Ckriman/General365_Public huggingface dataset:
Question: Including myself, six of us went to the movies. The theater has twelve seats arranged in four rows, with three seats per row. No one sits in front of me; A is sitting one row ahead of me. C and I are in the same row. B and D sit next to each other, and I am sitting in front of B. E is seated far away from me. Both A and E say they can see the center of the screen. E tells A that he is farther from the screen than A. C mentions that it's nice no one is blocking his view of the screen. Everyone dislikes sitting in the first row, which is closest to the screen. The first row is closest to the screen, and the middle seat of each row has a direct view of the center. Seat numbering is as follows: the first seat from left to right in the first row is Z_{11}, the third seat in the first row is Z_{13}, the first seat in the fourth row is Z_{41}, and the third seat in the fourth row is Z_{43}. What fraction of the seating positions among the six of us is determined?
Answer: \boxed{\frac{1}{2} }
Question: An intercity bus with a rated capacity of 45 passengers departed from Wenquan Town, carrying 18 ticketed adult passengers, 2 elderly passengers who rode free of charge, and 3 mechanics heading to the terminal station for maintenance. After departure, a dispatcher boarded the bus for inspection and then left. During the journey, at Maple Forest Station, 5 people got off and 7 boarded; when the bus broke down in a tunnel, the 3 mechanics temporarily got off to carry out repairs, and 2 passengers took a taxi due to the delay. At Rainbow Bridge Station, 9 passengers got off and 4 got on; at a temporary stop, 5 people got off normally, and 1 fare-dodger slipped away. At the second-to-last stop, 6 passengers got off, and a cleaner boarded one stop early to begin cleaning. How many people were on the bus when it arrived at the final stop? (Passengers who got off and did not board again are considered to have left the vehicle.)
Answer: \boxed{8}
Question: The initial color configuration of a 3-layer Rubik's Cube is as follows: front face (blue), back face (blue), top face (white), bottom face (yellow), left face (orange), right face (red).
If each face is rotated clockwise 1 time in the order "bottom – front – right – top – back – left", and this sequence is repeated for 3 rounds, what will be the color distribution of the front face at that point? Please provide your answer in top-to-bottom, left-to-right format, for example:
First row: Red Orange Blue
Second row: White Orange White
Third row: Yellow White Yellow
Answer: First row: Yellow White Blue
Question: On the first day of each month, the real estate company evaluates employees based on the month-over-month change in their sales performance from the previous month. An increase results in a reward, while a decrease leads to a penalty. Which of the following statements is incorrect?
A: Employee A's total performance in the second half of the year dropped to 1/2 of that in the first half, so he received more penalties than rewards that year.
B: Employee B's performance increased every month during the year, so he did not receive any penalties that year.
C: Employee C earns performance as long as he is at work. If he took 4 months of leave during the year, then he must have received at least 1 penalty that year.
D: Employee D received only one penalty throughout the year. Therefore, his total sales for the year must have been higher than the previous year.
Answer: ABCD
Question: In a military exercise map, a square plain region is divided evenly into 9 rows and 9 columns. From north to south, the rows are labeled 1~9, and from east to west, the columns are labeled A~I. Thus, the southwest corner cell is designated as A9.
A pilot receives a mission to take off from the intersection point between zones I9 and H8, and fly in a straight line along the shortest path to zone A1. Upon reaching the boundary of the "row labeled 4", the pilot turns around and flies directly to the point at the map edge where zones B9 and C9 meet. After reaching the intersection point and completing reconnaissance, the pilot flies within the exercise zone along a curved path back to the original starting point, such that the flight path forms exactly a semicircular arc upon arrival. How many internal zones does the pilot pass through during the entire flight?
Answer: \boxed{15}
Question: Here is a 1A2B game. [Game Rules] One person sets a four-digit number as the secret code, and the other person tries to guess it. After each guess, the player who set the number gives a hint in the form of XAYB, until the correct number is guessed. Here, X indicates the number of digits that are correct and in the correct position, and Y indicates the number of digits that are correct but in the wrong position.
For example, if the secret code is 8123 and the guess is 1052, the hint must be 0A2B.
For example, if the secret code is 5637 and the guess is 4931, the hint must be 1A0B.
Here is a game session:
Welcome to the number guessing game! Please guess a 4-digit number with no repeating digits.
Enter your guess: 4189  Result: 0A1B
Enter your guess: 1239 
Result: 0A1B
Enter your guess: 5609 
Result: 2A2B
Enter your guess: 3476 
Result: 0A1B
Enter your guess: 5734 
Result: 0A1B
Based on the above guesses, what is the correct number?
Answer: \boxed{9605}
Question: A movable standard wire ring is looped around a donut-shaped torus that can be considered as formed by rotating a standard circle (the torus and the ring pass through each other's hollow centers, just like two adjacent links in a chain that cannot be separated).It is known that the wire ring has contact points with the surface of the torus, but the inner side of the ring is not in full contact with the torus, and the ring itself does not pass through the solid interior of the torus. What is the maximum number of contact points between the wire ring and the torus?
Answer: \boxed{3}
Question: There is a 9-digit number consisting of 7 distinct digits. This 9-digit number can be represented as abcdaefgd, and it satisfies the following conditions:
1. The two-digit number formed by a and b is ab, and satisfies ab=c^2.
2. The two-digit number formed by f and g is fg, and satisfies fg=b+c+d.
3. d, a, and e form an arithmetic sequence
4. d is the smallest prime number
What is this 9-digit number?
Answer: \boxed{497246182}
Question: The owner of a certain commercial bank is an enthusiast of Roman culture. The bank's anti-fraud system detected an abnormal operation: the encrypted safe of the risk control department was accessed outside of working hours. This safe stores the core parameters of the bank's customer risk evaluation models, and can only be opened by entering a six-digit dynamic password. It is known that this six-digit password is derived by rotating the symbol string "<>+×" into letters, and then converting those letters into numbers. Can you figure out what the password is?
Answer: \boxed{551010}
Question: Six people, A, B, C, D, E, and F, are seated in a circle. A cannot sit directly next to both B and D at the same time. D is to the left of E, and F sits directly opposite E. E is to the right of D, and C is not adjacent to A. If A's position is numbered as 1, and starting from A the positions are numbered clockwise as 1, 2, 3… then among all possible arrangements that meet the conditions, what is the average position number of F?
Answer: \boxed{4.25}
Question: In a 6*6 grid garden, there are trees of height 1~6, with six types of trees. Each row and each column contains trees of different heights, and no height repeats. A taller tree will block any shorter tree behind it in the line of sight. If the following statements are all true, what is the average height of the trees located at the four corners of the garden: northwest, northeast, southwest, and southeast?
A: I stand at the westernmost spot in the 2nd row from north to south, and looking east I can see only 2 trees.
B: I stand at the westernmost spot in the 3rd row from north to south, and looking east I can see only 2 trees.
C: I stand at the easternmost spot in the 2nd row from north to south, and looking west I can see only 4 trees.
D: I stand at the southernmost spot in the 3rd column from the west, and looking north I can see only 3 trees.
E: I stand at the southernmost spot in the 1st or 2nd column from the east, and in both cases, looking north I can see only 4 trees.
F: I stand at the northernmost spot in the 2nd column from the east, and looking south I can see only 3 trees:I stand at the northernmost spot in the 2nd column from the east, and looking south I can see only 3 trees.
G: I stand at the northernmost spot in the 3rd column from the east, and looking south I can see only 6 trees:I stand at the northernmost spot in the 3rd column from the east, and looking south I can see only 6 trees.
Answer: \boxed{4}
Question: Xiaoye told a thrilling but ultimately safe story to a reporter. In his account, he mentioned that he was in a car accident and lost consciousness at 22:34, was taken to the hospital at 23:10, and arrived with a faint heartbeat. At 23:25, the ECG showed a heart rate of 0, and ten minutes later, the doctor informed the family that Xiaoye had passed away.
Was Xiaoye's actual time of death before or after 24:00 on that day?
Answer: After 24:00
Question: At a university with 9 colleges, a celebration event is planned for National Day, and the venue is set on the sports field. Each college will be allocated a section of the field. Given that the sports field is very large, to make the celebration more engaging, the university administration has proposed the following requirements:
1. One college is to organize a dance performance that can be seen by all the other colleges.
2. Four colleges are to set up fun mini-games, each positioned at one of the four corners of the field.
3. Before the event started, only the area assigned to the Mathematics College had two other college booths moved across it, one of which was from the Computer Science College.
4. The event budget is to be requested from the university.
5. Xiaoming watched a short historical play at the History College and, by simply turning around, could play an animal-themed guessing game at the Biology College.
6. In front of the Chemistry College's booth, Xiaohong found that no other place was closer to the Mathematics College's area than where she was standing.
7. No matter which college Xiaoyu visited, she could always see the beautiful girls at the Music College just by turning her head.
8. Luo from the Physics College and his friend from the History College were completely blocked by a college in the middle and couldn't see each other at all.
9. It's said that the candy from the Electronics College is the best. Right after eating candy from the Mathematics College, Xiaofan immediately went to the opposite side.
10. Due to a disagreement over the boundary line between their areas, students from the Chemistry College and the Physics College had a small conflict, so before the celebration began, the Chemistry College swapped locations with another college.
11. The four colleges that neither prepared dance performances nor offered mini-games were to set up candy stations in four directions, so that everyone could enjoy them at any time.
12. Students from the Engineering College built an automatic packaging machine, which surprised the students from the neighboring Electronics College on the day of the celebration.
It is known that the areas of the nine colleges form a grid of nine squares when viewed from above the sports field. At the end of the celebration, which colleges were directly adjacent to the Computer Science College (only those sharing a common edge are considered adjacent)?
Answer: Physics College, Mathematics College
Question: The supermarket has a rule that four empty bottles can be exchanged for one bottle of drink. Xiao Wang has 44 empty bottles and goes to the supermarket to exchange them for drinks. On the way, he picks up one more empty bottle of the same drink. When he arrives at the supermarket, he finds that there are three people in front of him in the queue. So, he buys the empty bottles from the people in front of him at a price of 50 cents each. The owner of the supermarket is a generous person and allows  Xiao Wang  to borrow bottles temporarily. It is known that each bottle of this kind of bottled water costs 3 yuan. If Xiao Wang exchanges the drinks and then sells them, each bottle can also be sold for 3 yuan. After selling them, the bottles can be exchanged again. Under the condition of buying the least number of bottles, what is the maximum profit that Xiao Wang can make in the end? (Assume that the bottles of the drinks sold are all kept.)
Answer: \boxed{51}
Question: A, B, C, D are playing table tennis doubles, known: A is younger than B, C is older than his two opponents, if you want to meet B-A>C-D, how many possibilities are there in the age order of the four?
Answer: \boxed{5}
Question: A, B, C, and D are four individuals with different occupations. The four occupations are teacher, designer, store manager, and programmer. It is known that:

1. A is a programmer  
2. C is a teacher  
3. B is not a programmer  
4. D is not a designer  

However, among these four statements, exactly three are false. How many possible occupational combinations exist for the four individuals?
Answer: \boxed{6}
Question: Xiaoming and his several good friends participated in the gymnastics competition. Each of them performed the same movements. After entering the venue, they stood in a row. From right to left in the eyes of the audience in the north, they were Xiao Hong, Xiao Bai, Xiaoming, and Xiao Huang. When Xiaoming turned 90 degrees to the right, without considering any obstructions, how many teammates could Xiaoming see at least?
Answer: \boxed{1}
Question: The family of Xiao A is going to have a family dinner. There are six people: ABCDEF. They will have the dinner on a rectangular table. The long side of the rectangle can accommodate two people, while the short side can only accommodate one person. Person A has someone on his left, B and C are directly opposite each other, and D's left side is F. How many different seating arrangements that meet all these requirements are there?
Answer: \boxed{2}
Question: A moves while checking the distance with a horizontal rangefinder. The starting point was originally facing west, then turned right by 180 degrees, then straight ahead for one kilometer, then turned left by 90 degrees and straight ahead for one kilometer to reach an altitude of 300 meters. Then, she continued straight for one kilometer to the west to reach an altitude of 600 meters. Finally, she turned left by 90 degrees and straight ahead for one kilometer. How many kilometers horizontally is her final location from where she started?
Answer: \boxed{0}
Question: You are a single man, idly wandering around in society.
Suddenly one day, you met a group of people. They said, "Join us! We'll handle the pairing for you. After you join, you'll start the matching game. Each single man will pair up with the female on the right, and then leave here to live a sweet life. The last man remaining will become the king of single persons." As soon as you heard this, you got excited. The king of single persons, how powerful! I must become the king of single persons!
It is known that their current arrangement is as follows (numbers 1 to 32): "Woman-Male-Male-Woman-Male-Woman-Male-Male-Woman-Woman-Male-Woman-Woman-Male-Male-Woman-Male-Woman-Woman-Male-Male-Male-Male-Woman-Woman-Woman-Male-Male-Woman-Woman-Woman-Male" They formed a circle by connecting the ends (1 is on the right of 2). Then, which number on the right do you need to insert to achieve your dream? Provide all correct answers.
Answer: \boxed{1,19}
Question: Xiao Ming has a habit of factoring opportunity costs into his actual costs. For instance, if he forgoes an option to earn 10 yuan in favor of an option to earn 5 yuan, he considers his actual cost to be a loss of 5 yuan.

In a game where the goal is to earn gold coins, Xiao Ming can choose from the following one-time use items (multiple selections are allowed):

A: This item restores 1 Health Point (HP) and grants 20 gold coins;
B: This item restores 3 HP and grants 10 gold coins;
C: This item restores 50 HP but deducts 10 gold coins;
D: This item grants 40 gold coins;
E: This item grants 100 gold coins. Additionally, for every other item selected alongside this one, 30 gold coins will be deducted;
F: This item triggers an additional settlement after the selection process. Based on the effects of other items, you will gain 5 gold coins for every 1 HP finally restored, and lose 5 gold coins for every 1 HP finally deducted;
G: This item deducts 10 HP and grants 50 gold coins.

After making his selection, Xiao Ming realized he had made a misjudgment. It turned out that his actual cost in terms of gold coins resulted in the highest possible loss value. What is this actual cost loss value?
Answer: \boxed{340}
Question: If the probability that each person in Xiao Zhao's bloodline family will not have children is 7%, then what is the probability that both Xiao Zhao and his great-grandfather have never had sons but have daughters?
Answer: \boxed{0}
Question: On a frictionless ice surface, Xiao Zhang pushed a stone of the same weight as him with a strong force. After 10 seconds, the distance between them was 20.5 meters. After 20 seconds, the distance was 40.5 meters. When the distance between them reached 60 meters, the time was reversed by 1 minute. At this point, what was the distance between them?
Answer: \boxed{0.5}
Question: You have 100 cards, numbered from 1 to 100. Each card has two sides, with the front side showing the number and the back side showing a red flower. Currently, all 100 cards are facing upwards. First, flip all the cards whose numbers are multiples of 1, then flip all the cards whose numbers are multiples of 2, then flip all the cards whose numbers are multiples of 3, then flip all the cards whose numbers are multiples of 4. Then how many cards will be facing upwards in the end?
Answer: \boxed{42}
Question: A, B, C, and D all live in the town and their houses are arranged in a row next to each other. Each person's house has a different color, they have diffrent hobbies,and work in different professions. It is known that:
1. One person among them lives in the red house.
2. D likes billiards and is also a programmer.
3. C is a lawyer.
4. The white house is to the right of the gray house.
5. The owner of the white house is a farmer.
6. The person who likes basketball is a teacher.
7. The owner of the pink house likes badminton.
8. The farmer lives next to the person who likes basketball.
9. The person who likes badminton lives next to the teacher.
10. The person who likes rugby lives next to the person who likes billiards.
How many possible combinations of house color, hobbies, and occupations are there for the four people?
Answer: \boxed{4}
Question: There are six people: A, B, C, D, E, and F. Their ages are in the order A > B > C > D > E > F. These six people are going to have a meal at a round table, but no one wants to sit next to the two people whose ages are closest to theirs (one is older than him and the other younger than him). Now C says he doesn't want to sit next to E. Then,how many seating arrangements are possible?
Answer: \boxed{2}
Question: A, B, C, D, E, and F six people went to a coffee shop to catch up. They sat on both sides of a square table, with three people on each side. Each person ordered a different type of coffee. It is known that:
1. B was sitting next to C.
2. C wsa sitting opposite the person adjacent to E.
3. D was sitting opposite A, and D ordered cappuccino.
4. Those who ordered iced espresso are sitting opposite E.
5. Neither D nor F ordered mocha.
6. F did not order cold brew coffee.
7. The person who ordered cold brew coffee was sitting opposite D.
8. The person sitting next to B ordered Irish coffee.
Among them, there was one person who ordered espresso. How many possible seating arrangements were there for these six people at that time?
Answer: \boxed{8}
Question: The Wang and Liu families had a dinner together and brought their children along. The Wang family has 3 children, while the Liu family has 2 children. There were 5 children in the restaurant, namely A, B, C, D, and E. It is known that:
1. The two children from the Wang family and one child from the Liu family are no older than 5 years old.
2. None of the children from both families are 0 years old, and their ages do not exceed 10 years old.
3. A is three years older than D.
4. A is the oldest among all the children.
5. B is 7 years younger than his elder brother.
6. C is 4 years younger than the oldest child from the Liu family.
7. D is 5 years older than his younger sister.
8. E is 1 year younger than the youngest child from the Wang family.
Considering all the possibilities, what is the maximum age difference between the two children from the Wang family and the Liu family?
Answer: \boxed{8}
Question: You have a shovel and you are flipping over a stack of pancakes. These pancakes are all round but of different sizes. To make them look nice, you decide to sort them. But you only have one shovel, so you cleverly think that you can insert the shovel from any position, scoop up all the pancakes on top at once, and then place them back in their original positions. Of course, you can't do this with your hands, as it's unhygienic.
The current order of the pancakes in front of you from top to bottom is: large, medium, medium, small, small, large, medium, large, small, small.
Could you please tell me how many steps are needed at least to arrange the pancakes so that the larger ones are at the bottom and the smaller ones are on top, and to stack them all together?
Answer: \boxed{5}
Question: Five people, A, B, C, D, and E, were invited to go fishing by the Mississippi River. They came from different states, had different occupations, sat in a row by the river, used different fishing tackle brands, and each caught a different number of fish. It is known that: 
1. A is a teacher and he caught one less fish than B.
2. The designer sitting next to the salesperson uses an S brand fishing rod.
3. The salesperson is sitting at the northernmost position, and next to him is C.
4. The farmer caught only two fish and is sitting at the southernmost position.
5. The Californian uses a D brand fishing rod and is sitting next to the person who caught two fish.
6. D is from Florida and uses a P brand fishing rod.
7. E uses an A brand fishing rod and the person from Texas caught 20 fish.
8. The person sitting in the middle is from Illinois and uses a C brand fishing rod.
9. The salesperson caught 10 fish.
10. B is sitting in the middle and there is one person between him and the person from New York.
11. The construction worker sitting next to the Californian caught 12 fish.
12. A is not sitting next to D.
What fraction of the total number of fish caught does A and the designer's catch make up?
Answer: boxed{\frac{31}{55}}
Question: 

Your boss has assigned you to deliver a confidential document, which is secured inside two nested safes. Each safe has a 5-digit mechanical rotary combination lock, with each digit set by a wheel numbered 0–9 sequentially. You have forgotten both combinations, but you still remember the following clues: 1. When the two 5-digit passwords are combined, no digit repeats. 2. For each digit position, the digits for the two safes add up to the same constant value. 3. The digits 0, 1, 2, and 3 appear in order at positions 1 through 4 across the two passwords, though you do not know which belong to the inner or outer safe. Changing one wheel to alter a digit counts as one step (e.g., rotating a wheel from 0 to 5 counts as one step). In the worst-case scenario, how many total steps would a rational person need to dial to retrieve the document?
Answer: \boxed{41}
Question: 111, 9, ?, 9. A student solved this problem using only squaring and addition, without using any additional numbers beyond those already given. What is the most likely number that should replace the question mark?
Answer: \boxed{9}
Question: 25, 13, 16, ?, 16. A student solved this problem using only squaring and addition, without using any additional numbers beyond those already given. What is the most likely number that should replace the question mark?
Answer: \boxed{13}
Question: 4, 7, 13, ?, 13. A student solved this problem using only squaring and addition, without using any additional numbers beyond those already given. What is the most likely number that should replace the question mark?
Answer: \boxed{16}
Question: You are about to set a lock screen password for your new phone and first think of using your birthday "0816". However, concerned about security, you decide to use a more complex combination "Music_0816". At this point, how many English letters are there in your phone's lock screen password?
Answer: \boxed{0}
Question: You are preparing a PPT for the company's annual meeting, and for one of the slides, you originally plan to title it "Review of 2023". Before submission, your supervisor suggests changing it to "Summary of 2023, Outlook for 2024" to make it more complete, and you agree with the change. At this moment, how many digits "4" are there in the title of that slide in the PPT?
Answer: \boxed{0}
Question: You are getting ready to go out and plan to wear a black baseball cap. Your partner suggests that, since it's a sunny day, a straw hat would be more fitting and provide better sun protection. You think that's reasonable and change your mind. At this moment, how many woven straw hats are there on your head?
Answer: \boxed{0}
Question: Agent Liam and his partner are trapped in an enemy underground base. On the wall, there are four 5×5 digital matrix-press the correct button and the door will open:
Matrix 1:
50061
42397
53067
93393
52068
Matrix 2:
33669
51249
93393
51249
93669
Matrix 3:
93369
51246
93369
61248
63369
Matrix 4:
51348
81347
81347
51948
50651
His partner taps the wall and realizes that the passcode is related to multiples of 3, and this isn't a standard cryptography problem. He whispers: "I've got it!" Which of the following options is the correct passcode?
A. 1357
B. 2580
C. 9876
D. 4321
Answer: D
Question: Explorer Jack and his guide are trapped in an ancient pyramid. On the wall are four 5×5 digital matrix. Pressing the correct button will open the door:

Matrix 1:
24168
02146
80124
68102
46180
Matrix 2:
13579
10243
57913
02465
13597
Matrix 3:
35791
32465
79135
24687
33719
Matrix 4:
13579
10246
35791
30245
79135
After carefully studying the mural, the guide realizes that the passcode is related to odd numbers and doesn't require complicated calculations. "I've got it!" he exclaims. Which of the following options is the correct passcode?

A. 2008
B. 1996
C. 8848
D. 1776
Answer: B
Question: A professor and his student are trapped in an abandoned alchemist's workshop. On the wall are four 5×5 digital matrix, and pressing the correct button will open the door:

Matrix 1:
23572
14683
57235
46897
23572

Matrix 2:
14268
01346
89510
46789
01246

Matrix 3:
21463
54687
23572
14683
01465

Matrix 4:
89210
14368
06589
14761
46280

The professor adjusts his glasses and notices that the passcode is related to prime numbers, but it doesn't seem to require any calculations. Suddenly, it dawns on him: "I've got it!"

Which of the following is the correct passcode?

A. 2718
B. 3141
C. 1618
D. 9999
Answer: B
Question: There are currently two paint cans with a diameter of 25 cm and a height of 12 cm (including the base), with a base thickness of 2 cm, and two paint cans with a diameter of 20 cm and a height of 11 cm (including the base), with a base thickness of 1 cm. Both types of paint cans are of the same style. There is also a packaging box measuring 25 cm × 25 cm × 17 cm in length, width, and height. What is the maximum number of paint cans that can be placed inside this box?
Answer: \boxed{4}
Question: You are given:
Two identical ceramic pots of Style A, each with:
Diameter: 14 cm  
Total height (including the base): 9 cm  
Base thickness: 3 cm  
Two identical ceramic pots of Style B, each with:
Diameter: 12 cm  
Total height (including the base): 6 cm  
Base thickness: 2 cm  
A rectangular box with interior dimensions:
Length: 15 cm  
Width: 15 cm  
Height: 14 cm  

Both styles of pots share the same overall design.
Determine the maximum number of these pots that can be simultaneously placed inside the box without exceeding its interior space.
Answer: \boxed{4}
Question: Two food containers have a diameter of 28 cm and a height of 18 cm (including base), with a base thickness of 4 cm; two more have a diameter of 25 cm and a height of 15 cm (including base), with a base thickness of 2 cm. Both types are geometrically similar. The refrigerator has an internal space of 30 cm × 30 cm × 26 cm. What is the maximum number of food containers that can fit in the refrigerator?
Answer: \boxed{4}
Question: There are 16 circles arranged in a 4×4 grid as follows, from top to bottom:
Row 1: a, b, c, d
Row 2: e, f, g, h
Row 3: i, j, k, l
Row 4: m, n, o, p
The white circles are a, b, c, d, e, f, h, j, l, o, p, and the remaining circles are black.
The task is to connect all the white circles using exactly four line segments to form a continuous path. Each line segment must not pass through any black circles, and each white circle can be visited only once along the path. Line segments may extend beyond the positions of the circles. The path must start at a and end at f. How many different such paths exist in total?
????
????
????
????
Answer: \boxed{1}
Question: Sixteen spheres are arranged in a regular 4×4 grid as follows: from top to bottom, they are named Row 1: a, b, c, d; Row 2: e, f, g, h; Row 3: i, j, k, l; Row 4: m, n, o, p. Among them, the white spheres are a, b, c, d, e, g, h, j, l, o, p, and the rest are black spheres.
Now, you need to connect all white spheres with four line segments without touching any black spheres (the four line segments must form a continuous single-stroke path, each white sphere can only be passed through once on the connection route, and the line segments can extend beyond the range of the spheres). In addition, the starting point is specified as d and the ending point as g. How many different connection sequences are there in total?
????
????
????
????
Answer: \boxed{2}
Question: Sixteen balls are arranged in a 4×4 grid as shown below. The rows are labeled from top to bottom:
Row 1: a, b, c, d
Row 2: e, f, g, h
Row 3: i, j, k, l
Row 4: m, n, o, p

The white balls are {a, b, c, d, e, f, i, l, m, o}, and the remaining balls are black.
Connect all the white balls using a single continuous stroke consisting of exactly four line segments, subject to the following conditions:
The path must not pass through the position of any black ball.
Each white ball must be visited exactly once along the path.
The line segments may extend beyond the boundary of the 4×4 grid.
The path must start at a and end at f.

How many distinct permutations (orderings) of the white balls can be formed by such a path?
Answer: \boxed{2}
Question: On a Galactic War simulation board, an unfinished game of "Galactic Duel" is in progress, and you lean in to take a closer look.
The board is a 10 × 10 grid. Columns are labeled A through J from left to right; rows are numbered from 1 to 10, with row 1 being the side nearest to you. Positions are denoted by column–row pairs.
Two destroyers of the "Federation" are on B2 and I2 respectively, and two destroyers of the "Empire" are on B9 and I9 respectively.
Disregarding all other units, if the two sides take turns moving these four destroyers (one grid per move only), until each destroyer reaches the opponent's home (the opponent's baseline). What is the minimum total number of moves required?
Answer: \boxed{4}
Question: An unfinished chess game is set on a park table. From your viewpoint, the leftmost file is labeled as A and the nearest rank is labeled as 1. The two White rooks are on A2 and H2, and the two Black rooks are on A7 and H7. Ignore all other pieces: only these four rooks may be moved. White and Black move alternately, moving exactly one rook per turn in accordance with the rook's normal movement. The goal is for each rook to reach the opponent's back rank: the White rooks must reach rank 8, and the Black rooks must reach rank 1. Under these conditions, what is the minimum total number of moves (one rook move per turn) required for all four rooks to reach their respective target ranks?
Answer: \boxed{4}
Question: In a "Wilderness Survival" themed board game, you see two red markers representing the Survivors at C2 and F2, and two blue markers representing the Hunters at C7 and F7. From your perspective, the board is labeled with columns A–H and rows 1–8. Each side's goal is to move its markers to the opponent's starting row. On each turn, the two sides move alternately, and the side to move must move one of its own markers by exactly one square. What is the minimum total number of one-square moves required for all four markers to reach their respective goals?
Answer: \boxed{4}
Question: Mr. Li plans to distribute 8 identical exercise books using 5 identical file folders. The folders may be nested inside one another, and all five folders must be used. Any folder that directly contains exercise books must contain an even number of books. Under these conditions, how many distinct distribution arrangements are possible in total?
Answer: \boxed{38}
Question: A student has 8 identical glass marbles and wants to place them into 5 identical small cloth bags. The bags may be nested inside one another, and all five bags must be used. Any bag that directly contains marbles must contain an even number of marbles. Under these conditions, how many distinct storage arrangements are possible in total?
Answer: \boxed{38}
Question: A charitable organization has prepared 8 identical blankets to be packed in 5 identical wrapping bags. The bags can be nested inside one another. The requirements are as follows: all 5 bags must be used, and each bag that directly contacts blankets must contain an even number of blankets. How many different packing methods are there in total?
Answer: \boxed{38}
Question: There's a group of numbers as follows:
2183, 
4189, 
8147, 
2123.
Alex has stared at these numbers for a long time and found that there seems to be a connection between the corresponding digits of these numbers. However, he cannot figure out what it is. Try to find the pattern of these numbers and answer: what should the next number be?
Answer: \boxed{6181}
Question: There's a group of numbers as follows:
1234,
5678,
5212,
5276.
Mr. Smith has stared at these numbers for a long time and found that there seems to be a connection between the corresponding digits of these numbers. However, he cannot figure out what it is. Try to find the pattern of these numbers and answer: what should the next number be?
Answer: \boxed{5472}
Question: There is a group of numbers as follows:
76851, 
34258,
14658,
36254.
Professor Chow has stared at these numbers for a long time and found that there seems to be a connection between the corresponding digits of these numbers. However, he cannot figure out what it is. Try to find the pattern of these numbers and answer: what should the next number be?
Answer: \boxed{34252}
Question: A card game is played according to the following rules.

All cards are classified as either trump or side-suit (non-trump). Four players sit around a square table, with partners seated opposite each other. During the drawing/dealing process, the first player who throws down (reveals) a 2 of any suit declares that suit as the trump suit; all other suits become side suits. Any trump card beats any side-suit card.

Regardless of the declared trump suit, the following cards are always treated as trump: the four 2s, the four 7s, both Jokers, and the Ace of Hearts. Once the trump suit is determined, the 7 of the trump suit becomes the highest-ranking card in the game, and the 2 of the trump suit becomes the highest among all 2s.

Trump ranking (from highest to lowest):
7 of the trump suit > Ace of Hearts > Big Joker > Small Joker > the remaining 7s > 2 of the trump suit > the remaining 2s > A > K > Q > ... > 3
Among the remaining 7s (and likewise among the remaining 2s), the card played earlier in the trick outranks the one played later.

Side-suit ranking (from highest to lowest):
A > K > Q > ... > 3

All 10s and Kings are point cards, each worth 10 points.
Each trick proceeds with every player playing exactly one card in turn. The player who wins the trick collects all point cards played in that trick and leads the first card of the next trick. The objective of each partnership is to prevent the opposing team from scoring points.

If the first card of a trick is a side-suit card of a given suit, all players must follow that suit with a side-suit card of that suit if possible. (Trump cards that happen to have that suit, such as a 2 or 7, do not count as side-suit cards.) A player who cannot follow suit may either discard another side-suit card (which is treated as the lowest card in the trick) or play a trump card to attempt to win the trick.

Current Game State:
In this round, players ① and ③ form one partnership, while players ② and ④ form the other. Diamonds are the trump suit.
A total of 22 cards have already been played, including 9 side-suit Clubs. Each player now holds 8 cards, listed below:
① A of Diamonds, 7 of Diamonds, J of Hearts, 10 of Hearts, A of Clubs, 8 of Spades, 10 of Spades, 6 of Diamonds
② Big Joker, 2 of Hearts, Q of Hearts, K of Clubs, 6 of Spades, K of Spades, 10 of Diamonds, 8 of Diamonds
③ Small Joker, 7 of Spades, 2 of Diamonds, K of Hearts, 9 of Spades, 5 of Spades, 9 of Diamonds, K of Diamonds
④ 7 of Diamonds, 7 of Clubs, 2 of Clubs, 2 of Spades, J of Spades, 5 of Diamonds, Q of Diamonds, 4 of Diamonds

Current Trick:
Player ① leads with A of Clubs.
Player ② plays K of Clubs.
It is now ③'s turn to play.

Each suit is assigned a numerical value:
Hearts = 100, Spades = 200, Diamonds = 300, Clubs = 400
Each rank is assigned a numerical value, where number cards use their face value (2–10), and J = 11, Q = 12, K = 13, A = 1.
The code number of a card is defined as: (suit value) + (rank value)

Question: What is the code number of player ③'s optimal play in this trick?
Answer: \boxed{207}
Question: A poker game is played as follows: all cards are classified as trump or non-trump. Four players sit on the four sides of a square table, and the two players sitting opposite each other are teammates. During the card-drawing process, the first player to throw down a 2 of a suit designates that suit as the trump suit; all other suits become non-trump. Any trump beats any non-trump.

All four 2s, all four 7s, the Big Joker, the Little Joker, and the Ace of Hearts are default trumps regardless of suit. Once the trump suit is determined, the 7 of the trump suit becomes the highest card in play, and the 2 of the trump suit is the highest among all 2s.

Trump rank order:
7 (trump suit) > Ace of Hearts > Big Joker > Little Joker > other 7s > 2 (trump suit) > other 2s > A > K > Q > ... > 3
(Among the other 7s or the other 2s, whichever is played first is higher.)

Non-trump rank order: A > K > Q > ... > 3

All 10s and Ks are scoring cards, worth 10 points each. In each trick, each player plays one card in turn. The player who plays the highest card wins the trick and has the right to lead the next trick. If the trick contains scoring cards, the points go to the side that played the highest card.

When the first player plays a non-trump suit, the other players must play a non-trump card of the same suit if they have one. If they do not have any non-trump card of that suit, they may play any other non-trump card, but it is treated as the lowest in the trick; they may also use a trump card to beat the trick. Each side should try to prevent the other side from scoring.

In this hand, players ① and ③ are teammates, and players ② and ④ are teammates. The trump suit is Clubs. A total of 22 cards have already been played, including nine Diamonds non-trump cards. Each player has 8 cards remaining, as follows:

Player ①: Diamond A, Diamond 10, Club J, Club 9, Heart K, Spade K, Spade 9, Spade 5
Player ②: Diamond K, Diamond 5, Club Q, Club 8, Heart Q, Heart 8, Spade 10, Spade 8
Player ③: Club 7, Spade 7, Heart A, Heart 9, Spade Q, Spade 2, Spade 4, Club 4
Player ④: Spade J, Spade 6, Spade 3, Heart 2, Heart J, Club 10, Club 5, Club 2

Player ① has played Diamond A, and Player ② has played Diamond K. It is now Player ③'s turn.
If Hearts represent 100, Spades represent 200, Diamonds represent 300, and Clubs represent 400, a card's "code number" equals the suit value plus the rank value (where J, Q, K, A represent 11, 12, 13, 1).
What is the "code number" of Player ③'s optimal card choice in this trick?
Answer: \boxed{207}
Question: There is a poker game played as follows: Cards are categorized into trumps and side suits. Four players sit around a square table, with those sitting opposite each other acting as teammates. During the deal, the first player to play a 2 of any suit establishes that suit as the trump suit. All cards of this suit are trumps, and all others are side suits. Any trump card beats any side-suit card. The four 2s, four 7s, the Jokers (Big and Small), and the Ace of Hearts are permanent trumps, regardless of the established trump suit.
Once the trump suit is determined, the ranking is: 7 of the trump suit > Ace of Hearts > Big Joker > Small Joker > other 7s > 2 of the trump suit > other 2s > Ace > King > Queen > … > 3. Among non-trump 7s or 2s, the first one played ranks higher. For side suits, the ranking is: Ace > King > Queen > … > 3.
All 10s and Kings are "point cards," each worth 10 points. In each round, players play one card in clockwise order. The winner of the round gains the lead for the next round and collects any point cards played. When a player leads with a side suit, others must follow suit. If a player is void in that suit, they may "sluff" (play a card from another side suit, which counts as the lowest) or "trump in" (play a trump card to win the round). Each team aims to maximize their points while preventing the opponents from scoring.
Players ① and ③ are teammates; Players ② and ④ are teammates. Spades are trumps. 22 cards have been played, including 9 Hearts (side suit). Each player has 8 cards remaining:
Player ①: K♥, 10♥, A♠, 8♠, A♣, 9♣, 5♣, 9♦
Player ②: Q♥, 5♥, J♠, 10♠, K♣, 8♣, K♦, 8♦
Player ③: 7♣, 2♠, J♦, 7♦, Q♣, 2♣, 4♣, 4♠
Player ④: 2♦, Q♦, 10♦, 10♣, J♣, 6♠, 3♠, 5♠
Current round: ① leads with K♥, ② plays Q♥. It is now ③'s turn.
Code Number Rules: The "code number" of a card = Suit Value + Rank Value. (Suits: Hearts = 100, Spades = 200, Diamonds = 300, Clubs = 400. Ranks: A=1, J=11, Q=12, K=13).
What is the code number of Player ③'s optimal card for this round?
Answer: \boxed{402}
Question: A flat cylindrical magnet is leaning obliquely with the edge of its base against the surface of a bank card. The thickness of the bank card is 1.5 times the magnet's radius. Remove the bank card. Under ideal conditions, project the magnet from its edge with a vertically upward force (assuming the magnet is subject only to this force and gravity). If all of the magnet's kinetic energy is absorbed upon its first impact with the ground, the magnet has a probability of 1/2 of standing upright. What is the ratio of the magnet's diameter to its thickness?
Answer: \boxed{1}
Question: A uniform cylindrical wheel leans with its lower rim against the surface of a phone. The phone's thickness is 0.5 times the wheel's radius. Remove the phone. Under ideal conditions, project the cylindrical wheel from its edge with a vertically upward force (assuming the cylindrical wheel is subject only to this force and gravity). If all of the wheel's kinetic energy is absorbed upon its first impact with the ground, then there is a 2/3 probability that the wheel comes to rest standing upright. What is the ratio of the wheel's diameter to its thickness?
Answer: \boxed{\frac{\sqrt{3}}{3}}
Question: A hockey puck is leaning with its bottom edge against the face of a sugar cube. The thickness of the sugar cube is √3  times the radius of the puck. Remove the sugar cube. Under ideal conditions, project the puck from its edge with a vertically upward force (assuming the puck is subject only to this force and gravity). Given that all kinetic energy is absorbed upon first impact, the probability that the puck ends up standing upright on its rim is 1/3. 
What is the ratio of the diameter of the puck to its thickness?
Answer: \boxed{\sqrt{3}}
Question: Observe this set of numbers: 61, 48, 67,?.
These numbers are related to four consecutive distinct  integers, and each of these integers is greater than 20. According to the pattern, what number should fill in the "?"?
Answer: \boxed{24}
Question: Observe this set of numbers: ?, 401, 096, 561. These numbers are related to four consecutive distinct integers, and each of these integers is less than 10. According to the pattern, what number should fill in the question mark?
Answer: \boxed{296}
Question: Observe this set of numbers:  12, 29, 00, 31, ?, 97. These numbers are related to six consecutive distinct integers, and each of these integers is less than 15. According to the pattern, what number should fill in the question mark?
Answer: \boxed{28}
Question: A newly opened gym held a soft opening raffle, giving random raffle numbers to the first 16 customers by arrival order. The first 15 numbers are: (listed in order):
01, 35, 62, 16,
28, 77, 13, 90,
81, 45, 22, 19,
54, 66, 12, ?
The manager walked by, glanced at the list, and gave a hint: "Although most of the numbers are random,  the numbers received by the 1st, 4th, and 9th customers are not; instead, they strictly follow a certain mathematical pattern."
If the 16th customer's number must also conform to this pattern, what should it be?
A. 160
B. 256
C. 100
D. 40
Answer: B
Question: Arthur is a manager at a logistics warehouse and is currently taking inventory of a 4x4 shelving section. The unit consists of 16 slots, numbered sequentially from 1 to 16. The recorded weights of the goods in the first 15 slots are as follows (in kg):
15, 09, 21, 04,
33, 07, 40, 16,
11, 52, 29, 36,
18, 65, 30, ?
Arthur, a senior employee, glanced at the data and said to his apprentice, "The arrangement of these goods might appear chaotic, but actually, the weight of the goods in the last slot of each row is strictly determined by a specific rule, following the same mathematical pattern."
After examining the data for the 4th, 8th, and 12th slots, the apprentice quickly calculated the weight for the 16th slot.
What is the weight in the 16th slot?
A. 48
B. 64
C. 52
D. 72
Answer: B
Question: A cybersecurity engineer is testing a new intelligent firewall. To test the system's response mechanism, the engineer sent a simulated attack sequence consisting of 16 data packets.
The "Threat Level Codes" generated after the first 15 packets were intercepted are as follows:
11, 12, 99, 14,
63, 27, 45, 18,
72, 30, 88, 59,
21, 94, 05, ?
The engineer explained, "The system logs are a bit messy because most of the packets are just randomly generated interference. The real system diagnostic signals are only triggered in the 1st, 2nd, 4th, and 8th packets, which strictly follow a specific pattern."
The intern realized that by focusing on these specific positions, the Threat Level Code for the 16th packet could be calculated immediately.
What is the 16th code?
A. 16
B. 36
C. 26
D. 32
Answer: C
Question: A printing factory is processing rectangular leaflets. To facilitate binding, the following mechanized folding process is performed: first, the paper is folded once along its longer side, reducing its length; then, it is folded again along the newly formed longer side. These two consecutive folds result in a smaller rectangle.
Ignoring paper thickness, if the machine performs this folding sequence for a total of 16 folds, how many independent small rectangular regions will the leaflet be divided into by the creases?
Answer: \boxed{65536 }