Ckriman/General365_Public huggingface dataset:
Question: Six professors-P, Q, R, S, T, and U-are seated around a circular table for a meeting. The seating rules are as follows: R is to the left of Q; S is positioned directly opposite R; Q is to the right of R; U is not adjacent to P; and P cannot be adjacent to both Q and S simultaneously. If P's position is numbered 1, and the seats are numbered sequentially as 1, 2, 3 ... in a clockwise direction starting from P, what is the average seat number of U across all possible valid distributions?
Answer: \boxed{3.5}
Question: Six advisors-P, Q, R, S, T, and U-are arranged in a circle for a discussion. The positioning rules are as follows: R is to the left of Q; S is positioned directly opposite R; Q is to the right of R; T is not adjacent to U; and P cannot be adjacent to both Q and S simultaneously. If P is assigned to Position 1, and the positions are numbered as 1, 2, 3, … in a clockwise direction starting from P, what is the average position number of U across all possible valid distributions?
Answer: \boxed{3.75}
Question: In a 5×5 orchard, five types of fruit trees with heights ranging from 1 to 5 are planted. Each row and each column contains exactly one tree of each height. A taller tree blocks the view of any shorter tree behind it. If the following statements are true, what is the average height of the trees at the four corners (Northwest, Northeast, Southwest, and Southeast)?
A: Looking east from the western end of the 2nd row, exactly 2 trees are visible.
B: Looking east from the western end of the 3rd row, exactly 3 trees are visible.
C: Looking north from the southern end of the 2nd column, exactly 4 trees are visible.
D: Looking north from the southern end of the 3rd column, exactly 2 trees are visible.
E: Looking south from the northern end of the 4th column, exactly 5 trees are visible.
Answer: \boxed{3.25}
Question: In a 5×5 vegetable garden, five types of vegetables with heights ranging from 1 to 5 are planted such that each row and each column contains exactly one vegetable of each height. A taller vegetable blocks the view of any shorter vegetable behind it. If all the following statements are true, what is the average height of the vegetables at the four corners (Northwest, Northeast, Southwest, and Southeast)?
A: Looking east from the western end of the 1st row, exactly 3 vegetables are visible.
B: Looking east from the western end of the 4th row, exactly 2 vegetables are visible.
C: Looking north from the southern end of the 3rd column, exactly 3 vegetables are visible.
D: Looking north from the southern end of the 4th column, exactly 5 vegetables are visible.
E: Looking south from the northern end of the 5th column, exactly 4 vegetables are visible.
Answer: \boxed{3}
Question: In a 5×5 herbal garden, five types of medicinal herbs with heights ranging from 1 to 5 are planted such that each row and each column contains exactly one herb of each height. A taller herb blocks the view of any shorter herb behind it. If all the following statements are true, what is the average height of the herbs at the four corners (Northwest, Northeast, Southwest, and Southeast)?
A: Looking east from the western end of the 2nd row, exactly 4 herbs are visible.
B: Looking east from the western end of the 5th row, exactly 2 herbs are visible.
C: Looking north from the southern end of the 1st column, exactly 3 herbs are visible.
D: Looking north from the southern end of the 4th column, exactly 5 herbs are visible.
E: Looking south from the northern end of the 3rd column, exactly 3 herbs are visible.
Answer: \boxed{2.25}
Question: The renowned magician David revealed the secret behind his most controversial trick during his farewell performance. In a 1999 show, he "vanished into thin air" and did not reappear as planned. At the time, everyone believed the trick had failed and that he had died, leading to his expulsion from the World Magicians' Association.
Did David's real "disappearance" take place in the 20th century or the 21st century?
Answer: 21st century.
Question: During a class, Professor Lewis shared a firsthand case from his own experience. One morning at 10:00 AM, he accidentally inhaled a new neurotoxic gas in the laboratory and collapsed unconscious at 10:05 AM. When paramedics arrived at 11:30 AM, they could not detect any vital signs and pronounced him dead at the scene.
Did Professor Lewis's actual time of death occur before 12:00 noon that day, or after 12:00 noon?
Answer: After noon (12:00 PM).
Question: Michael recalled a harrowing experience to his friends. He mentioned that at 8:15 a.m. on May 1st of a certain year, he slipped and fell while climbing a snowy mountain. When the rescue team found him at 4:40 p.m., he showed no signs of life. At 5:20 p.m., the team doctor pronounced him dead and recorded the death officially.
Did Michael's actual time of death occur before 6:00 p.m. or after 6:00 p.m.?
Answer: after 6:00 p.m.
Question: A zoo has nine enclosures. On Labor Day, they plan to hold a celebration on the central lawn, with each enclosure assigned a plot. The lawn is very large, and to make the event more interesting, the zoo set the following requirements:
1. One enclosure will put on a parrot flight show, and it must be visible from all enclosures.
2. Four enclosures will offer animal petting experiences, located at the four corners of the plots.
3. Before the event, only the Monkey Hill plot had two booths from other enclosures moved onto it; one of them was the Reptile House.
4. Event funding is applied for from the Animal Protection Foundation.
5. David watched a peacock display at Bird Paradise, and could immediately turn to play a feeding game at the Big Cat Zone.
6. Emily found that there was nowhere closer to the Monkey Hill plot than the spot in front of the Amphibian House booth.
7. No matter which enclosure Michael visited, he could turn and see the Elephant House's parrots.
8. James at the Panda House and a friend at Bird Paradise were blocked by an enclosure in the middle and could not see each other at all.
9. Hearing that the cotton candy at the Giraffe Zone was the biggest, after finishing bananas at Monkey Hill, Tom immediately went to the opposite side.
10. Students from the Amphibian House and the Panda House had a dispute over the dividing line between their plots; consequently, before the celebration began, the Amphibian House swapped locations with a different enclosure. 
11. The four enclosures that neither put on a show nor provide petting experiences will prepare fruit at the four cardinal directions so that everyone can eat at any time.
12. On the day of the celebration, the parrot-show caretaker demonstrated parrots mimicking speech, which surprised students from the adjacent Giraffe Zone.

From an aerial view, the nine plots form a 3×3 grid. By the end of the celebration, which enclosures are directly adjacent to the Reptile House (defined as sharing a common boundary line)?
Answer: Monkey Hill and Panda House
Question: In a fantasy continent, there are nine kingdoms. To celebrate a millennium of peace, they plan to hold a grand festival at the Holy Ground, with each kingdom assigned a plot. The Holy Ground is vast, and to make the festival more distinctive, the guardians of the Holy Ground set the following requirements:
1. One kingdom will be tasked with lighting the Sacred Fire, which must be visible from all other kingdoms' plots.
2. Four kingdoms will display their magical wonders, each stationed at one of the four corners of the Holy Ground.
3. Before the festival, only the Silver Kingdom's plot had two other kingdoms' ceremonial squads pass through, one of which was the Obsidian Kingdom's.
4.Festival expenses are covered by the Dragon Treasury.
5.Emily watched the Dance of the Winds in the Storm Kingdom, and as soon as she turned around, she could participate in the Forest Treasure Hunt in the Emerald Kingdom.
6.Jack found that in the Golden Kingdom's plot, no plot was closer to the Silver Kingdom than its own.
7.No matter which kingdom's plot one is in, one can see the sacred fire of the Flame Kingdom.
8.The general of the Red Iron Kingdom and a friend from the Storm Kingdom were blocked by a kingdom in the middle and were completely unable to see each other.
9.Hearing that the magical potion of the Crystal Kingdom was the best, after having juice at the Silver Kingdom's plot, Arnold immediately went to the opposite side.
10.Knights from the Golden Kingdom and Red Iron Kingdom had a conflict over the position of their plot boundaries, so before the festival, the Golden Kingdom swapped its plot with that of another kingdom.
11.The four kingdoms that neither light the sacred fire nor display magical wonders should prepare delicacies for guests at the four cardinal directions for everyone to enjoy.
12.The druids of the Divine Wood Kingdom cultivated glowing plants, surprising alchemists from the adjacent Crystal Kingdom on the day of the festival.
It is known that when viewed from above, the nine kingdoms' plots form a 3×3 grid.
Question:
By the end of the festival, which kingdoms are adjacent (sharing a common side) to the Obsidian Kingdom?
Answer: Silver Kingdom and Red Iron Kingdom
Question: A magic academy consists of nine departments. For the school's anniversary, they plan to host a carnival on the playground, with each department assigned a specific plot. To enhance the magical atmosphere of the event, the school has established the following requirements:
1. One department will summon a Guardian Beast that must be visible to all other departments for admiration.
2. Four departments will provide potion experiences, located at the four corners of the site layout.
3. Before the carnival begins, only the Alchemy Department's plot was used to transmit equipment for two other departments, one of which was the Curse Department.
4. Catering for the carnival is managed and provided by the School Staff Union.
5. After Hermione identifies Mandrakes at the Herbology Department, she can turn and immediately be at the Transfiguration Department to play a transformation game.
6. While standing at the Charms Department's tent, Snape noted that no other location was closer to the Alchemy Department's plot than this spot.
7. No matter which department a visitor is in, they can turn around and see the Guardian Beast of the Divination Department.
8. Harry from the Flying Department and his friend at the Herbology Department are blocked by a department situated directly between them, making it impossible to see each other.
9. Hearing that the candies from the Dark Arts Department are the most unique, Ron immediately headed to the plot directly opposite after finishing his candies at the Alchemy Department.
10. Students from the Charms Department and the Flying Department had a dispute regarding their dividing line; as a result, before the carnival started, the Charms Department swapped its plot with another department.
11. The four departments that neither summon a beast nor offer potion experiences will provide magical snacks at the four cardinal directions for all attendees.
12. Students from the Magical Devices Department created a self-transforming chair, which amazed the students from the adjacent Dark Arts Department on the day of the event.

From an aerial view, the nine plots form a 3×3 grid. By the end of the carnival, which department(s) are adjacent to the Curse Department? ("Adjacent" is defined as sharing a common boundary line.)
Answer: The Alchemy Department and the Flying Department
Question: The corner shop has a rule: 5 empty bottles can be exchanged for 1 new bottle of drink. David starts with 20 empty bottles. On his way to the shop, he finds 3 more identical empty bottles. Upon arrival, he sees two people waiting in line and decides to buy their empty bottles for 1 yuan each. The shop owner is easygoing and allows customers to borrow bottles temporarily. It is known that a full bottle of this drink costs 4 yuan. If David sells the drinks he gets from his exchanges, he can sell them for 4 yuan each. He keeps the empty bottles from the drinks he sells to use for further exchanges.
Under the condition that David buys the minimum number of bottles, what is the maximum profit (in yuan) he can ultimately make? (Assume every drink sold leaves behind an empty bottle.)
Answer: \boxed{22}
Question: The corner shop has a rule: 6 empty bottles can be exchanged for 1 new bottle of drink. Sam starts with 50 empty bottles. On his way to the shop, he finds 5 more identical empty bottles. Upon arrival, he sees three people waiting in line and decides to buy their empty bottles for 1.5 yuan each. The shop owner is easygoing and allows customers to borrow bottles temporarily. It is known that a full bottle of this drink costs 5 yuan. If Sam sells the drinks he gets from his exchanges, he can sell them for 5 yuan each. He keeps the empty bottles from the drinks he sells to use for further exchanges.
Under the condition that Sam buys the minimum number of bottles, what is the maximum profit (in yuan) he can ultimately make? (Assume every drink sold leaves behind an empty bottle.)
Answer: \boxed{43}
Question: The corner shop has a rule: 4 empty bottles can be exchanged for 1 new bottle of drink. John starts with 30 empty bottles. On his way to the shop, he finds 2 more identical empty bottles. Upon arrival, he sees four people waiting in line and decides to buy their empty bottles for 0.8 yuan each. The shop owner is easygoing and allows customers to borrow bottles temporarily. It is known that a full bottle of this drink costs 3.5 yuan. If John sells the drinks he gets from his exchanges, he can sell them for 3.5 yuan each. He keeps the empty bottles from the drinks he sells to use for further exchanges.
Under the condition that John buys the minimum number of bottles, what is the maximum profit (in yuan) he can ultimately make? (Assume every drink sold leaves behind an empty bottle.)
Answer: \boxed{43.2}
Question: Four players, A, B, C, and D, are playing a Go doubles match. Their skill points are as follows:
A has fewer points than B.
C has more points than both of his opponents.
Question:
To satisfy the condition:
B's points − A's points > C's points − D's points
how many possible ranking orders of the four players' skill points are there?
Answer: \boxed{4}
Question: Four merchants-W, X, Y, and Z-are engaged in business negotiations, divided into two opposing teams. Regarding their personal wealth: W has less wealth than X. Y is wealthier than both merchants on the opposing team.
To satisfy the condition:
X's wealth − W's wealth > Y's wealth − Z's wealth
How many different wealth rankings are possible for these four individuals?
Answer: \boxed{4}
Question: Four cities-Gold City, Wood City, Water City, and Fire City-are divided into two opposing teams for an economic competition. Regarding their populations: Gold City has a smaller population than Wood City. Water City is more populous than both cities on the opposing team.
To satisfy the inequality:
Wood's population − Gold's population > Water's population − Fire's population
How many different population size rankings are possible for these four cities?
Answer: \boxed{4}
Question: Four students-Daniel, Emma, Ryan, and Lily-are majoring in four different subjects: Physics, Chemistry, Biology, and Mathematics. The following four statements are made:
1. Daniel is a Physics major.
2. Ryan is a Chemistry major.
3. Emma is not a Physics major.
4. Lily is not a Biology major.
Given that exactly one of these statements is true, how many different assignments of majors to students are possible?
Answer: \boxed{6}
Question: There are four teachers-A, B, C, and D-who teach Chinese, Mathematics, English, and Physics. Each teacher specializes in one subject.
The following four statements are made:
1. A teaches Chinese.
2. C teaches English.
3. B does not teach Chinese.
4. D does not teach Mathematics.
Given that only one of these four statements is true, how many combinations of subject assignments are possible for these four teachers?
Answer: \boxed{6}
Question: In a zoo, the Lion, Tiger, Elephant, and Giraffe exhibits are managed by four individuals: A, B, C, and D.  The following four statements are provided:
1. A is the head of the Lion exhibit.
2. C is the head of the Elephant exhibit.
3. B is not the head of the Lion exhibit.
4. D is not the head of the Tiger exhibit.
Given that exactly three of these statements are false, how many different assignments of heads to exhibits are possible?
Answer: \boxed{6}
Question: Four robots-Mercury, Venus, Earth, and Mars-are standing in a straight line and executing synchronized commands. The ground control center is located to the north. From the control center's perspective, looking from west to east, the robots are positioned in this order: Mercury, Venus, Earth, Mars. If Earth turns 90° to its left, and ignoring any potential occlusion, what is the minimum number of other robots that Earth can see?
Answer: \boxed{1}
Question: Four participants-John, David, Michael, and Kevin-take part in a parade, moving in perfect unison. After entering, they stand in a single row. From the reviewing stand located on the north side, the participants are seen from the stand's right to left in the following order: John, David, Michael, and Kevin. When Michael turns 90° to his left, and ignoring any occlusion, what is the minimum number of teammates Michael can see?
Answer: \boxed{1}
Question: Four little lambs-Pleasant Goat, Lazy Goat, Fit Goat, and Gentle Goat-are participating in a parade, moving in perfect unison. After entering, they stand in a single column. From the west, the village chief sees them lined up from north to south in that order. If Lazy Goat turns 90° to his left, and ignoring any occlusion, what is the minimum number of teammates he can see?
Answer: \boxed{1}
Question: A 6-person project team-consisting of a Team Leader, Deputy Leader, Programmer, Tester, Designer, and Product Manager-is meeting around a rectangular table. Two people sit on each of the two long sides, and one person sits at each of the two short ends. The Team Leader and the Product Manager must sit directly across from each other. The Tester sits immediately to the left of the Programmer. The Designer sits immediately to the left of the Deputy Leader. ("Left" is defined from the perspective of the seated person facing the table.)

How many distinct seating arrangements are possible?
Answer: \boxed{2}
Question: Six animals - lion, tiger, elephant, giraffe, monkey, and zebra - are to be placed in 6 adjacent enclosures arranged in a hexagon. 
Constraints:
The lion and the elephant must be in directly opposite enclosures.
The zebra must be on the immediate left of the tiger.
The monkey must be on the immediate left of the giraffe.
Question: How many possible arrangements are there in total?
Answer: \boxed{2}
Question: Six knights (A, B, C, D, E, and F) are to be seated around a hexagonal conference table, with one person occupying each side. A and D must sit directly opposite each other. C must sit immediately to B's left. F must sit immediately to E's left. ( Left and right are determined from the perspective of the knight seated at the table, facing inward.) 

How many distinct seating arrangements satisfy all of these requirements?
Answer: \boxed{2}
Question: A drone ascends vertically 100 meters from the ground. It then travels 200 meters due northeast (NE). From there, it changes course to fly 300 meters due east (E). It then changes course again to fly another 200 meters due northeast (NE). Finally, the drone descends vertically to land on the ground.
What is the distance between the landing point and the takeoff point?
Answer: \boxed{580}
Question: Mr. D is traveling while monitoring his distance with a horizontal rangefinder. He first walks 500 meters due northwest. He then turns right by 135° and walks 1000 meters due east. Finally, he walks 500 meters due southeast.
At this point, what is his distance from the starting point in meters?
Answer: \boxed{293}
Question: According to a horizontal rangefinder, a ship first sails 10 nautical miles due southwest (SW). It then turns left by 135° and sails 20 nautical miles due east (E). Finally, it sails another 10 nautical miles due southwest (SW).
At this point, what is the ship's distance from its departure port?
Answer: \boxed{6}
Question: You are a young job seeker looking for employment opportunities.
One day, you come across a group of people who say:"Join us-we guarantee job assignments! Once you join us, we'll start a pairing game. Every job seeker will pair up with the recruiter on their right, then leave here to sign an employment contract. The last person remaining will be the Job Hunting King."
 You're instantly fired up-Job Hunting King sounds awesome! You're determined to claim that title!
Currently, the 1–26 positions are arranged as follows:
Recruiter, Job Seeker, Job Seeker, Recruiter, Job Seeker, Recruiter, Job Seeker, Job Seeker, Recruiter, Recruiter, Job Seeker, Recruiter, Recruiter,  Job Seeker, Job Seeker, Recruiter, Job Seeker, Recruiter, Recruiter, Job Seeker, Job Seeker, Job Seeker, Job Seeker, Recruiter, Recruiter, Recruiter
These positions form a closed circle. (the position to the right of No.1 is No.2)
Question: Which position(s) should you insert yourself into to fulfill your dream of becoming the Job Hunting King? List all correct answers.
Answer: \boxed{1,17}
Question: You are a novice programmer looking for a mentor. Suddenly, you encounter a group of 30 people standing in a circle. They invite you to join their "Pairing Game": "Every Rookie will pair up with the Expert immediately to their right. Each pair will then leave the circle to study programming. The very last person remaining in the circle will be crowned the Programming King!" Fired up by the title, you decide to join and strive for the Programming King.

The current sequence of the 30 people (from No. 1 to No. 30) is: "E R R E R E R R E E R E E R R E R E E R R R R E E E R R E E" (E = Expert, R = Rookie) They form a closed loop where No. 2 is to the right of No. 1.

Question: At which position(s) should you insert yourself into this circle to make your dream come true? Provide all possible answers.
Answer: \boxed{1,19}
Question: You are a fitness beginner and want to find a coach.
One day, you come across a group of people who say:"Join us, and we'll assign you a coach! Once you join, a pairing game will begin: each trainee will pair up with the coach to their right, then leave here to train at the gym. The last person remaining will become the Fitness King."
 You're instantly fired up-Fitness King sounds awesome! You're determined to claim that title!
Currently, the 1–26 positions are arranged as follows:
Trainee Coach Coach Trainee Coach Trainee Coach Coach Trainee Trainee Coach Trainee Trainee Coach Coach Trainee Coach Trainee Trainee Coach Coach Coach Coach Trainee Trainee Trainee
These positions form a circular ring (the position to the right of No.1 is No.2).
Question: Which position(s) should you insert yourself into to fulfill your dream of becoming the Fitness King? List all correct answers.
Answer: \boxed{1,22}
Question: A superhero calculates his "actual cost" based on opportunity cost. For instance, if he passes up an action that provides +100 to the Safety Index to take one that only provides +90, he considers himself to have suffered an actual cost (loss) of 10 points. A consultant provides him with the following one-time actions, which can be selected in multiple combinations:

A: Support +10; Safety +20.
B: Support +30; Safety +10.
C: Support +100; Safety −30.
D: Safety +50.
E: Safety +200; however, for each use of an additional unconventional weapon, the Safety Index decreases by 70.
F (Volunteer Service): Every +1 point of Public Support gained adds +1 to Safety; every −1 point of Support lost subtracts −1 from Safety.
G: Support −50; Safety +40.

The superhero makes a selection and later realizes he made the worst possible judgment: his actual cost(loss) was the highest it could be.
Question: What is the value of this maximum actual cost (loss)?
Answer: \boxed{250}
Question: A master chef is accustomed to counting opportunity cost as part of his actual costs. For example, if he abandons a dish that could score 95 points and chooses to make one that scores 80 points, the actual cost to him is a loss of 15 points. In a cooking competition, the following disposable ingredients are available for multiple selections:

A: Increases the dish's freshness by 10 and grants 20 points.
B: Increases the dish's freshness by 5 and grants 30 points.
C: Increases the dish's freshness by 30 but deducts 10 points.
D: Grants 40 points directly.
E: Grants 100 points. However, for every other ingredient selected besides E, 50 points are deducted.
F: Triggers the "Judge's Favor" effect. For every 1-point increase in the dish's final freshness, you gain an extra 3 points; for every 1-point decrease, you lose an extra 3 points.
G: A special condiment that reduces the dish's freshness by 20 but grants 80 points.

After making his ingredient selections, the chef realizes he has made a wrong judgment, and the actual cost loss calculated from his score turns out to be the highest possible. What is the value of this maximum actual cost loss?
Answer: \boxed{255}
Question: A student at a magic academy is accustomed to counting opportunity cost as part of his actual cost. For example, if he gives up a course that would earn him 20 credits and chooses one that only earns him 15 credits, the actual cost for him is a loss of 5 credits.
Now the Academic Affairs Office offers him the following one-time optional courses that can be selected in combination:
Course A: This course will increase your supervisor's favorability by 5 and earn you 10 credits.
Course B: This course will increase your supervisor's favorability by 20 and earn you 5 credits.
Course C: This course will increase your supervisor's favorability by 40 but deduct 15 credits from you.
Course D: This course will earn you 20 credits.
Course E: This course will earn you 80 credits; in addition, each course you choose other than this one will cost you 30 credits.
Course F: This course comes with a "Supervisor's Recommendation Letter". When final settlement is made, every 1-point increase in supervisor's favorability will bring an additional 2 credits, and every 1-point decrease in supervisor's favorability will lead to an additional deduction of 2 credits.
Course G: This course will decrease your supervisor's favorability by 10 and earn you 30 credits.
After making his course selection, he realizes that he has made a wrong decision, and the actual cost loss calculated in terms of credits turns out to be the maximum possible. What is the value of this maximum actual cost loss?
Answer: \boxed{180}
Question: In the pedigree of a purebred racehorse, the probability that any given stallion is unable to produce male offspring is 8%. What is the probability that a male racehorse named "Lightning" and his paternal grandfather have each never produced any male offspring, but have both produced female offspring?
Answer: \boxed{0}
Question: Given that the computer virus "Y" has a 1% chance of failing to replicate each time it attempts to copy itself, what is the probability that both a virus "Z"-which arose from a successful replication of "Y"-and its direct parent virus "Y" have themselves never successfully produced any new virus through replication?
Answer: \boxed{0}
Question: In a renowned academic school of thought, each scholar has a 20% probability of never having any successful protégés throughout their lifetime.

What is the probability that a PhD student named Brown and his advisor's advisor have both never have any successful protégés?
Answer: \boxed{0}
Question: On a frictionless horizontal surface, John pushes away Mary, who has the same mass as he does. Ten seconds later, the distance between them is 6.2 m. Fifty seconds later, the distance is 26.2 m. When they are 31.2 m apart, time is rewound by 100 seconds. How far apart are they at that earlier moment?
Answer: \boxed{1.2}
Question: On a calm lake, there are two identical boats, A and B. The person in each boat simultaneously uses an oar to push against the other boat, causing them to separate. Two seconds later, the boats are 12 meters apart. Eight seconds later, they are 42 meters apart. When the distance between them reaches 52 meters, time reverts to the starting moment. At this moment, how far apart are the two boats?
Answer: \boxed{2}
Question: On a perfectly smooth ice surface, two skaters of equal mass push against each other. Ten seconds later, they are 10.8 m apart. Thirty seconds later, they are 30.8 m apart. When the distance between them reaches 40.8 m, time is rewound by two minutes. How far apart are they immediately after the time reversal?
Answer: \boxed{0.8}
Question: You have 150 cards numbered 1 to 150, each with a red side and a blue side. Initially, all are placed with their red sides facing up.
You then flip, in order, all cards whose numbers are multiples of 1, then multiples of 2, then multiples of 3, then multiples of 4.
After these four rounds, how many cards are red-side up?
Answer: \boxed{62}
Question: In a fantasy-themed board game store, 120 limited-edition Destiny Tarot Cards are on display, numbered from 1 to 120. Each card has two sides: the front is printed with the "Paladin", a symbol of light, while the back features the "Abyssal Dragon", a symbol of darkness. Initially, all 120 cards are placed with their Paladin side facing up.
To test the fate-bond of the card deck, the storekeeper carries out several rounds of flipping: first, flip over all cards whose numbers are multiples of 1; next, flip over all cards whose numbers are multiples of 2; then, flip over all cards whose numbers are multiples of 3; finally, flip over all cards whose numbers are multiples of 5.
How many tarot cards still have their Paladin side facing up in the end?
Answer: \boxed{60}
Question: A collector has 200 rare sports star cards, numbered 1 to 200. Each card has two sides: one side features a player portrait and the other side shows detailed statistics. 
Initially, all cards lie with their player portrait side facing up.
A sorting robot hired by the collector performs four rounds of targeted flips:
1.Flip all cards that are multiples of 1
2.Flip all cards that are multiples of 2
3.Flip all cards that are multiples of 3
4.Flip all cards that are multiples of 4
After all four rounds, how many cards remain with their player portrait side facing up?
Answer: \boxed{82}
Question: Professors A, B, C, and D have their studies arranged in a row on the same floor of a building. Each professor has a distinct research field, a unique favorite drink, and a different wall color for their study. The following clues are given:
1.One of the studies has beige walls.
2.Professor D researches physics and likes to drink fruit juice.
3.Professor C's favorite drink is milk.
4.The study with gray walls is located to the right of the one with white walls.
5.The professor who owns the study with gray walls researches chemistry.
6.The professor who researches biology likes to drink tea.
7.The professor who owns the study with blue walls researches history.
8.The professor who researches chemistry lives adjacent to the professor who researches biology.
9.The professor who researches history lives adjacent to the professor who researches biology.
10.The professor who likes to drink coffee lives next to the professor who researches physics.
How many possible combinations are there among the four professors' research fields, favorite drinks, and study wall colors?
Answer: \boxed{6}
Question: Delegates from four countries-A, B, C and D-are assigned to four adjacent rooms. Each delegate has a distinct badge, travels by a unique means of transportation, and has a room with a different key tag color. The following information is given:
1.One of the key tags is copper-colored.
2.Delegate D wears the eagle badge and travels by train.
3.Delegate C travels by plane.
4.The room with the silver key tag is located to the right of the room with the gold key tag.
5.The delegate with the silver key tag wears the lion badge.
6.The delegate wearing the bear badge travels by ship.
7.The owner of the room with the wooden key tag wears the olive branch badge.
8.The delegate wearing the lion badge lives adjacent to the delegate wearing the bear badge.
9.The delegate wearing the olive branch badge lives adjacent to the delegate who travels by ship.
10.The delegate who travels by car lives adjacent to the delegate who travels by train.
How many possible combinations are there for the four delegates' badges, means of transportation and key tag colors?
Answer: \boxed{6}
Question: In a science fiction story, four starships (α, β, γ, δ) are docked side by side at a space station. Each has a unique combination of captain, energy core, and hull color. The following facts are known:
1.One starship has a black hull.
2.The captain of starship δ is a robot, and its energy core is a "Singularity".
3.The energy core of starship γ is a "Crystal".
4.The silver starship is docked immediately to the right of the gray starship.
5.The captain of the silver starship is human.
6.The starship with a clone captain is powered by an "Antimatter" core.
7.The captain of the white starship is an extraterrestrial (alien).
8.The human captain's starship is adjacent to the clone captain's starship.
9.The extraterrestrial (alien) captain's starship and the clone captain's starship are adjacent.
10.The starship with a "Plasma" core is docked next to the one with a "Singularity" core.

How many possible combinations of captain, energy core, and hull color are possible for the four starships?
Answer: \boxed{6}
Question: Six wizards-Merlin, Gandalf, Dumbledore, Saruman, Radagast, and Elminster-are to stand at the six nodes of a circular magic array. Their magical power is ranked as follows: Merlin > Gandalf > Dumbledore > Saruman > Radagast > Elminster. Each wizard refuses to stand adjacent to the two wizards whose magical power is immediately above or below their own. Additionally, Gandalf refuses to be adjacent to Saruman. How many valid distinct arrangements are there?
Answer: \boxed{2}
Question: There are six types of gemstones: diamond, ruby, sapphire, emerald, topaz, and amethyst. Their hardness is ranked as follows: diamond > ruby > sapphire > emerald > topaz > amethyst. These gemstones are to be arranged in a circular showcase. The requirement is that no gemstone can be adjacent to those whose hardness is immediately above or below its own. Additionally, the curator specifies that sapphire cannot be adjacent to amethyst. How many distinct arrangements are possible?
Answer: \boxed{4}
Question: There are six novels, N1 through N6, ranked by publication year in chronological order: N1>N2>N3>N4>N5>N6 (where N1 is the earliest). The six novels are to be arranged on a circular bookshelf. The requirement is that no novel can be adjacent to those whose publication years are immediately before or after its own. Additionally, the librarian stipulates that N2 cannot be adjacent to N5. How many distinct arrangements are possible?
Answer: \boxed{2}
Question: Six friends - A, B, C, D, E, and F - meet at a bar and sit along the two longer sides of a rectangular table, three persons on each side. Each orders a different drink. The following conditions apply:
1. B sits next to C.
2. C sits directly across from someone who is adjacent to E.
3. D sits directly across from A, and D ordered whisky.
4. The person who ordered vodka sits directly across from E.
5. Neither D nor F ordered brandy.
6. F did not order rum.
7. The person who ordered rum sits directly across from D.
8. One of B's neighbors ordered gin.

One of the six ordered tequila. How many possible seating arrangements satisfy all the given conditions?
Answer: \boxed{8}
Question: Six people-A, B, C, D, E, and F-go to the library and study together. They are seated along two opposite sides of a square table, with three people per side. Each person is studying a unique subject. 
Given that:
1. B sits beside C.
2. C sits directly opposite the person next to E.
3. D sits directly opposite A, and D is studying math.
4. The person studying physics sits directly opposite E.
5. Neither D nor F is studying chemistry.
6. F is not studying biology.
7. The person studying biology sits directly opposite D.
8. The person seated beside B is studying English.
One of them is studying history. How many possible seating arrangements are there for the six people?
Answer: \boxed{8}
Question: Six people-A, B, C, D, E, and F-go to a florist together. They sit along the two sides of a rectangular table, three on each side. Each chooses a different type of flower. The following facts are known:
1. B sits next to C.
2. C sits directly across from someone who is adjacent to E.
3. D sits directly across from A, and D chose roses.
4. The person who chose lilies sits directly across from E.
5. Neither D nor F chose carnations.
6. F did not choose tulips.
7. The person who chose tulips sits directly across from D.
8. The person sitting next to B chose sunflowers.

One of them chose baby's breath. How many possible arrangements of seating and flower choices satisfy all the conditions?
Answer: \boxed{8}
Question: The Gao and Guo families had a dinner gathering with all their children. Each family has 3 children. The six children at the restaurant are R, S, T, U, V, and W. The following information is known:
1. Two children from the Gao family and two from the Guo family are no older than 4 years old.
2. No child is older than 8 years old, and none are 0 years old.
3. R is one year older than U.
4. R is the oldest among all the children.
5. S is three years younger than their elder brother.
6. T is one year younger than the oldest child in the Guo family.
7. U is two years older than their younger sister.
8. V is one year younger than the youngest child in the Gao family.
Considering all possibilities, what is the maximum age difference between a child from the Gao family and a child from the Guo family?
Answer: \boxed{4}
Question: The He and Hu families had a dinner gathering with all their children. The He family has 2 children and the Hu family has 4 children. The six children at the restaurant are K, L, M, N, O, and P. The following information is known:
1. One child from the He family and three children from the Hu family are no older than 5 years old.
2. None of the children are over 10 years old, and none are 0 years old.
3. K is two years older than N.
4. K is the oldest among all the children.
5. L is four years younger than their elder sister.
6. M is three years younger than the oldest child in the He family.
7. N is six years older than their younger brother.
8. O is two years younger than the youngest child in the Hu family.
Considering all possibilities, what is the maximum age difference between a child from the He family and a child from the Hu family?
Answer: \boxed{8}
Question: The Zhang and Li families had a dinner gathering with all their children. The Zhang family has 4 children and the Li family has 2 children. The six children at the restaurant are P, Q, R, S, T, and U. The following information is known:
1. Three children from the Zhang family and one child from the Li family are no older than 6 years old.
2. None of the children are over 12 years old, and none are 0 years old.
3. P is four years older than S.
4. P is the oldest among all the children.
5. Q is eight years younger than their elder sister.
6. R is three years younger than the oldest child in the Li family.
7. S is six years older than their younger brother.
8. T is two years younger than the youngest child in the Zhang family.
Considering all possibilities, what is the maximum age difference between a child from the Zhang family and a child from the Li family?
Answer: \boxed{10}
Question: You have a palette knife, and you are mixing some paint blocks which come in three colors: red, yellow, and blue. To organize them, you decide to sort the stack. In one operation, you may insert the knife at any point between two blocks, lift and reverse the entire section above the knife, and then place it back on top. The current stack order (from top to bottom) is:
Blue, Yellow, Red, Red, Blue, Yellow, Blue, Red.
What is the minimum number of operations required to rearrange the stack so that all red blocks are on top, followed by all yellow blocks, and finally all blue blocks at the bottom?
Answer: \boxed{5}
Question: You are preparing a skewer with three types of ingredients: chicken, mushroom, and green pepper. To ensure even cooking, you need to rearrange them. Holding one end of the skewer, you can perform the following operation: choose any gap between two pieces, slide off the entire section in front of the gap, and thread it back onto the skewer in reverse order. The initial order from the tip to your hand is:
Mushroom, Chicken, Green pepper, Mushroom, Chicken, Green pepper, Chicken.
Find the minimum number of such operations needed so that all chicken pieces are at the tip, followed by all mushroom pieces, and with all green peppers at the end.
Answer: \boxed{6}
Question: You are sorting a messy stack of game cards of two rarities: Common and Rare. In one operation, you may insert a rigid card at any point in the stack, lift and reverse the entire section of cards above it, and then return them to the stack.
The stack's current order from top to bottom is:
Rare, Common, Common, Rare, Common, Rare, Rare, Common.
What is the minimum number of operations required so that all Common cards are on top and all Rare cards are at the bottom?
Answer: \boxed{5}
Question: Five people-A, B, C, D, and E-were invited to fish along the Colorado River. They are seated in a row along the riverbank from north to south. Each person comes from a different state, has a different profession, uses a different brand of fishing gear, and caught a different number of fish. The following information is given:
1. A is a nurse and caught 3 fewer fish than B.
2. The chef, who sits next to the programmer, uses an R-brand rod.
3. The programmer sits at the northernmost position, and C sits next to the programmer.
4. The mechanic caught only 1 fish and sits at the southernmost position.
5. The person from Georgia uses an H-brand rod and sits next to the person who caught 1 fish.
6. D is from Montana and uses an M-brand rod.
7. E uses an L-brand rod, and the person from Ohio caught 25 fish.
8. The person sitting in the middle position is from Pennsylvania and uses an N-brand rod.
9. The programmer caught 14 fish.
10. B sits in the middle, and there is exactly one person between B and the person from Alaska.
11. The person sitting next to the person from Georgia is a driver and caught 16 fish.
12. A does not sit next to D.
Question: What fraction of the total fish caught is accounted for by A and the driver combined?
Answer: \boxed{\frac{29}{69}}
Question: Five people-A, B, C, D, and E-were invited to fish along the Red River. They are seated in a row along the riverbank from north to south. Each person comes from a different state, has a different profession, uses a different brand of fishing gear, and caught a different number of fish. The following information is given:
1. A is a host and caught 2 fewer fish than B.
2. The director who sits next to the editor uses an A-brand rod.
3. The editor sits at the northernmost position, and C sits next to the editor.
4. The customer service representative caught only 9 fish and sits at the southernmost position.
5. The person from Wyoming uses a B-brand rod and sits next to the person who caught 9 fish.
6. D is from Delaware and uses a C-brand rod.
7. E uses a D-brand rod, and the person from Mississippi caught 26 fish.
8. The person sitting in the middle position is from Tennessee and uses an E-brand rod.
9. The editor caught 15 fish.
10. B sits in the middle, and there is exactly one person between B and the person from Kentucky.
11. The person sitting next to the person from Wyoming is a pilot and caught 20 fish.
12. A does not sit next to D.
Question: What fraction of the total fish caught is accounted for by A and the director combined?
Answer: \boxed{\frac{1}{2}}
Question: Five people-A, B, C, D, and E-were invited to fish along the Columbia River. They are seated in a row along the riverbank from north to south. Each person comes from a different state, has a different profession, uses a different brand of fishing gear, and caught a different number of fish. The following information is given:
1. A is a trainer and caught 3 fewer fish than B.
2. The planner who sits next to the consultant uses a CC-brand rod.
3. The consultant sits at the northernmost position, and C sits next to the consultant.
4. The repairman caught only 11 fish and sits at the southernmost position.
5. The person from Utah uses a DD-brand rod and sits next to the person who caught 11 fish.
6. D is from Alaska and uses an EE-brand rod.
7. E uses an FF-brand rod, and the person from Washington caught 28 fish.
8. The person sitting in the middle position is from Oregon and uses a GG-brand rod.
9. The consultant caught 17 fish.
10. B sits in the middle, and there is exactly one person between B and the person from Idaho.
11. The person sitting next to the person from Utah is a translator and caught 22 fish.
12. A does not sit next to D.
Question: What fraction of the total fish caught is accounted for by A and the repairman combined?
Answer: \boxed{\frac{30}{97}}
Question: You need to open a cabinet secured by two nested safes. Each safe has a 4-digit mechanical dial lock, with each digit ranging from 1 to 8. You've forgotten both passwords but recall three clues:
1. The eight digits forming the two passwords are all distinct.
2. In each of the four positions, the sum of the outer digit and the inner digit is the same constant value.
3. The four positions show the digits 1, 2, 3, 4 in that order, but each digit may come from either the outer or inner safe.

Changing one digit on a dial counts as one step. Assuming optimal strategy in the worst case, what is the total number of steps required to open both safes?
Answer: \boxed{23}
Question: You need to open the medicine safe in the hospital. This safe is equipped with two nested password systems, both of which are 4-digit mechanical dial combination locks. Each digit of the password is entered via a single dial that is ordered from 0 to 7.
You have forgotten the passwords for both the inner and outer systems, and only remember the following information:
1.When the correct passwords of the two systems are put together, there will be no repeated digits.
2.For the digits in the same position of the inner and outer password systems, the sum of each pair is always the same number.
3.The four digits 0, 1, 2, 3 appear in the 1st, 2nd, 3rd and 4th positions of the passwords of the two systems respectively in sequence. The only thing you don't know is which of these four digits belong to the inner password system and which belong to the outer one.
If turning a single dial to change one digit of the password counts as one step, what is the total number of steps that a rational person would have to take in the worst-case scenario to retrieve the documents?
Answer: \boxed{23}
Question: To retrieve a historical document, you must open two nested security boxes. Each box has a 3-digit mechanical dial lock, with each dial numbered sequentially from 1 to 6.
You have forgotten both 3-digit passwords but recall three facts:
1. The six digits that make up the two passwords are all different.
2. For each of the three positions, the sum of the digit on the outer box and the digit on the inner box is equal to the same constant, S.
3. The digits 1, 2, and 3 occupy the first, second, and third positions respectively. It is unknown which of these digits belongs to the outer box and which to the inner box.

Changing one digit on any dial counts as one step. Assuming an optimal strategy in the worst case, what is the minimum total number of steps required to open both boxes and retrieve the document?
Answer: \boxed{13}