling to a different destination: Star System 1, 2, 3, or 4. Each star system will receive exactly one spaceship.
The control center has received the following final automated messages from the ships:
P says: "Q's destination is not Star System 1."
Q says: "R's destination is not Star System 2."
R says: "S's destination is not Star System 3."
S says: "Among the other three (P, Q, and R), exactly two told the truth."
Exactly three out of the four messages listed above are true.
Based on these conditions, how many possible valid assignments of spaceships to star systems exist?
Answer: \boxed{20}
Question: Four scholars-Ⅰ, Ⅱ, Ⅲ, and Ⅳ-each specialize in exactly one unique ancient civilization, numbered 1, 2, 3, or 4. Each civilization is studied by exactly one scholar. A history enthusiast interviews them to identify their fields of expertise.
Scholar Ⅰ: "Scholar Ⅱ does not specialize in Civilization 1."
Scholar Ⅱ: "I do not specialize in Civilization 2."
Scholar Ⅲ: "Scholar Ⅳ does not specialize in Civilization 3."
Scholar Ⅳ: "Among the other three (Ⅰ, Ⅱ, and Ⅲ), the individuals who are telling the truth specialize in civilizations with even-numbered designations."
Exactly two out of the four scholars are telling the truth.
How many distinct assignments of scholars to civilizations satisfy all of the conditions above?
Answer: \boxed{10}
Question: A doctor, a teacher, and a programmer are neighbors, living in three adjacent rooms on the same floor. The following conditions hold:

1. Each person has exactly one favorite sport (soccer or basketball), exactly one favorite drink (coffee or juice), and exactly one favorite cuisine (Chinese or Western).

2. The doctor lives next to a person who prefers Chinese cuisine. The teacher lives next to a soccer fan. The programmer lives next to a soccer fan.

3. No one who prefers Western cuisine drinks juice.  One person who likes basketball prefers Western cuisine.

4. At least one coffee drinker lives next to at least one soccer fan.

5. Any two people share at most one preference (sport, drink, or cuisine).
How many possible preference configurations satisfy all the conditions?
Answer: \boxed{2}
Question: Three roommates-Alice, Bob, and Charlie-share a three-bedroom apartment with a living room. Their bedrooms are three consecutive adjacent rooms in a row (left–middle–right). The following conditions hold:
1. Each person has exactly one pet preference (cat or dog), one favorite season (summer or winter), and one favorite fruit (apple or banana).
2. Alice lives next to an apple lover. Bob lives next to a cat lover. Charlie lives next to a cat lover.
3. No one who prefers bananas likes winter. At least one dog lover prefers bananas.
4. At least one person who prefers summer lives next to at least one cat lover.
5. Any two roommates share at most one preference (i.e., for any pair, they match in no more than one of the three categories).                                                                                      How many different assignments of (pet, season, fruit) to (Alice, Bob, Charlie) satisfy all the conditions?
Answer: \boxed{2}
Question: Three students-A, B, and C-are studying in a library, seated in three consecutive seats in a row. The following conditions hold:
1. Each student has a favorite subject (history or geography), a favorite music genre (classical or rock), and a favorite movie genre (sci-fi or comedy).
2. A sits next to the student who prefers sci-fi movies. B sits next to a student who prefers history. C sits next to a student who prefers history.
3. No one who prefers comedy movies likes rock music. At least one student who prefers geography prefers comedy movies.
4. At least one student who prefers classical music sits next to at least one student who prefers history.
5. Any two students share at most one common preference (i.e., for any pair, they match in no more than one of the three categories).
How many different assignments of (subject, music, movie) to (A, B, C) satisfy all the conditions?
Answer: \boxed{2}
Question: Owner Sam runs a chemical plant where two core chemical formulations are stored in a laboratory. The lab contains two reagent racks: one labeled "Acidic" (containing 25 acidic bottles) and one labeled "Basic" (containing 25 basic bottles). 
One day. the formulations were stolen. Upon inspection, it was discovered that all bottles on the two racks had been completely swapped, though they remained neatly arranged under the original labels.
The police questioned three researchers to find out who might struggle to distinguish between acids and bases:
Suspect A (Ph.D. in Chemistry): Claims that Suspect B has a poor academic record in school and lacks basic chemical knowledge.
Suspect B: Has recently incurred massive gambling debts.
Suspect C: Admits he cannot distinguish between acids and bases, but has a confirmed alibi.
Based on the evidence, who is most likely to have stolen the formulations?
Answer: A
Question: Ms. Carter is a perfumer who created two unique, highly valuable perfumes, "Morning Dew" and "Evening Mist". She kept the perfume formulas in her workshop.

The workshop has two scent burners: one always burns a floral fragrance, and the other always burns a woody fragrance. Nearby shelves hold the corresponding essential oils-30 bottles of floral oils and 30 bottles of woody oils.

One day, Ms. Carter discovered the formulas were missing. The two sets of essential oils had been neatly swapped: all floral oils were placed next to the woody burner, and all woody oils were placed next to the floral burner.

The police questioned three people who knew about the situation. When asked who had an issue with their sense of smell, suspect A-Ms. Carter's rival with an unusually keen sense of smell-claimed that suspect B has hyposmia (a reduced sense of smell). Suspect C admitted having anosmia (a loss of smell) but had an alibi. Suspect B had long wanted to imitate Ms. Carter's perfumes.

Who is most likely to have stolen the formulas?
Answer: A
Question: Professor John, a music historian, kept two priceless classic-music manuscripts-one by Mozart and one by Beethoven-hidden in his listening room. The room contained two cabinets: one for Classical records and one for Rock records, each holding 100 discs. One day, the manuscripts went missing and the cabinets had been tampered with. It was found that the contents of the two cabinets had been completely swapped: the "Classical" cabinet was filled with rock records, and the "Rock" cabinet contained only classical ones. Both were still neatly organized.
The police questioned three suspects who were familiar with the room about who among them was "unable to distinguish musical genres":
Suspect A (A top music academy graduate): Claims that Suspect B cannot distinguish between musical genres at all.
Suspect B: Has long coveted Professor Wang's collection.
Suspect C: Admits to being unable to distinguish musical genres, but has a solid alibi.
Based on the evidence, who is most likely the thief?
Answer: A
Question: A high-tech corporate park has four concentric circular security rings, labeled L1, L2, L3, and L4 from outer to inner. Four straight corridors (radial passages) connect these rings, located at the North, South, West, and East Buildings. There are no roads inside ring L4.

Due to a VIP visit, the following closures apply:

From 9:00 to 18:00, the segment of the L2 ring between the North Building and the East Building is closed.

From 10:00 to 14:00, the segment of the L3 ring between the South Building and the East Building is closed, and the segment of the East corridor between the L3 and L4 junctions is closed.

From 13:00 to 18:00, the entire West corridor is closed; personnel cannot pass through the West Building L2 or L3 junctions.

The segment of the L4 ring between the North Building and the East Building is permanently blocked due to construction.

At 13:00, the head of security must travel from the North Building L2 junction to the South Building L3 junction as quickly as possible.
What route should he take? (Describe the route in a format like "West Building L4 - North Building L4 - ...".)
Answer: North Building L2 - North Building L3 - North Building L4 - West Building L4 - South Building L4 - South Building L3
Question: This is a large amusement park with circular walkways. There are four concentric circular paths, named P1, P2, P3, and P4 from the outermost to the innermost. These rings are connected by four straight scenic avenues oriented to the east, west, south, and north. The innermost area, within P4, is a lake with no paths.

Due to equipment maintenance and parade performances, certain sections have restricted access. At 13:00, the following restrictions are active:

The arc of the P2 circular path between its north point and its east point is closed (closed from 09:00 to 18:00).

The arc of the P3 circular path between its south point and its east point is closed. Additionally, the segment of the East scenic avenue between the P3 junction and the P4 junction is closed (both closed from 10:00 to 14:00).

The entire West scenic avenue is closed; visitors cannot pass through the P2 or P3 junctions on the west side (closed from 13:00 to 18:00).
Furthermore, a huge parade float is permanently parked on the arc of the P4 circular path between its north point and its east point, blocking that section.

At 13:00, a visitor named Alice wants to travel from the P2 junction on the North scenic avenue to the P3 junction on the South scenic avenue. She is in a hurry. What is the optimal route she should take? (Please describe the route in a format like "West P4 - North P4 - ...")
Answer: North P2 → North P3 → North P4 → West P4 → South P4 → South P3
Question: There is a large circular library. Inside, the ring corridors are arranged as four concentric circles. From outermost to innermost, they are Zone A, Zone B, Zone C, and Zone D. These four rings are connected by four straight passageways located in the directions of the Front Hall, Rear Hall, Left Wing, and Right Wing. Inside Zone D is a rare-book archive, and there are no corridors within it.

Because the library is closed for reorganization, the following closures apply:
1) 09:00-18:00: The Zone B ring segment between the Front Hall and the Right Wing is closed.
2) 10:00-14:00: The Zone C ring segment between the Rear Hall and the Right Wing is closed, and the straight passageway on the Right Wing connecting Zone C to Zone D is also closed.
3) 13:00-18:00: The entire Left Wing passageway is closed, so the Left Wing junctions at Zone B and Zone C cannot be used.
4) All year round: Old bookshelves are stacked between the Front Hall Zone D and the Right Wing Zone D, blocking that segment.

At 13:00, a library staff member needs to go from the Zone B ring corridor at the Front Hall to the Zone C ring corridor at the Rear Hall, and he is in a hurry. What is the optimal route he should take? (Please describe the route in a format like "Left Wing Zone D - Front Hall Zone D - ...".)
Answer: Front Hall Zone B - Front Hall Zone C - Right Wing Zone C - Right Wing Zone B - Rear Hall Zone B - Rear Hall Zone C
Question: At an international summit's round-table banquet, the main table has 9 seats numbered 1 to 9 clockwise.

The seats are occupied by delegates from six countries-United States (U), United Kingdom (K), France (F), Germany (G), Italy (I), and Canada (C)-and three international organization observers (X, Y, Z).

To ensure smooth communication and diplomatic protocol, the following rules must be observed:

1. The observers cannot sit in adjacent seats, nor can they occupy seat 1 or seat 9.

2. Observer X must be seated clockwise after observer Y (i.e., X's seat number > Y's seat number).

3. If delegate U attends (and in fact everyone attends), delegate K must attend; if K is present, K must sit in seat 4.

4. Delegates F and G cannot be adjacent; unless delegate C sits exactly between them, at least two seats must separate F and G.

5. For the occupants seated in odd-numbered seats, the sum of the alphabetical position values of their initials (C=3, F=6, G=7, I=9, K=11, U=21, X=24, Y=25, Z=26) must be greater than 80.

6. If delegate I sits in an even-numbered seat, delegate U cannot sit in an odd-numbered seat.

7. Observer Z cannot sit in seat 8 or seat 2; if Z and C are both present, C must sit in seat 1.

8. The observers' codes X, Y, Z must appear in reverse alphabetical order by seat number (i.e., Z's seat number < Y's seat number < X's seat number).

9. The initial value of the occupant of seat 5 must be less than that of seat 3; the initial value of the occupant of seat 2 must be less than that of seat 3.

10. The initial value of the person in seat 1 must be less than that of every occupant in seats 2 through 6.

11. The initial values of the occupants of seats 6 and 4 must sum to 18.

12. When delegate G is seated anywhere, if K is present, K's seat number is treated as 0 when computing the sum in rule 5 (without changing K's physical seat).

In each option below, the nine symbols are listed in order from seat 1 to seat 9. Which of the following arrangements satisfies all these conditions?
A. C, I, G, K, U, F, Z, Y, X
B. C, I, Z, K, Y, G, X, U, F
C. U, Z, F, K, G, I, X, Y, C
D. C, F, I, K, G, U, Z, Y, X
Answer: B
Question: A modern art museum plans to display 9 exhibits in sequence along a long corridor. The exhibits fall into two categories: 6 oil paintings (numbered 1-6) and 3 sculptures (labeled A, B, C). The display stands are numbered P1 to P9 from left to right. The curator has formulated the following display rules:
1. Sculptures cannot be placed on adjacent stands, and stand P1 must hold an oil painting.
2. Sculpture B must be placed to the right of Sculpture A (not necessarily adjacent), and the position numbers of the three sculptures must satisfy that of A < that of C < that of B.
3. Oil painting 4 must be fixed at stand P4.
4. Oil painting 2 and oil painting 3 cannot be adjacent. Unless oil painting 5 is placed exactly between them (e.g., 2 → 5 → 3), there must be a gap of at least two stands between them.
5. The sum of the numerical values of all exhibits placed on odd-numbered stands (P1, P3, P5, P7, P9) must be greater than 60. (Numerical values: A=10, B=20, C=30; the numerical values of oil paintings correspond to their own numbers.)
6. The sum of the numerical values of the exhibits at stands P6 and P4 must equal 9.
7. Sculpture C cannot be placed at P3 or P5. If Sculpture C and oil painting 6 are included in the arrangement, then oil painting 6 must be placed at P1.
8. The numerical value of the exhibit at P5 must be less than that at P3, and the numerical value of the exhibit at P2 must be less than that at P3.
9. The numerical value of the exhibit at P1 must be greater than that at P2.
10. When Sculpture C is placed at P8, the numerical value of oil painting 4 is temporarily treated as 0 when calculating Rules 5 and 6.
Which of the following arrangement schemes meets the curator's requirements?
A. 6, A, 2, 4, 3, 5, C, 1, B
B. 1, 2, A, 4, 3, 5, C, 6, B
C. 6, 2, A, 4, 3, 5, C, 1, B
D. 6, 2, A, 4, 3, 5, B, 1, C
Answer: C
Question: A freight train consists of 9 cars, numbered 1 through 9 from the front to the rear. The cars carry two types of cargo: six cars carry ordinary goods (labeled 1-6), and three cars carry hazardous chemicals (coded X, Y, Z).

Value settings: X = 8, Y = 9, Z = 10, and the value of each ordinary good equals its label number.

Assembly constraints:

Hazardous-chemical cars cannot be adjacent, and neither Car 1 nor Car 9 may carry hazardous chemicals.

The hazardous chemicals must be arranged in the order Z, then X, then Y along the train (i.e., car number of Z < car number of X < car number of Y).

Goods 1 and goods 4 must both be present, and goods 4 must be in Car 4.

The car carrying goods 2 must be before the car carrying goods 3, and goods 5 must be between them (i.e., car number of goods 2 < car number of goods 5 < car number of goods 3; not necessarily adjacent).

The sum of the values of the cargo in all odd-numbered cars (1, 3, 5, 7, 9) must be less than 25.

The value in Car 1 must be less than the value in Car 2, and the value in Car 5 must be greater than the value in Car 3.

Z cannot be in Car 3 or Car 5; if both Z and goods 6 are present, then goods 6 must be in Car 1.

The sum of the values in Car 6 and Car 4 must equal 9.

Which of the following sequences satisfies all the above rules?
A. 6, 2, Z, 4, 3, 5, X, 1, Y
B. 1, Z, 2, 4, X, 5, 3, Y, 6
C. 6, Z, 2, 4, X, 5, 3, Y, 1
D. 6, Z, 1, 4, X, 5, 3, Y, 2
Answer: C