Ckriman/General365_Public huggingface dataset:
Question: On a 9×9 board, what is the minimum number of white stones that must be placed so that, no matter how many black stones are placed afterward on the remaining empty squares, black can never form five in a row horizontally, vertically, or diagonally?
Answer: \boxed{16}
Question: On a 6×6 board, what is the minimum number of white stones that must be placed so that, no matter how many black stones are placed afterward, black can never form four in a row horizontally, vertically, or diagonally?
Answer: \boxed{9}
Question: On a 7×7 board, what is the minimum number of white stones that must be placed so that, no matter how many black stones are placed afterward on the remaining empty squares, black can never form five in a row horizontally, vertically, or diagonally?
Answer: \boxed{9}
Question: A school is preparing a synchronized group gymnastics performance. The routine is coordinated and includes movements in different directions. If the minimum separation between any two performers is 2 meters, then each performer will have enough room to move.

If 25 people are to perform on a rectangular stage, what is the minimum stage area (in square meters) required to guarantee that the performance will have sufficient space?
Answer: \boxed{144}
Question: A large dance show requires 32 performers to stand in a grid formation (rows and columns) on a rectangular stage. The choreography is synchronized and includes movement in one direction. If the minimum distance between any two performers is at least 2.5 m, everyone will have enough room to move. What is the smallest possible stage area (in square meters) that can accommodate all 32 performers?
Answer: \boxed{281.25}
Question: A drone formation performance is being planned in a plaza. The drones stay on a single horizontal plane and move uniformly in the same direction. If the minimum separation between drones is 5 meters, each drone will have enough room to move.

If 60 drones are to be arranged in a formation, what is the minimum area (in square meters) that must be reserved to guarantee sufficient space for the performance?
Answer: \boxed{1925}
Question: There are four married couples (8 individuals in total). The people and their ages are: Chen (31), Sun (32), Zhou (33), Wu (34), Feng (35), Wang (36), Zheng (37), and Chu (38). Chen (31) hosted a housewarming party. Sun (32) came to congratulate Chen, and Zhou (33), Wu (34), and Feng (35) also attended. Wang's (36) spouse is the older brother of Zheng's (37) spouse.
Zheng and Zheng's spouse had their car break down on the road. Among those who came to help-Zhou (33), Sun (32), Chu (38), and Wang (36)-there was one married couple who are also relatives of Zheng and Zheng's spouse.
Wang (36), Zhou (33), and Sun (32) once served in the same military platoon. Wu (34) performed a male-female vocal duet with Wang's spouse.

It is known that, apart from marital and in-law relationships, only one pair of people among the eight are related by blood.

Question: What is the sum of the products of the ages of each married couple?
Answer: \boxed{4769}
Question: There are four couples. Alex (aged 31) is celebrating a birthday. Casey (aged 32) came to offer congratulations, and Morgan (aged 33), Taylor (aged 34), and Jordan (aged 35) also attended the party. The spouse of Riley (aged 36) is the uncle of the spouse of Quinn (aged 37). A water pipe at the Quinn couple's home was leaking, and Morgan, Casey, Avery (aged 38), and Riley all came to help-among these helpers, two people are married to each other, and that couple is also related to the Quinn couple. Riley, Morgan, and Casey shared the same dormitory in college. Taylor and Riley's spouse took part in a mixed-gender piano duet together. It is known that, apart from marriages and in-law relations, exactly one pair of people (two individuals) among the eight are relatives. What is the sum of the products of the two spouses'ages in each couple?
Answer: \boxed{4769}
Question:  There are four married couples. Dong (31) has just taken his company public, and Nan (32) comes to congratulate him. Xi (33), Bei (34), and Chun (35) also attend the celebration.

Xia's (36) spouse is the older brother of Qiu's (37) spouse. Qiu and Qiu's spouse need to weed their garden, so Xi, Nan, Winter (38), and Xia come to help. Among these four helpers, there is exactly one married couple, and they are related to the Qiu couple.

Xia, Xi, and Nan were college roommates. Bei and Xia's spouse competed together in a mixed-gender three-legged race. It is known that besides spousal and in-law relationships, exactly one pair of the eight people are blood relatives.

What is the sum of the four products obtained by multiplying the two ages in each couple?
Answer: \boxed{4769}
Question: There are two types of candies: chocolate candies and fruit candies,and the ratio of chocolate candies to fruit candies is the same. The candies are distributed among three jars labeled 1, 2, and 3, . The total number of candies in Jar 1 is no less than that in Jar 2. Jar 3 contains more chocolate candies than fruit candies. Which type of candy is more in Jar 1?

A. More chocolate candies
B. More fruit candies
C. The two types are equal
D. Cannot be determined
Answer: D
Question: There are two types of coins: gold coins and silver coins, and their total numbers are equal. They are distributed among three boxes: Large, Medium, and Small.

It is given that:

The total number of coins in the Large box is not less than that in the Medium box.

In the Small box, there are more gold coins than silver coins.

Based on this, which of the following is true regarding the Large box?
A. There are more gold coins than silver coins.
B. There are more silver coins than gold coins.
C. The numbers of gold and silver coins are equal.
D. Cannot be determined.
Answer: D
Question: A library has two types of books-novels and comics-and the total number of novels is equal to that of comics. The books are placed on three shelves (A, B, and C). With Shelf A having at least as many books as Shelf B and Shelf C having fewer novels than comics, which type of book is more numerous on Shelf A?
A. More novels than comics
B. More comics than novels
C. The number of novels equals that of comics
D. Cannot be determined
Answer: D
Question: A lab has 24 identical-looking test tubes containing a colorless solution. One tube has a different concentration from the other 23. You have an uncalibrated comparator that only indicates which side has the higher total concentration, but it can hold multiple test tubes on each side at once.
In the worst-case scenario, exactly four tests are required to identify the abnormal tube. Across the first two tests, the cumulative number of test tubes placed on the left side was 16.

What is the cumulative number of test tubes placed on the left side after all four tests are completed?
Answer: \boxed{20}
Question: In a warehouse, there are 24 identical-looking packages. Due to a packing oversight, one package has a different weight than the other 23, but they are otherwise indistinguishable. You only have a balance scale (no markings) to compare weights between the left and right pans.
Conditions:
In the worst-case scenario, exactly four weighings are required to identify the anomalous package. Across the first two weighings, the cumulative number of packages placed on the left pan was 16.

Question: What is the cumulative total of packages placed on the left pan of the scale after all four weighings are completed?
Answer: \boxed{20}
Question: A factory has produced 24 identical-looking precision gears. One gear is defective: its thickness differs slightly from the others, but the difference is not visible to the naked eye.
For inspection, a technician has only an old laser comparator. Gears can be placed on the left side and the right side, and the device compares the total thickness on the two sides.

Conditions:
In the worst-case scenario, exactly 4 comparisons are needed to determine which gear is defective. Across the first two comparisons, the cumulative number of gears placed on the left side was 16.

Question: After all 4 comparisons are completed, what is the cumulative total number of gears placed on the left side?
Answer: \boxed{20}
Question: Classes 1–5 are holding a friendly basketball tournament in which each pair of classes plays each other exactly once. So far, Class 1 has played 4 games, Class 2 has played 3 games, Class 3 has played 3 games, and Class 4 has played 2 games. How many games has Class 5 played?

A. 1 or 2
B. 2 or 4
C. 2, 3, or 4
D. 1, 2, 3, or 4
Answer: B
Question: Five people-A, B, C, D, and E-are playing a card game together. The rule is that, in total, every pair of players will be partners exactly once. So far, A has been partnered 4 times, while B, C, and D have each been partnered 2 times. How many times has E been partnered so far?

A. 1 or 2
B. 2 or 4
C. 2, 3, or 4
D. 1, 2, 3, or 4
Answer: B
Question: Five departments-East Department, South Department, West Department, North Department, and Central Department-are conducting a business evaluation. Each pair of departments reviews each other exactly once.
So far, East Dept. has completed 4 reviews, South Dept. has completed 3 reviews, West Dept. has completed 3 reviews, and North Dept. has completed at most 2 reviews.
How many reviews has Central Dept. completed exactly so far?
A. 1 or 2
B. 2 or 4
C. 2, 3, or 4
D. 1, 2, 3, or 4
Answer: C
Question: A doctor and a nurse are on duty on day a and day b of the same week. The absolute difference in days between the day two days before the doctor's duty day and the day two days after the nurse's duty day is as large as possible, and both of those days fall within the same week. What is the value of a^b?
Answer: \boxed{243}
Question: Dad: "The day 4 days before the day I go to the supermarket to shop and the day 2 days after the day Mom goes to the supermarket to shop have the maximum difference in days, and these two days are also in the same week. Dad and Mom go to the supermarket to shop on day a and day b of that week, respectively. What is the value of a^b?"
Answer: \boxed{3125}
Question: Teacher: The absolute difference in days between the day 3 days before I collect the homework and the day 2 days after a student submits the homework is as large as possible, and both of those days fall within the same week. If I collect the homework on day a of that week and the student submits it on day b, what is the value of a^b?
Answer: \boxed{1024}
Question: A plastic cylindrical tube that can be cut and spliced back together is open at both ends. It contains 2 circular chips and 2 square chips. Each chip is sized to fit snugly inside the tube, matching its inner diameter. The initial arrangement is "circle-square-circle-square." How many distinct schemes of cutting and reassembling the tube are there to change the arrangement to "circle-square-square-circle" without removing any chips from the tube?
Answer: \boxed{5}
Question: There is a long, transparent book sleeve that is open at both ends and has no special design or pattern. Inside the sleeve, four books are packed side by side, all the same size and fitting the sleeve exactly: two math textbooks (S) and two Chinese-language textbooks (Y). The initial arrangement is "SYSY." The sleeve itself can be cut and then glued back together. Without pulling any book out of the sleeve, how many distinct cutting-and-rejoining methods can change the arrangement to "SYYS"?
Answer: \boxed{5}
Question: A hollow rod of uniform length, open at both ends, contains 2 black checkers and 2 white checkers. The diameter of each checker matches the rod's inner diameter. The rod  can be cut and rejoined.Starting with the arrangement "Black-White-Black-White," determine the number of distinct ways to cut so that the arrangement becomes "Black-White-White-Black," without removing any checkers.
Answer: \boxed{5}
Question: Three magic apprentices-Wind, Fire, and Thunder-each received a bag of magic gems. The number of gems in each bag is between 1 and 10 inclusive, and the three bags together contain a total of 16 gems. Each apprentice knows only how many gems are in their own bag.
Wind looked into the bag and said: "The numbers of gems in Fire's bag and Thunder's bag must be different."
After hearing this, Fire thought for a moment and said: "Then the number of gems in my bag must be different from the number in Wind's bag."
Thunder smiled and said: "Then I know exactly how many gems each of you has."
How many gems are in Fire's bag?
Answer: \boxed{9}
Question: Three explorers-Alpha, Beta and Gamma-discovered energy cubes in a relic. The number of cubes each of them got was between 1 and 10, and the total number of cubes was 18. Each explorer only knew the number of cubes in his own hand.
Alpha asserted: "The number of cubes that Beta and Gamma got is definitely not equal."
Beta replied: "Then the number of cubes I got is absolutely different from yours, Alpha." 
After hearing this, Gamma said: "In that case, I have already figured out the number of cubes each of you two has."
How many energy cubes did Beta get?
Answer: \boxed{9}
Question: Agents X, Y, and Z each intercepted a number from a numeric code fragment. Each number is an integer from 1 to 10 inclusive, and the sum of the three numbers is 12.

After some analysis, X said: "The numbers held by Y and Z must be different."

Y did a quick calculation and said: "Then the number I hold must be different from the one X holds."

After hearing both statements, Z said: "That's enough-I have already deduced your numbers."

What is the number held by Y?
Answer: \boxed{7}
Question: Zoe was solving a problem related to World Cup data. She tried using "goals scored by national teams" and "ranking by number of World Cup titles won," but she couldn't solve the problem with either approach. After thinking hard, she finally worked it out and said that both approaches have their merits.

Please determine the number represented by the question mark:
① Argentina − Brazil = 2
② Italy + Argentina = 8
③ France × Spain = 24
Spain − Brazil = ?
Answer: \boxed{5}
Question: Alex was working on a problem about the Solar System. He tried using "planetary mass values" and "the ranking of planets by distance from the Sun" but couldn't solve it with either approach. After thinking it over, he felt that both approaches had merit, and he eventually got the correct answer.

Please find the number represented by the question mark:
① Mercury + Venus = 4
② Jupiter − Neptune = 2
③ Earth × Mars = 8
Saturn ÷ Venus = ?
Answer: \boxed{\frac{7}{3}}
Question: Ryan came across an interesting problem. He tried solving it by ordering the elements by atomic mass and by alphabetical order, but both attempts failed. He thought that perhaps these two failed approaches might still have something useful in them.
Please find the number represented by the question mark:
① Neon + Krypton = 6
② Radon - Argon = 3
③ Helium × Xenon = 5
Argon × Neon = ?
Answer: \boxed{6}
Question: Game Rules:
A 5-digit number with no repeated digits is used as the answer. After submitting a guess, you receive two values, A and B:

A represents the number of digits in your guess that are correct in both value and position.
B represents the number of digits in your guess that are correct in value but incorrect in position.

Example: If the answer is 12345 and the guess is 23546, the result is 1A3B.

Puzzle:
Round 1: 12345 → 1A2B
Round 2: 67890 → 0A2B
Round 3: 51937 → 1A4B
Round 4: 73951 → 3A2B
Round 5: 91357 → ?

What should the output be at the question mark?
A. 0A5B
B. 1A4B
C. 5A0B
D. 2A3B
Answer: A
Question: Game Rules:
The answer is a 5-digit number with no repeated digits.
After each guess, two values, A and B, will be returned.
A is the number of digits in your guess that are correct in both value and position.
B is the number of digits in your guess that are correct in value but incorrect in position.

Example: Answer: 12345; Guess: 23546; Result: 1A3B.

Puzzle:
Round 1: 12345 → 0A0B
Round 2: 67890 → 0A5B
Round 3: 78906 → 0A5B
Round 4: 98076 → 3A2B
Round 5: 09768 → ?

What should replace the question mark?
A. 1A4B
B. 0A5B
C. 2A3B
D. 0A4B
Answer: A
Question: Game Rules:
The answer is a 5-digit number with no repeated digits.
After each guess, you receive two values, A and B.
A is the number of digits in your guess that are correct in both value and position.
B is the number of digits in your guess that are correct in value but in the wrong position.
Example: If the answer is 12345 and the guess is 23546, the result is 1A3B.

Puzzle:
Round 1: 12345 - 0A2B
Round 2: 67890 - 1A2B
Round 3: 36082 - 3A2B
Round 4: 20863 - 1A4B
Round 5: 80623 - ?

What should replace "?"
A. 0A5B
B. 1A4B
C. 2A3B
D. 5A0B
Answer: A
Question: Alice, Bob, and a host play a number-guessing game. The host writes one number on each of two slips of paper and places them on Alice's and Bob's foreheads. Alice and Bob know that both numbers are positive integers and that the absolute difference between the two numbers is 3. They cannot see the number on the other person's forehead.

The host then announces that one of the two numbers is 10 (without revealing which person has it). The host proceeds to ask them in turn what number is on their own forehead. In each round, both players state their guesses aloud. The game ends as soon as, in the same round, both players state their own numbers correctly.

What is the minimum number of rounds needed to guarantee that the game will end?
Answer: \boxed{4}
Question: Players A, B, and a referee are playing a number-guessing game. The referee writes an integer on two separate slips of paper. It is known that both numbers are positive integers and their difference is exactly 10. The referee places a slip on the forehead of each player so that each can see the other's number but cannot see their own.

The referee announces that one of the numbers is 20. Then, the players take turns publicly guessing their own numbers. The game ends once both players correctly state their numbers in the same round. What is the minimum number of rounds required to guarantee the game ends?
Answer: \boxed{4}
Question: An older brother, his younger brother, and their mother are playing a number-guessing game. The mother writes one number on each of two slips of paper. The two brothers know that both numbers are positive integers and that the absolute difference between them is 4. The mother sticks the slips on the foreheads of the older brother and the younger brother. Neither brother can see the number on the other brother's forehead.

The mother then announces that one of the two numbers is 5 (without saying which brother has it). She asks them in turn what number is on their own forehead. They publicly state their guesses round by round. The game ends as soon as, in the same round, both brothers state their own numbers correctly. What is the minimum number of rounds after which the game is guaranteed to end?
Answer: \boxed{4}
Question: Twelve iron rings are welded into a single long chain, with a weld joint connecting every two adjacent rings. You are allowed to break exactly 2 weld joints. The requirement is to divide the chain into 3 shorter segments such that you can take away 2 rings each day (accumulating 2 more rings daily). According to this rule, if the number of rings in the three segments, ordered from largest to smallest, are a, b, and c, what is the value of a^b + c?
Answer: \boxed{1298}
Question: Forty-five iron rings are welded into a single long chain. Each pair of adjacent rings is joined by a weld point, and you are allowed to break only four weld points in total.

You must remove exactly three rings per day. Under this rule, the long chain is split into five shorter chains. Let the numbers of rings in these five chains, in ascending order, be a, b, c, d, and e. Find the value of a*b + c*d + e.
Answer: \boxed{141}
Question: Forty-two iron rings are welded into one long chain, with a weld at each connection between adjacent rings. You may break only five welds in total. You must take away exactly two rings each day. Following this rule, divide the long chain into six shorter chains. Let the numbers of rings in these six chains, in increasing order, be a, b, c, d, e, and f. What is the value of a*b + c*d + e*f?
Answer: \boxed{176}
Question: A strange village has a total of 200 people, consisting of adults and children. Children always tell the truth, while adults always lie.

One day, a stranger arrives and asks the villagers, "How many adults are there in your village?" The first 20 villagers respond in order. The nth villager (1 <= n <= 20) answers: (n mod 20) + 170, where "mod" means the remainder upon division by 20 (so the remainder ranges from 0 to 19).

The stranger then asks how many children there are. The 21st villager says, "The number of children is a two-digit number."

What is the sum of all possible values for the number of adults in the village?
Answer: \boxed{19690}
Question: In a strange village of 100 inhabitants, consisting of adults and children, children always tell the truth while adults always lie. One day, a stranger arrived and asked, "How many adults are there in your village?" The first 10 villagers answered sequentially with the value (n mod 10) + 80, where n represents the order of the villager being asked (1 to 10). The stranger then asked the 11th villager, who replied, "The number of adults is an odd number." What is the sum of all possible numbers of adults in this village?
Answer: \boxed{4895}
Question: In a peculiar village of 150 people, everyone is either an adult or a child. Children always tell the truth, while adults always lie.

One day, a stranger comes to the village and asks, "How many adults are there in your village?" For n = 1, 2, ..., 12, the nth villager answers: (n mod 12) + 130, where n is the order in which the villager is asked.

The stranger then asks, "How many children are there?" The 13th villager replies, "The number of children is a prime number."

Based on this information, find the sum of all possible values for the number of adults in the village.
Answer: \boxed{11097}
Question: After confirming that all current members of R&D Team A were present, the team lead asked everyone to go to the conference room for an internal team meeting. During the meeting, he said, "There are 18 people in the conference room, but two new members will join the team tomorrow. How many members will Team A have tomorrow?"
Answer: \boxed{19}
Question: Alex runs his own after-school English tutoring class. After taking attendance and confirming that all students were present, he announced: "There are currently 23 people in the classroom, and 3 new students will join tomorrow."

How many students will be in the tutoring class tomorrow?
Answer: \boxed{25}
Question: A hospital ward room is housing several patients who have no caregivers. After finishing his rounds, the on-duty doctor confirms that all the patients are present and doing okay, but they will need to stay in the hospital for a few more days. Seeing that there was no one else in the room besides the patients and the medical staff,the doctor says, "There are five people in this room right now, but two more patients will be transferred into this room tomorrow." How many patients will be in this ward room tomorrow?
Answer: \boxed{6}
Question: Twenty players sit in a circle in clockwise order, with seats labeled 1–20. Starting with the player in seat 1, the current baton holder stands up, walks clockwise around the outside of the circle, and goes to the seat such that exactly x players are seated between the holder's current seat and that seat along the clockwise direction. The holder hands the baton to the player in that seat and then sits down in that seat. The receiver then stands up and repeats the same procedure.

At the start of each move, x is set equal to the total number of players who have touched the baton up to that moment (including the current holder). The game ends exactly when the baton's movement path around the circle has completed two full revolutions.

At that moment, how many seats have been occupied by at most one person in total?
Answer: \boxed{13}
Question: A party game has 40 people seated in a circle in clockwise order, with seats labeled 1–40. The person in seat 1 starts with a baton. On each move, the current baton holder stands up from their current seat, walks clockwise along the outside of the circle to the seat that is x players ahead of that seat (i.e., when counting clockwise, there are exactly x seated players between the two seats), hands the baton to the player currently sitting there, and then sits down in that seat. The receiver then stands up and repeats the same procedure.

At each move, x is defined as the number of distinct people who have touched the baton at least once so far (including the current holder). The game stops exactly when the baton's cumulative clockwise travel along the circle totals two full laps.

At that moment, how many seats have been sat in by no more than one person in total?
Answer: \boxed{31}
Question: A party game has 42 players seated in a clockwise circle, with seats labeled 1–42. Starting with the player in Seat 1, the current baton holder stands up and walks clockwise around the outside of the circle to a seat such that exactly x players are seated between the holder's current seat and that seat along the clockwise direction. The holder hands the baton to the player in that seat and then sits down in that seat. The receiver then stands up and repeats the same procedure, continuing to pass the baton and swap seats.

At the start of each move, x is set equal to the number of players who have touched the baton so far (including the current holder). When the cumulative clockwise travel of the baton totals exactly three full laps around the circle, how many seats have been occupied by at most one person?
Answer: \boxed{30}
Question: You have been given the following ten statements and are required to determine a specific number:

1. At least one of Statements 8 and 9 is true.

2. This is the first true statement or the first false statement.

3. The number is 7 times the difference between the index of the last true statement and the index of the first true statement.

4. The number is approximately twice the sum of the indices of all true statements.

5. This is not the last true statement.

6. The sum of the indices of all true statements divides 10 times the index of Statement 6.

7. There are three consecutive true statements.

8. The units digit of the number is 4.

9. This is not the last false statement.

10. There are no three consecutive false statements.

What is the most likely value of this specific number?
A. 40
B. 48
C. 56
D. 64
E. 72
Answer: C
Question: You are given the following ten statements and asked to determine a specific number.

1. At least one of Statements 8 and 9 is true.

2. This is either the first true statement or the first false statement.

3. The number is twice the sum of the statement numbers of the first true statement and the last true statement.

4. The sum of the statement numbers of all true statements is greater than the number.

5. This is not the last true statement.

6. The number of this statement is a factor of the number.

7. There are three consecutive true statements.

8. The number is odd.

9. This is not the last false statement.

10. There are no three consecutive false statements.

What is the most likely value of this specific number?

A. 12
B. 24
C. 28
D. 30
E. 36
Answer: B
Question: You are given the following ten statements and required to determine a specific number. 
1. At least one of Statement 8 and Statement 9 is true. 
2. This is either the first true statement, or the first false statement. 
3. The number is 9 times the difference between the number of the last true statement and the number of the first true statement. 
4. The number is 2 times the sum of the numbers of all true statements, plus 10. 
5. This is not the last true statement. 
6. The number of every true statement is a divisor of 60. 
7. There exist three consecutive true statements. 
8. The number is a multiple of 10. 
9. This is not the last false statement. 
10. There are no three consecutive false statements.  
What is the most probable value of this specific number? 
A. 54
B. 63
C. 72
D. 81
E. 90
Answer: C
Question: There are 11 children in a class: L, O, P, Q, R, S, T, U, V, W, and X. The list of best friends for each child is as follows:
L: (X, T) 
O: (X, U, Q) 
P: (X, V, W) 
Q: (O, T, W) 
R: (X, U) 
S: (T, V) 
T: (S, Q, L) 
U: (R, O) 
V: (P, S) 
W: (P, V, X, Q) 
X: (L, R, O, P, W)
One day, all children except "L" are standing outside the classroom. The teacher instructs "L" to call one of their best friends into the room, and then the children who enter the room call their best friends in turn. Eventually, no children are left outside. If the 5th child to enter is "P" and the last child to enter is "X", who is the third-to-last child to enter the room?
Answer: U
Question: There are 11 children in a class: P, X, Q, R, Y, U, V, W, Z, T, and S. Each child has some best friends, as listed below:

-P: (S, V)
-X: (S, W, R)
-Q: (S, Z, T)
-R: (X, V, T)
-Y: (S, W)
-U: (V, Z)
-V: (U, R, P)
-W: (Y, X)
-Z: (Q, U)
-T: (Q, Z, S, R)
-S: (P, Y, X, Q, T)

 One day, everyone except "P" is outside the classroom. The teacher instructs "P" to call one of their best friends into the room, and then the child who enters calls one of their best friends, and so on sequentially. Eventually, no children are left outside. If the 5th child to enter is "Q" and the last child to be called in is "S", who is the third-to-last child to be called into the classroom?
Answer: W
Question: A class has 11 children named Z, Y, X, W, V, U, T, S, R, Q, and P.
Each child has a set of best friends, listed as follows:
Z: (P, T)
Y: (P, S, W)
X: (P, R, Q)
W: (Y, T, Q)
V: (P, S)
U: (T, R)
T: (U, W, Z)
S: (V, Y)
R: (X, U)
Q: (X, R, P, W)
P: (Z, V, Y, X, Q)
One day, only Z was in the classroom, while all the other children were outside. The teacher asked Z to start calling his best friends into the classroom, and each newly arrived child would then call their own best friends, continuing this process one by one. It is known that the fifth child to enter the classroom was X, and the last child to enter was P.
Question: Which child was the third-to-last to be called into the classroom?
Answer: S
Question: [Non-integer Sequence]
Determine the missing number according to the pattern.

★★★★★ = 6
☆★★★★ = 8
☆★☆★★ = 14
☆★☆★☆ = 24
★★★☆☆ = 26
★☆★★☆ = ?

After looking at it, Tom said: "The hollow stars may not correspond to a single fixed value."
Lily said: "It may be related to the row number."
Ben said: "The solid stars must correspond to a fixed value."

Which option is the final answer?
A. 23
B. 24
C. 17
D. 29
Answer: A
Question: [Symbol Pattern]
Calculate the missing number according to the rule.
XXXXX = 21
YXXXX = 23
YXYXX = 23
YXYXY = 21
XXXYY = 20
XYXXY = ?
David looked at it and said: Y might not represent a number.
Lucy looked at it and said: It might be related to the row number.
Tom looked at it and said: X must be a fixed value.
Which of the following options is the correct result?
A. 20
B. 21
C. 22
D. 23
Answer: D
Question: [Non-integer Sequence]
Determine the missing number according to the pattern.

▲▲▲▲▲ = 16
△▲▲▲▲ = 18
△▲△▲▲ = 28
△▲△▲△ = 42
▲▲▲△△ = 40
▲△▲▲△ = ?

After looking at it, Alex said: "The hollow triangles may not correspond to a single fixed value."
Lily said: "It may be related to the row number."
Ben said: "The solid triangles must correspond to a fixed value."

Which option is correct?
A. 30
B. 36
C. 39
D. 45
Answer: B
Question: Jack is organizing books on a bookshelf.
Initial arrangement (positions 1–6):
A B A B A B
Target arrangement (positions 7–12):
B B B A A A
Rules:
Removing two adjacent books (with no empty space between them) and inserting them-keeping their original order and only moving them into empty slots-into another separate pair of consecutive empty slots counts as one move.
What is the minimum number of moves required?
Answer: \boxed{4}
Question: A robot is sorting parts.

Start positions (slots 1–6):
⚙️🔩⚙️🔩⚙️🔩

Target positions (slots 7–12):
🔩🔩🔩⚙️⚙️⚙️

Rule:
In one operation, the robotic arm picks up two adjacent parts and moves them, keeping their relative order unchanged, into two consecutive empty slots elsewhere. (There is no empty slot between any two adjacent parts, and parts can be moved only into empty slots.)

What is the minimum number of operations required?
Answer: \boxed{4}
Question: Kids are playing a checkers game.
Initial arrangement (positions 1–6):
🔴 🔵 🔴 🔵 🔴 🔵
Target arrangement (positions 7–12):
🔵 🔵 🔵 🔴 🔴 🔴
Rule:
In one move, you pick up two adjacent pieces (with no empty space between them) and jump them-keeping their original order and only landing in empty spaces-into another pair of consecutive empty spaces.
What is the minimum number of moves required?
Answer: \boxed{4}
Question: You are the head chef at a high-end restaurant. One evening, a pipe suddenly bursts in the kitchen, and the floor is instantly flooded with water. After the chaos subsides, you discover that your secret sauce recipe is missing. Everyone was busy saving ingredients and equipment, so the scene was extremely chaotic. You decide to question the few chefs closest to your office.

Chef A says: "When the pipe burst, I was chopping vegetables. Water splashed all over me-look, my pant legs are still wet."
…You notice that water is indeed dripping from A's pant legs.

Chef B says: "I'm in charge of desserts. At that moment, I was piping hair-thin icing lines to decorate a cake-it requires extreme precision."
…You look at the half-finished cake: the icing lines are hair-thin, and the pattern is flawless.

Chef C says: "I got scared-I'm terrified of water. I immediately climbed onto the highest shelf and didn't come down until the water stopped."
…You see that C's clothes are dry, but there are water marks on the soles of C's shoes.

Chef D says: "I was watching a recipe video on my phone. When the water came, I quickly held the phone up high-luckily it didn't get wet."
…You see that D's phone screen still shows the video player interface. 

Who is most likely lying?
Answer: B
Question: You are a ranger of a forest park. One noon, a sudden torrential downpour struck, accompanied by lightning and thunder. After the rain stopped, you received a report that a rare millennium-old ancient tree in the park had been carved with characters. The sound of the heavy rain had drowned out all other sounds, so you had to question several tourists who had taken shelter from the rain in the nearby pavilion at that time. 
Tourist A said: "The rain was so heavy that I got soaked to the skin. I was wringing the water out of my clothes just now." … You noticed that A's clothes were indeed still dripping. 
Tourist B said: "I am an entomologist. I took advantage of the rain to observe the earthworms and snails that came out after the rain, and made detailed sketch notes in my notebook." … You checked B's sketchbook; the paper was completely dry, with clear, highly detailed lines on the drawings.
Tourist C said: "The thunder was so loud. I was so scared that I squatted in the corner with my ears covered. My ears are still buzzing now." … C spoke in a much louder voice than usual. 
Tourist D said: "I was playing a mobile game in the pavilion. The signal was poor, but fortunately, it was an offline game." … You saw that D's phone screen displayed a game-over screen. 
Who might have told a lie?
Answer: B
Question: You are the captain of a submarine. During a deep-dive mission, a pipe unexpectedly ruptures, and a piercing alarm blares in the cabin for several minutes. After the malfunction is fixed, you discover that a classified nautical chart marked with secret sea lanes has gone missing from the chart room. During the alarm, everyone's attention was on dealing with the malfunction, so you can only question the crew members who were near the chart room at the time.
Crew member A says: "The alarm was so shrill I thought my eardrums would rupture. I strained every muscle to close the emergency valve." ...You notice A's hands are still trembling from the exertion.
Crew member B says: "I'm a musician and very sensitive to sound. I tried to identify the pitch and frequency of the alarm and jotted it down on sheet music." ...You look at B's sheet music: the notes are clear and steady, with no sign of shaking.
Crew member C says: "I was asleep and was startled awake by the alarm. My heart is still pounding." ...You see that C's face is a little pale.
Crew member D says: "I was running a route simulation on the computer. As soon as the alarm went off, I immediately started checking the instruments in my section and didn't notice anything else." ...D's computer screen still shows various instrument readings.
Who is most likely lying?
Answer: B
Question: A geological exploration team has set up camp deep in the Lop Nur region. Team member B reports to the team leader that he found team member A lying on the ground about two kilometers from the camp, near an ancient riverbed site. A had no signs of life and seemed to have died from heatstroke and dehydration. B claims that after discovering A, he panicked and immediately sprinted back to camp for help (the outbound and return routes did not exactly overlap).
After inspecting the scene, the team leader immediately orders the others to restrain B, concluding that B killed A and disposed of the body.
What was the team leader's main reason for reaching this conclusion?
Answer: Different footprint depths
Question: A new concrete road has just been paved in the village. The surface has set but has not fully dried, so stepping on it will leave clear marks.
Villager Tom, out of breath, ran home and told his wife that he had found Jack's body by the well at the village entrance, apparently from a sudden heart attack. Tom said he had been pushing a wheelbarrow to the well to fetch water, but after seeing the body, he was so scared that he didn't fetch any water and rushed back while pushing the empty wheelbarrow to call for help.
When the police arrived and examined the scene, they immediately concluded that Tom was lying and that he was the real killer.
What was the main reason the police made this judgment?
Answer: Varying footprint depths
Question: A ski instructor, Dean, took his student, Will, to ski off-piste. After Dean returned, he called the police, looking grief-stricken, saying that Will had fallen mid-slope and was injured and unconscious.
Dean explained that he told Will to wait there and planned to carry him on his back down the mountain for medical help. However, after attempting to carry him for some distance, Dean realized he was too exhausted to continue. He had no choice but to put Will down and ski down the mountain first to fetch the rescue team.
The police reached the site by snowmobile and found that Will was already dead. After examining the snow at the scene, the police arrested Dean, accusing him of murdering Will and attempting to stage a rescue.
What was the main basis for the police's conclusion?
Answer: The depths of the footprints were different
Question: A football team has hired five highly professional coaches responsible for the following positions respectively: striker, goalkeeper, midfielder, defender, and captain. The core skills they teach are: shooting technique, saving ability, passing vision, defensive tactics, and leadership.  

They are providing one-on-one training for five players: A, B, C, D, and E. Each player must switch coaches after completing a training session. The five players have similar talent, so each training session takes the same amount of time. After several rounds, all five players have been trained by all five coaches.  

The clues are:  
- A's final skill is B's second skill.  
- C's final skill is B's fourth skill.  
- C's second skill is A's first skill.  
- D's final skill is C's third skill.  
- B's fourth skill is E's third skill.  
- D's third skill is C's first skill.  

It is known that the final skills mastered by A, B, C, D, and E are, in order: shooting technique, saving ability, passing vision, defensive tactics, and leadership.

Question: For the skills shooting technique, saving ability, passing vision, defensive tactics, and leadership in that order, who mastered each as their fourth skill?  

Answer in the format: "A:xxx,B:xxx,C:xxx,D:xxx,E:xxx"
Answer: A: defensive tactics, B: passing vision, C: saving ability, D: leadership command, E: shooting technique
Question: In the history of the International Dessert Championship, five world-renowned legendary pastry masters were celebrated for five original dessert-making techniques: Rich Chocolate Cake, Fresh Strawberry Mousse, Refreshing Lemon Tart, Flavorful Matcha Ice Cream, and Smooth Blueberry Cheesecake. Years later, these five techniques were passed down, one to each of contestants A, B, C, D, and E.
To learn from one another, the five contestants agreed on the following: each would first master the technique they inherited, and then they would begin mutual exchanges of techniques simultaneously. In each round of exchanges, each contestant would learn exactly one new technique from another contestant. Since all five techniques are equally difficult, all contestants have equal natural talent, and everyone learns at the same pace, after several rounds, all five contestants would eventually master all five techniques.
It is known that:
The last technique A mastered was the second technique B mastered.
The last technique C mastered was the fourth technique B mastered.
The second technique C mastered was the first technique A mastered.
The last technique D mastered was the third technique C mastered.
The fourth technique B mastered was the third technique E mastered.
The third technique D mastered was the first technique C mastered.
Suppose the technique each contestant mastered last was:
A - Rich Chocolate Cake
B - Fresh Strawberry Mousse
C - Refreshing Lemon Tart
D - Flavorful Matcha Ice Cream
E - Smooth Blueberry Cheesecake
What was the fourth technique each contestant mastered?
(Answer in the format: "A:xxx,B:xxx,C:xxx,D:xxx,E:xxx")
Answer: A: Flavorful Matcha Ice Cream, B: Refreshing Lemon Tart, C: Fresh Strawberry Mousse, D: Smooth Blueberry Cheesecake, E: Rich Chocolate Cake
Question: In an international top-tier racing training camp, there are five senior coaches, each specializing in one racing technique: emergency braking, maximum acceleration, precision cornering, drifting, and race strategy. They need to pass these five skills on to drivers A, B, C, D, and E.
They decide that each coach will first train one driver. Once the driver has mastered the skill, the coaches and drivers will begin swapping coach-driver pairings. Since the five skills are equally difficult and the drivers have similar aptitude and learning speed, after several swaps, all five drivers eventually master all five skills.
It is known that:
1. The last skill mastered by A is the second skill mastered by B.
2. The last skill mastered by C is the fourth skill mastered by B.
3. The second skill mastered by C is the first skill mastered by A.
4. The last skill mastered by D is the third skill mastered by C.
5. The fourth skill mastered by B is the third skill mastered by E.
6. The third skill mastered by D is the first skill mastered by C.
If the last skills mastered by A, B, C, D, and E are emergency braking, maximum acceleration, precision cornering, drifting, and race strategy respectively, what are the fourth skills mastered by A, B, C, D, and E? (Please answer in the format: "A:xxx,B:xxx,C:xxx,D:xxx,E:xxx")
Answer: A:drifting skills,B:precise cornering,C:extreme acceleration,D:track strategy,E:emergency braking
Question: A new notice letter from the Phantom Thief Joker appeared on the museum director's desk.
To the Museum Director:
On the eve of Halloween, when ghosts emerge,
Caesar brought me the key, and fence gathered intelligence for me.
INOU,QFCM.
                                       --Phantom Thief Joker
The director immediately reported it to the police, who requested the assistance of a cryptography expert. Can you determine at what time and which item Joker is targeting?
A. October 30, 12:00, Golden Scepter
B. October 31, 12:00, Golden Mask
C. October 31, 12:00, Tutankhamun Mask
D. November 1, 12:00, Golden Mask
Answer: B
Question: The Crow's message has sent shockwaves through the archaeological world.
To the Archaeological Association:
On the Day of the Dead, at the border of life and death,
Caesar brought me the key, and fence gathered intelligence for me.
EAVNMN,TUCUWN.
                                       --The Crow
The association called in decryption expert Dr. Zhang, who soon cracked it. Can you determine the time and target of The Crow's plan?
A. November 1, midnight, Crystal Skull
B. November 2, midnight, Maya Skull
C. November 1, noon, Crystal Skull
D. October 31, midnight, Crystal Skull
Answer: A
Question: A letter signed "Siren" appeared in the Titanic exhibition curator's inbox.
To the Curator:
On the anniversary of the great ship's sinking, when the hour hand points straight down,
A Roman emperor gave me his scepter, and intersecting wooden planks guard my secret.
VGGTQVGEC,JJCVHJQGP.
                                                 --Siren
The curator immediately activated the maximum security protocol and called in decryption experts to analyze it. Can you determine the time and target gem of Siren's plan?
A. April 15, 6:30 AM, Star of Africa
B. April 14, 6:30 PM, Heart of the Ocean
C. April 15, 6:30 PM, Heart of the Ocean
D. April 15, 6:30 AM, Hope Diamond
Answer: C
Question: A project team has 72 tasks to be completed by five members. They each claimed tasks exactly once; after this single round, all 72 tasks were allocated, but the claiming order is unknown.

Member A says: "At my turn, I claimed one-third of the remaining tasks."
Member B says: "At my turn, I also claimed one-third of the remaining tasks."
Member C says: "At my turn, I took all the remaining tasks."
Member D says: "At my turn, I also claimed one-third of the remaining tasks."
Member E says: "Each of us claimed an integer number of tasks, and no two of us claimed the same number."

Among the possible numbers of tasks that Member E could have claimed, how many are divisible by 9?
Answer: \boxed{1}
Question: Four children-Danny, Sophie, Nina, and Ben-take turns taking strawberries from a basket containing 39 strawberries. Each child takes exactly one turn, and together they take all the strawberries, but the order of turns is unknown.

Danny says: "I took half of the strawberries that were remaining at the time of my turn."
Sophie says: "I took two-thirds of the strawberries that were remaining at the time of my turn."
Nina says: "I took all the strawberries that were remaining at the time of my turn."
Ben says: "Each of us took an integer number of strawberries, and no two of us took the same number."

Question: Among all possible numbers of strawberries Ben could have taken, how many are less than 10?
Answer: \boxed{2}
Question: A charity book drive collected 56 books to be distributed among five children. They took turns choosing books. Each child took exactly one turn; after this single round, all 56 books were taken, but the picking order is unknown.

Alex said: "When it was my turn, I took half of the books remaining."
Brooke said: "When it was my turn, I took two-thirds of the books remaining."
Casey said: "When it was my turn, I took all the books remaining."
Daisy said: "When it was my turn, I took half of the books remaining."
Evan said: "Each of us took an integer number of books, and no two of us took the same number."

Among the possible numbers of books that Evan could have taken, how many are divisible by 8?
Answer: \boxed{3}
Question: Leo accidentally wanders into a mysterious maze represented by the letter grid below. He starts on the letter T. On each move, he may move one step to any adjacent cell, and each cell may be visited only once. Additionally, exactly once during his traversal, he may make a jump from his current cell to any unvisited cell. The sequence of letters he visits forms the password.

Grid:
T H E P A
R O W S S
D W I S F
A L E V I
K E Y V R

Which of the following is most likely the password?
A. SOLAR
B. KEY
C. FIVE
D. SOFA
E. SAFE
Answer: C