Ckriman/General365_Public huggingface dataset:
Question: The office has nine connected rooms arranged in a 3×3 grid. Eight rooms contain office items, and one room is empty (row 3, column 2). The initial layout (row by row) is:

Row 1: Desk, Computer, Filing Cabinet
Row 2: Cot, Wardrobe, Tea Cabinet
Row 3: Projector, Empty Room, Sofa

Because the manager likes reading documents, he wants the desk to be adjacent to the filing cabinet, while the filing cabinet must stay in its original position. The desired configuration is:
The desk is moved to where the tea cabinet was originally.
The positions of the filing cabinet, the empty room, the projector, and the cot remain unchanged.
The remaining items (the computer, wardrobe, sofa, and tea cabinet) can be placed anywhere.

Only one item may be in a room at a time, and in one move, you may move exactly one item into an orthogonally adjacent empty room (no diagonal moves).

What is the minimum number of moves to achieve the desired configuration?
Answer: \boxed{12}
Question: The warehouse has nine interconnected rooms arranged in a 3×3 grid. Eight rooms contain items, and one room is empty (row 3, column 2). The initial layout (row by row) is:

Row 1: Desk, Packaging Machine, Storage Shelf
Row 2: Cot, Locker, Tool Cabinet
Row 3: Surveillance Camera, Empty Room, Sofa

The warehouse manager wants to move the desk to a position adjacent to the storage shelf, while the storage shelf must remain in its original position.

The desired configuration is:
The desk is moved to the position originally occupied by the tool cabinet.
The positions of the storage shelf, the empty room, the surveillance camera, and the cot remain unchanged.
The remaining items (packaging machine, locker, sofa, and the tool cabinet) may be placed in any available room.

Only one item may be in a room at a time, and in one move, exactly one item may be moved into an orthogonally adjacent empty room (no diagonal moves).

What is the minimum number of moves required to achieve the desired configuration?
Answer: \boxed{12}
Question: From the four given options, choose the most appropriate one to fill in the question mark so that the sequence follows a consistent pattern:
T S A N W ?
A. K
B. Z
C. E
D. F
Answer: B
Question: Choose the most appropriate option from the four given choices to replace the question mark and complete the pattern:
M S A Z T ?
A. N 
B. V 
C. C 
D. B
Answer: A
Question: Choose the most appropriate option from the four given choices to replace the question mark and complete the pattern:
S H Z M N ? 
A. Y 
B. G 
C. P 
D. S
Answer: A
Question: A bank's vault security system set off an alarm overnight, but no theft was found. The bank president suspected an attempted break-in and questioned four employees who knew the password: Manager A, Teller B, Technician C, and Loan Officer D.

Manager A remained silent.
Teller B said: "Technician C tried to break in, and it was not a false alarm."
Technician C said: "It was a system false alarm, and it was not Manager A who did it."
Loan Officer D said: "It wasn't me; it was Teller B who did it."

It is known that in each of B, C, and D's statements, exactly one part is true and the other is false.

How many of these employees cannot be conclusively identified as the intruder?
Answer: \boxed{4}
Question: A masterpiece in a gallery was found defaced with graffiti after the gallery closed. The owner questioned the four staff members on duty that night: Security Guard A, Security Guard B, Cleaner C, and Intern D.

Guard A said nothing while reviewing the surveillance footage. The other three each made a statement consisting of two separate claims. For each of these three people, exactly one claim is true and the other is false:
Guard B: "Cleaner C did it. This is not a pre-existing stain."
Cleaner C: "This is a pre-existing stain. Guard A did not do it."
Intern D: "I did not do it. Guard B did it."

Based on these statements, how many of the four people cannot be identified as the vandal?
Answer: \boxed{4}
Question: A software company's core source code repository was deleted. Management questioned four programmers who had the necessary access: A, B, C, and D.
A remained silent and said nothing. The other three each made a statement consisting of two separate claims. For each of these three people, exactly one claim is true and the other is false:
B: "C did it. This was not an accident caused by a system failure."
C: "This was a system failure. It definitely wasn't A."
D: "I didn't do it. B did."

Based on these statements, how many of the four people cannot be determined to be the one who deleted the code?
Answer: \boxed{4}
Question: A research lab has commissioned a square LED matrix display with 17 rows and 17 columns, totaling 289 pixel positions. There are 145 yellow LED bulbs and 144 blue LED bulbs to be installed, one in each position.
The requirement is that once the installation is complete, exactly one row is composed entirely of yellow LED bulbs. The total number of installation configurations satisfying this condition is N.
Select all correct statements from the options below:

A. N is a multiple of 17
B. N is a multiple of 277
C. N is a multiple of 281
D. N is a multiple of 283
Answer: A
Question: The seats in a large cinema hall are arranged in a 13 by 13 square matrix, totaling 169 seats. For this screening, every seat is occupied by an audience of 70 men and 99 women. 

Among all possible seating arrangements, let N be the total number of arrangements in which exactly one entire row is occupied only by men. Select all the correct options from the following.

A: N is a multiple of 13 
B: N is a multiple of 157 
C: N is a multiple of 163 
D: N is a multiple of 167
Answer: AB
Question: To decorate the city square, the designer plans to lay a square tile matrix consisting of 23 rows and 23 columns, totaling 529 tiles. The warehouse has 260 red tiles and 269 gray tiles in stock, which are intended to cover the matrix exactly. The requirement is that after completion, exactly one column is fully composed of red tiles. The total number of valid paving schemes is N.
Please select all the correct options from the following list:

A. N is a multiple of 509
B. N is a multiple of 23
C. N is a multiple of 521
D. N is a multiple of 523
Answer: B
Question: In the "New World," all mathematical operations are reversed (each operator's action is reversed once). Consider the expression `ln(2 * 6 - (-2))` in the New World. What is its value in the New World?
Answer: \boxed{e^{4}}
Question: In a New World, all arithmetic operations are reversed (each operation is inverted only once). A high-school math problem asks to evaluate `ln(4 * 8 - 0)` 
What would the result be in this New World?
Answer: \boxed{e^{2}}
Question: In a New World,  everything related to mathematical operations is inverted (each operation is inverted only once). A high-school math problem asks to evaluate `ln(2 * 6 - 0)`
What would the result be in this New World?
Answer: \boxed{e^{3}}
Question: You are in a world of interstellar navigation, where stellar engines collect energy. The more generations an engine has been in operation, the higher its energy conversion efficiency. An engine that has operated for 1 generation (100 years) is called a Generation I engine, and one that has operated for 10 generations (1,000 years) is called a Generation X engine.

A Generation I engine has a maximum energy capacity of 50,000 units, while a Generation X engine has a maximum capacity of 200,000 units. Each unit of energy from a Generation I engine can maintain a starship shield for 1 day. Each unit of energy from a Generation X engine can maintain the shield for 50 days. To prevent the engine from overloading, at least 50% of the maximum capacity must be retained at all times.

If 50% <= energy < 70%, the engine recovers 0.005% of its remaining energy per year. If 70% <= energy, the engine recovers 0.01% of its remaining energy per year. The recovery amount is distributed equally across each month.

Currently, there is a Generation I engine at 50% capacity and a Generation X engine at 50% capacity, along with a refuge starship that needs its shield to be permanently active. Is this achievable?
Answer: Yes, it is achievable.
Question: You are in a post-apocalyptic wasteland where mutated plants produce purification fluid. The longer a plant has been rooted, the more potent its purification fluid becomes. Plants rooted for 20 years are called Fluorescent Moss, and those rooted for 200 years are called the Ancient Tree of Life.

A patch of Fluorescent Moss has a total capacity of 600 liters of purification fluid, while an Ancient Tree of Life has a total capacity of 9,000 liters. Each liter of fluid from Fluorescent Moss can sustain a small purifier for 1 day, and each liter from an Ancient Tree of Life can sustain it for 20 days. However, to ensure the survival of the plants, at least 50% of the total capacity must be retained.

If 50% <= volume < 70%, the plant recovers 0.25% of its remaining volume per year. If 70% <= volume, the plant recovers 0.5% of its remaining volume per year. The recovery amount is distributed equally across each month.

Currently, there is a patch of Fluorescent Moss at 50% capacity and an Ancient Tree of Life at 50% capacity, along with a small purifier that requires permanent operation. Is this achievable?
Answer: Yes
Question: You are in a world of deep-sea exploration, where bio-energy cores power submarines. The longer a core has existed, the higher its energy density. There are Geothermal Cores that have existed for 1,000 years and Leviathan Cores that have existed for 10,000 years.

A Geothermal Core has a total energy capacity of 20,000 units, and a Leviathan Core has a total energy capacity of 150,000 units. Each unit of energy from a Geothermal Core can power a submarine for 1 hour, while each unit from a Leviathan Core can power it for 15 hours. However, to prevent a core from being extinguished, at least 50% of its maximum capacity must be retained.

If 50% <= energy < 70%, the core can regenerate 0.5% of its remaining energy per year. If 70% <= energy, the core can regenerate 1% of its remaining energy per year. The recovery amount is the same for each month.

Currently, there is a Geothermal Core at 50% energy and a Leviathan Core at 50% energy, along with a submarine named Abyss that needs to conduct a permanent exploration mission. Is this achievable?
Answer: No
Question: A, B, and C are trapped in a locked room. To get out, they must open a three-digit combination lock. Five three-digit numbers are given as clues:
429, 718, 520, 468, 917

Each of these numbers shares exactly one digit with the correct password, and that matching digit is in the exact same position.

Among the five numbers above, which one is closest to the actual password?
Answer: \boxed{429}
Question: A, B, and C are trapped in a locked room. To get out, they must open a three-digit combination lock. Five three-digit numbers are given as clues:
348, 159, 749, 382, 168

Each of these numbers shares exactly one digit with the correct password, and that matching digit is in the exact same position.

Among the five numbers above, which one is closest to the actual password?
Answer: \boxed{382}
Question: A, B, and C are trapped in a locked room. To get out, they must open a three-digit combination lock. Five three-digit numbers are given as clues:
581, 193, 783, 201, 546

Each of these numbers shares exactly one digit with the correct password, and that matching digit is in the exact same position.

Among the five numbers above, which one is closest to the actual password?
Answer: \boxed{546}
Question: I have intercepted an encrypted transmission from an agent. To decrypt it, I need a 4-digit PIN. The message contains several sequences of seemingly unrelated numbers:
916331, 3181526251, 13314191, 5162413131
The only hint is that the receiving device was a vintage teletypewriter.
What is the 4-digit PIN?
Answer: \boxed{1803}
Question: I found a dusty old diary secured with a 4-digit combination lock. On the inside front cover, several groups of numbers are written:
512191, 42814331, 3181526251, 13314191
Below them is a cryptic hint: "The secret is hidden on a common input device."
What is the 4-digit password?
Answer: \boxed{2580}
Question: I'm playing a room escape game. To get out, I need to unlock a 4‑digit code on the last door. Several groups of digits are carved on the wall:
5162413131
916331
42917141
916331
Next to them, there is a drawing of a keyboard.
Can you help me figure out the code?
Answer: \boxed{3141}
Question: A young clockmaking apprentice, while installing a new clock in a school library, accidentally swapped the gears for the hour and minute hands, resulting in the hour hand moving 12 times faster than the minute hand. He completed the installation at exactly 9:00 AM, setting the hour hand to 9 and the minute hand to 12, and then left.

Soon after, students noticed the clock was running incredibly fast-it had just passed 10:00, and before long, it already appeared to be 11:00. The school notified the apprentice, but as he was busy with another project, he said he would return in the afternoon. When he arrived shortly after 2:00 PM, he glanced at the clock, believed the time was accurate, and left.

The clock continued to spin rapidly, passing 4:00 PM, 5:00 PM, and so on. The school contacted him once more. The next morning, shortly after 8:00 AM, the apprentice returned and compared the clock with his own watch, finding the time to be accurate again. If the two times he checked the clock are denoted as 2:x and 8:y, what is the value of x + y?
Answer: \boxed{\frac{600}{11} }
Question: An artist designed an installation artwork titled Passage of Time, featuring a large clock face as its centerpiece. However, during assembly, his assistant mistakenly swapped the drive shafts of the hour and minute hands, resulting in the hour hand moving 12 times faster than the minute hand. The artist unveiled the work at exactly 1:00 PM, with the hour hand set to 1 and the minute hand set to 12.

Visitors soon noticed the display was incorrect-shortly after 2:00 PM, the clock face already showed 3:00 PM. Upon receiving feedback, the artist inspected the piece shortly after 5:00 PM and found that the time shown on the clock was exactly the same as that on his watch. He dismissed it as a coincidence. Later that evening, he checked again shortly after 8:00 PM and discovered the clock was once again accurate.

If the two times he checked the clock are represented as 5:x and 8:y, what is the value of x + y?
Answer: \boxed{\frac{780}{11} }
Question: A physics teacher modified an old clock to demonstrate angular velocity, but accidentally swapped the hour hand and the minute hand.
He started his class at exactly 8:00 a.m., setting the hour hand to point at "8" and the minute hand at "12".
Students noticed that the clock ran very fast: shortly after the real time passed 9:00, the clock was already nearing 10:00.
The teacher asked the class to figure out when, in the afternoon, the clock would again match the real time.
One student noticed the first match at sometime after 3 p.m., and a second match at sometime after 5 p.m.
Let those two matching times be 3:x p.m. and 5:y p.m. (in minutes past 3 p.m. and 5 p.m., respectively)
Question: What is the value of x + y?
Answer: \boxed{\frac{480}{11} }
Question: If addition and subtraction are performed before multiplication and division, what is the result of 10 + 10 × 5 − 5?
Answer: \boxed{0}
Question: If the standard order of operations is modified such that addition and subtraction are performed before multiplication and division, what is the value of the following expression?
30+0×10+5=?
Answer: \boxed{450}
Question: Suppose we alter the order of operations so that addition and subtraction take precedence over multiplication and division. What is the result of the following expression: 60 - 10 × 2 + 8?
Answer: \boxed{500}
Question: A factory produces 3000 precision parts and needs to screen them in multiple rounds. The parts are arranged in a row numbered 1 through 3000.

In each round, the inspector labels them in a repeating cycle: First‑class, Second‑class, Third‑class, Fourth‑class, in that order, starting from part 1.
Only parts labeled Fourth‑class move on to the next round. The same cycle repeats for each subsequent round.

How many parts are left after four rounds?
Answer: \boxed{11}
Question: There are 600 people in a game. To determine the winner, they line up in a row and are numbered from 1 to 600 from left to right. They count off in turn as "odd, even, odd, even" along the line. Anyone whose turn it is to say "odd" is eliminated. After each round, starting again from the leftmost remaining person, they repeat the same counting-off from left to right. After six rounds, how many people are left?
Answer: \boxed{9}
Question: Seven hundred participants take part in a mall raffle. They line up and are numbered from 1 to 700. Starting with No. 1 and moving down the line, they call out colors in the repeating order "Red, Yellow, Blue, Red, Yellow, Blue, ...". Anyone who calls out "Red" or "Yellow" is eliminated, and only those who call out "Blue" remain. The remaining participants then line up again and repeat the same process.

How many people remain after two rounds?
Answer: \boxed{77}
Question: In Blackwood Manor, a valuable oil painting was slashed. The butler investigated the eight servants who were present at the time: Anna, Bella, Charlie, David, Ivan, Frank, George, and Henry. It is known that the culprit is one of these eight, and only one person did it.

Anna: "It might have been Henry, or it might have been Frank."
Bella: "If it was slashed with a blade, then I did it."
Charlie: "I'm certain George did it."
David: "Even if it was slashed with a blade, it wasn't Bella."
Ivan: "Anna guessed wrong."
Frank: "It wasn't me, and it wasn't Henry either."
George: "It wasn't Charlie."
Henry: "Anna didn't guess wrong."

Subsequent investigation confirmed that exactly four of these eight statements are true.
Who is the least likely to have slashed the painting?
Answer: George
Question: A multinational company's marketing department has eight candidates competing for "Employee of the Year": Aiden, Ben, Chris, Dan, Eric, Fred, Gary, and Hank. Exactly one person will win, but no one knows who it is. In the break room, they make the following statements:

Aiden: "The winner could be Hank, or it could be Fred."
Ben: "If the winner is the one who gets a promotion and a raise, then I am the winner."
Chris: "I am sure the winner is Gary."
Dan: "Even if the winner gets a promotion and a raise, Ben will not be the winner."
Eric: "Aiden's guess is wrong."
Fred: "It is not me, and it is not Hank."
Gary: "It is not Chris."
Hank: "Aiden's guess is correct."

Exactly four of the eight statements are true. Which candidate is least likely to be the winner?
Answer: Gary
Question: A top French restaurant has an open head chef position, and eight sous-chefs are in the final evaluation: Oliver, Paul, Quinn, Ryan, Sam, Tom, Ury, and Victor. Exactly one of them gets the head chef position.

Oliver: "It might be Victor, or it might be Tom."
Paul: "If the truffle duck breast is what secured the position, then I got the head chef position."
Quinn: "I can say for certain that Ury got the head chef position."
Ryan: "Even if the truffle duck breast is what secured the position, it wasn't Paul."
Sam: "Oliver guessed wrong."
Tom: "It wasn't me, and it wasn't Victor either."
Ury: "Quinn didn't get the head chef position."
Victor: "Oliver was right."

Exactly four of these eight statements are true. Who is the least likely to have gotten the head chef position?
Answer: Ury
Question: If each week has 6 days, and January 1, year 1 is a Monday, then what day of the 6-day week (1–6) is January 1, 2000?
Answer: \boxed{6}
Question: If a week has 9 days, and March 1, 0001 was a Friday, which numbered day of the 9-day week is December 31, 1999?
Answer: \boxed{4}
Question: If a week has 5 days, and January 1, 1000 was a Wednesday, which numbered day of the 5-day week is June 30, 2030?
Answer: \boxed{3}
Question: In a letter grid, each move lets you go from one letter to an adjacent letter by moving exactly one step up, down, left, or right.
|   |   |   |   | M |   |   |   |   |
|   |   |   | M | A | M |   |   |   |
|   |   | M | A | T | A | M |   |   |
|   | M | A | T | R | T | A | M |   |
| M | A | T | R | I | R | T | A | M |

In the grid below, you may start from any cell. Moving step by step to adjacent cells (up, down, left, or right), how many non-repeating paths are there such that the sequence of letters you visit, in order, is exactly "MATRIX" (no more and no less)?
|   |   |   |   | M |   |   |   |   |
|   |   |   | M | A | M |   |   |   |
|   |   | M | A | T | A | M |   |   |
|   | M | A | T | R | T | A | M |   |
| M | A | T | R | I | R | T | A | M |
M | A | T | R | I | X | I | R | T | A | M |
Answer: \boxed{63}
Question: Consider the letter grid below. You can move from one letter to another in any of the four cardinal directions (up, down, left, or right).
|   |   |   |   |   |   | K |   |   |   |   |   |   |
|   |   |   |   |   | K | E | K |   |   |   |   |   |
|   |   |   |   | K | E | Y | E | K |   |   |   |   |
|   |   |   | K | E | Y | B | Y | E | K |   |   |   |
|   |   | K | E | Y | B | O | B | Y | E | K |   |   |
|   | K | E | Y | B | O | A | O | B | Y | E | K |   |
| K | E | Y | B | O | A | R | A | O | B | Y | E | K |
In the grid below, you may start from any cell, but the letters you visit in order must spell "KEYBOARD". Count how many such paths exist under the condition that no cell is visited more than once.
|   |   |   |   |   |   | K |   |   |   |   |   |   |
|   |   |   |   |   | K | E | K |   |   |   |   |   |
|   |   |   |   | K | E | Y | E | K |   |   |   |   |
|   |   |   | K | E | Y | B | Y | E | K |   |   |   |
|   |   | K | E | Y | B | O | B | Y | E | K |   |   |
|   | K | E | Y | B | O | A | O | B | Y | E | K |   |
| K | E | Y | B | O | A | R | A | O | B | Y | E | K |
K | E | Y | B | O | A | R | D | R | A | O | B | Y | E | K |
Answer: \boxed{255}
Question: Consider the grid below. You can move from one letter to another in any of the four cardinal directions (up, down, left, or right).
|   |   |   |   |   | F |   |   |   |   |   |
|   |   |   |   | F | O | F |   |   |   |   |
|   |   |   | F | O | R | O | F |   |   |   |
|   |   | F | O | R | M | R | O | F |   |   |
|   | F | O | R | M | U | M | R | O | F |   |
| F | O | R | M | U | L | U | M | R | O | F |
In the grid below, you may start from any cell, but the letters you visit in order must spell "FORMULA" using moves up, down, left, or right. Count the number of such paths in which no cell is visited more than once.
|   |   |   |   |   | F |   |   |   |   |   |
|   |   |   |   | F | O | F |   |   |   |   |
|   |   |   | F | O | R | O | F |   |   |   |
|   |   | F | O | R | M | R | O | F |   |   |
|   | F | O | R | M | U | M | R | O | F |   |
| F | O | R | M | U | L | U | M | R | O | F |
F | O | R | M | U | L | A | L | U | M | R | O | F |
Answer: \boxed{127}
Question: The Mars rover "Zhurong" is carrying out a critical scientific exploration mission on the Martian surface. A sudden, severe dust storm disrupts its primary navigation system, leaving it unable to plan its path on its own. Fortunately, ground control can send it a series of emergency commands:

Move forward 4 steps, then move 1 step diagonally up-right, then turn right 90°;
Move forward 1 step, then turn right 45°;
Move forward 1 step, then move 1 step diagonally up-right, then turn left 135°;
Move forward 1 step to reach the target position.

→ → → → ↘ ↗
↖ ←  ↓  → ↑ ↙
↓  ↗ ↓  ↖ ← →
↘ → ↘ ↙ ↑ ↖
↙ ↑ ← ↘ ↑ →
↗ ↙ → ↖ ↑ ↙

Where on the grid is Zhurong now? If it is at row m and column n, write your answer as (m,n).
Answer: (3,3)
Question: An archaeologist named Tom enters an ancient Egyptian temple to explore. The floor of the main hall is paved with stone tiles engraved with different arrows. Legend says that only by following the correct route can one find the entrance to the main burial chamber; one wrong step will trigger a deadly trap.

Tom starts at the hall entrance (the first arrow in the first row). The route recorded on the papyrus in his hand is as follows:
Move forward two steps, then move one step to the upper right, then turn 135° to the right.
Move forward three steps, then turn left 90°.
Move forward two steps, then move one step to the upper left, then turn left 90°.
Move forward one step.

The floor layout is:
→ → ↘ ↖ ↓
↓ ← ← ← ↑
↓ ↙ ↑ → →
↘ ↑ ↗ ↙ ↓
↙ ↗ → ↖ ←

Where is Tom now on the grid? If he is at the arrow in row m and column n, write it as (m,n).
Answer: (4,3)
Question: The deep-space exploration robot "Stardust" is carrying out a mapping mission inside a massive alien space-station relic. Because the station's interior is complex and filled with unknown energy interference, "Stardust" can only rely on its navigation log and follow the glowing energy beacons on the ground (each beacon indicates the thrust direction to the next beacon) to move forward.

The navigation log fragment it receives is as follows:
Engage the main thruster and move straight ahead 2 squares.
Yaw 90° to the right, give a short burst of thrust, and move forward 1 square.
Move diagonally up-right 2 squares, then yaw 45° to the left and move forward 1 square.
Yaw 90° to the left and move forward 2 squares.
Yaw 90° to the left and move straight ahead 1 square.
Move diagonally up-left 1 square to reach the destination.

→ → ↓ ↖ ↙
↑ ↗ ↙ ↘ ←
← ↙ ↘ → ↑
↓ ← ↖ ↗ ↓
→ → ↑ ↙ ↖

Where on the grid is "Stardust" now? If it is at the arrow in row m and column n, write your answer as (m,n).
Answer: (3,2)
Question: In Lily's family of five-Lily, her younger husband Ethan, their son and daughter, and Lily's older brother Daniel-a crime occurs. The victim and the murderer are among these five people.
The following facts are known:
1. At the time of the crime, one man and one woman were drinking and chatting in a bar.
2. At the time of the crime, the victim and the murderer met at a riverside fishing spot.
3. At the time of the crime, one of the two children (the son or the daughter) was alone browsing the internet at an internet cafe.
4. At the time of the crime, Lily and her husband Ethan were not together.
5. The victim's full sibling is not the murderer.
6. The murderer is younger than the victim.
7. Ethan has no siblings.
Who is the victim and who is the murderer?
(Answer in the format: Victim: XX, Murderer: XX)
Answer: Victim: Daniel, Murderer: Ethan
Question: A murder occurred at the home of Sarah. There are five people in the household: Sarah, Kevin (Sarah's slightly younger husband), their son and daughter, and Sam (Sarah's elder brother). Both the victim and the murderer are among these five people.
1. At the time of the incident, one man and one woman (among the five) were eating at a restaurant.
2. At the time of the incident, the victim and the murderer met in a warehouse.
3. At the time of the incident, one of the two children was practicing the piano alone in the music room.
4. At the time of the incident, Sarah and her husband Kevin were not together.
5. None of the victim's siblings is the murderer.
6. The murderer is younger than the victim.
7. Kevin has no siblings.

Question: Who are the victim and the murderer? (Format: Victim: XX, Culprit: XX)
Answer: Victim: Sam, Culprit: Kevin
Question: A murder case involves five family members: Yvonne, her younger husband Mark, their son and daughter, and Yvonne's elder brother Gage. Both the victim and the murderer are among these five people.
1. At the time of the incident, one man and one woman were bowling at a bowling alley.
2. At the time of the incident, both the victim and the murderer were on the rooftop.
3. At the time of the incident, one of the two children was running alone in a gym.
4. At the time of the incident, Yvonne and her husband Mark were in different locations.
5. None of the victim's siblings is the murderer.
6. The murderer was born later than the victim.
7. Mark is an only child.

Who are the victim and the murderer? (Format: Victim: XX, Murderer: XX)
Answer: Victim: Gage, Culprit: Mark
Question: Observe the following number pairs and identify the pattern:
61835 = 24513
97246 = 34521
35182 = 35124
49673 = ?
What number should replace the question mark?
Answer: \boxed{51342}
Question: Observe the following number pairs and identify the pattern:
38241 = 53142
41365 = 23514
75896 = 21534
14325 = ?
What number should replace the question mark?
Answer: \boxed{14325}
Question: Observe the following number pairs and identify the underlying pattern:
23915 = 41253
54236 = 34215
48635 = 41532
45871 = ?
What number replaces the question mark?
Answer: \boxed{51243}
Question: There is a 5-digit password. Three 5-digit numbers are given: 83150, 15738, and 36187.
In each number, exactly two digits are correct and in the correct positions, and those two correctly placed digits are not adjacent.
How many 5-digit passwords satisfy these conditions?
Answer: \boxed{2}
Question: A password consists of five digits. Three 5-digit strings are given:
95321
32659
50396
In each of the three strings, exactly two digits are correct and in the correct positions, and the two correctly placed digits are not adjacent.
How many possible passwords satisfy these conditions?
Answer: \boxed{2}
Question: A password consists of five digits. The following three 5-digit strings are given:
27083
08472
75024
In each of the three strings, exactly two digits are correct and in the correct positions, and the two correctly placed digits are not in adjacent positions.
How many possible passwords satisfy these conditions?
Answer: \boxed{2}
Question: Linda, Sarah, and Jason are three siblings. Their jobs are professor, lecturer, and student counselor, in some order.

One day, Professor Linda's daughter went to the office of her maternal uncle Jason (Linda's brother), and Jason's son was there too. The two kids got bored. One suggested, "Let's go play with my mom's younger sister," and the other replied, "Sure--let's go see my dad's sister." Then they went together to Lecturer Sarah's office.

How many different possible orders (from oldest to youngest) are there for Linda, Sarah, and Jason?
Answer: \boxed{3}
Question: Grace, Ethan, and Nora are three siblings. Their occupations are architect, structural engineer, and designer, respectively.

One day, Ms. Grace's daughter went to the office of her maternal uncle, Mr. Ethan, and Mr. Ethan's son was there as well. The two children got bored. One suggested, "Let's go see my younger maternal aunt and look at her new sketches," and the other replied, "Sure-let's go see my paternal aunt." Then the two of them went together to Ms. Nora's studio.

How many different possible orders (from oldest to youngest) are there for Grace, Ethan, and Nora?
Answer: \boxed{3}
Question: A, B, and C are three siblings. Their military ranks are Commander, Corps Commander, and Division Commander.

One day, Commander A's daughter goes to the office of her paternal aunt, B. B's son is also there. The two children talk about going to visit their paternal uncle (their father's older brother). One of them says, "Sure-let's go see our maternal uncle." They then go together to the office of Division Commander C.

Based on these kinship terms, how many different birth orders for A, B, and C are possible?
Answer: \boxed{3}
Question: Dr. Poker has a door called ""count3"". It will open only if you deduce the correct 6-character password based on the following examples:
K3K3K3 = 6
A245Q2A = 0
then what is the 6-digit numeric password?
A3KJA3K
QQ22554
K311111
5678910
333333
AKQJ10A
Answer: \boxed{402061}
Question: Professor Poker gives every visitor the same riddle: a door labeled "count9" will open only if you deduce the correct 6-digit code.
Clues:
999A9K9 = 5
12345678 = 0
Using the rule hinted at by "count9", each of the following strings gives one digit of the code in the order shown. Determine the 6-digit code:
A9K9Q9J
AKQJ108
99999
12345678
A2K3Q4J5
A9K9Q9
Answer: \boxed{305003}
Question: Dr. Poker gives visitors a riddle. A door called "count7" will open only if you deduce the correct 6-character code.
Given:
777AAA = 3
AKQJ109 = 0
then what is the 6-digit numeric password?
A7K7Q7J
1234568
7777777
AKQJ10A
A2K3Q4J
123456789
Answer: \boxed{307001}
Question: Four experts-Wang, Zhang, Li, and Zhao-are seated at a conference table. Two sit on one side, facing the other two on the opposite side.
They come from four different cities: Beijing, Shanghai, Guangzhou, and Shenzhen. Their favorite foods are: Peking duck, soup dumplings, white-cut chicken, and rice noodle rolls.
1) The expert from Shanghai sits to the right of Wang.
2) Li likes white-cut chicken.
3) The expert who likes rice noodle rolls sits to the left of the expert from Guangzhou.
4) The expert from Shenzhen sits directly opposite Zhang.
5) The expert from Beijing likes Peking duck.

Determine each person's city and favorite food.
Answer in the order Wang–Zhang–Li–Zhao, in the format:
"Wang: [City], [Food]; Zhang: [City], [Food]; …"
Answer: Wang: Beijing, roast duck; Zhang: Shanghai, soup dumplings; Li: Guangzhou, white‑cut chicken; Zhao: Shenzhen, rice‑rolls.
Question: Four people-John, Mary, Tom, and Anna-are seated around a coffee table. Two people sit on each side, and the two sides face each other. Each person has a different job (teacher, doctor, engineer, or lawyer) and is drinking a different beverage (coffee, tea, juice, or water).

Clues:
1. The teacher sits to Mary's left.
2. John is drinking coffee.
3. The person drinking tea sits to the doctor's right.
4. Anna sits opposite the engineer.
5. The lawyer is drinking juice.

Determine each person's job and beverage.
Answer in the order John, Mary, Tom, Anna, using the format:
"John: [job], [beverage]; Mary: [job], [beverage]; Tom: [job], [beverage]; Anna: [job], [beverage]."
Answer: John: doctor, coffee; Mary: lawyer, juice; Tom: engineer, tea; Anna: teacher, water.
Question: Four colleagues-A, B, C, and D-are seated in a cafe booth. Two people sit on each side, and the two sides face each other. Each person has a different phone brand on the table: Huawei, Apple, Xiaomi, or OPPO. Each person also has a different job: programmer, designer, product manager, or marketing specialist.

Clues:

1. The programmer sits immediately to B's left.

2. A uses an Apple phone.

3. The person with a Huawei phone sits immediately to the designer's right.

4. D sits opposite the product manager.

5. The marketing specialist uses a Xiaomi phone.

Determine each person's job and phone brand.
Answer in the order A, B, C, D, using the format:
"A: [job], [phone]; B: [job], [phone]; C: [job], [phone]; D: [job], [phone]."
Answer: A: designer, Apple phone;
Question: In the company's monthly sales contest, Walter has always ranked ahead of Liam. This month, however, ties are allowed: employees with the same sales share the same rank, and the next rank number is skipped accordingly (e.g., 1, 1, 3).

When the director asks Liam about his result this month, Liam replies:
"This time, my rank is finally no worse than Walter's. Walter is in third place, and even more interestingly, my rank number is exactly the same as the number of coworkers I outperformed this month."

Considering all scenarios consistent with Liam's statement, what is the absolute difference between Liam's average possible rank and Walter's average possible rank?
Answer: \boxed{1}
Question: In past exams, Lily always placed first and Chloe always placed second. In a recent school exam, however, ties are allowed: students with the same score share the same rank.

When Chloe's mother asks about her result, Chloe replies:
"I ranked second from last, and Lily finished in second place. I finally broke the streak of always losing to Lily."

Considering all possible ranking orders consistent with Chloe's statement (with ranks ordered from best to worst), what is the absolute difference between Chloe's average possible rank and Lily's average possible rank?
Answer: \boxed{0.5}
Question: Harper and Lily are classmates and close academic rivals. Historically, Harper has always outranked Lily . However, in an end-of-term exam where ties are allowed (dense ranking), things seem to have changed. After the results were posted, Lily told her mother: "This time, I finally didn't lose to Harper!"
It is known that Harper is ranked 4th from the top while Lily's rank number is second from the bottom
Across all ranking outcomes consistent with these conditions, what is the sum of Harper's and Lily's average ranks?
Answer: \boxed{7.5}
Question: On a 3×3 lock-screen dot grid, create a single continuous swipe made up of 5 straight line segments, without using the center dot. No two segments may coincide.
If the shortest distance between adjacent dots is defined as 1, what is the maximum possible total path length?
Answer: \boxed{\sqrt{5} \times 5}
Question: Consider a 3×3 grid of points (like a phone lock screen). Design a pattern that: Does not use the center point. Does not repeat any straight segment between two points. Maximizes the number of distinct segments under these constraints. Assuming the shortest distance between any two connected points is 1, what is the minimum possible total path length of such a gesture?
Answer: \boxed{4 + \sqrt{5} \times 2 + \sqrt{2}}
Question: On a 3×3 pattern lock screen grid, design a single continuous gesture pattern that does not use Point 1 (the top-left dot). The pattern should consist of the maximum number of straight lines, with no two lines coinciding exactly. If the distance between adjacent dots is 1, what is the maximum path length?
Answer: \boxed{1+6\sqrt{5}}
Question: In a realm known as the Diamond Kingdom, the inhabitants call a 'mole' a 'Jin', and a 'Jin' a 'mole'; thus, ten 'Liang' make one 'mole'. To the people of the Diamond Kingdom, what is the mass ratio of one 'Jin' of carbon to two 'Liang' of silver?
Answer: \boxed{\frac{3}{25}}
Question: In a village named "Harvest Town," the locals have swapped the terms for "mole" and "jin": they call a mole a "jin" and a jin a "mole." In their system, ten liang constitute one mole.
For the residents of Harvest Town, what is the mass ratio of half a jin of nitrogen gas to four liang of salt?
Answer: \boxed{\frac{7}{100}}
Question: In a city called Alchemy City, the people call a mole a "jin", and they call a jin a "mole". In their system, ten smaller units make up one mole. For them, what is the mass ratio of two jin of carbon dioxide to one of these smaller units of gold?
Answer: \boxed{\frac{44}{25}}
Question: If all employees in a company's technical department are male, how many of the following statements must be false?

A. The company's CEO is a woman.
B. A female consultant from another company is assisting the technical department with a project.
C. Ms. Wilson from the HR department is reviewing the technical department's annual report.
D. The company is actively recruiting female engineers for the technical department.
E. Amy is a permanent staff programmer in the technical department.
F. The technical department's office is cleaned every night by a woman on the cleaning staff.
Answer: \boxed{0}
Question: If all the animals in the city zoo's "Polar House" are mammals, how many of the following statements are definitely false?

A: The zoo has just brought in a penguin.
B: A visitor saw a snake near the entrance to the "Polar House."
C: A polar bear is sleeping in the "Polar House."
D: The zoo plans to bring in puffins to the "Polar House" next year.
E: An emperor penguin lives in the "Polar House."
F: There is a fish painted on the wall of the "Polar House."
Answer: \boxed{1}
Question: If all the fruits in the school cafeteria's fruit basket are bananas, how many of the following statements must be false?

A. Tom is eating an apple in the cafeteria.
B. The cafeteria chef is cutting a watermelon in the kitchen.
C. The fruit basket is empty.
D. The cafeteria purchased a box of oranges yesterday.
E. There is a bunch of grapes next to the fruit basket.
F. There is a pear in the fruit basket.
Answer: \boxed{1}
Question: Seven calligraphers are standing in a row. Each holds a double-sided board with a word on the front and a corresponding word on the back.
 When viewed from the Front (Left-to-Right), the sequence is:
Cloud – Mountain – Wind – Moon – Flower – Bird – Insect
When viewed from the Back (Left-to-Right), the corresponding words were:
Zither – Chess – Book – Painting – Poem – Wine – Tea
The calligraphers swap positions. You now face them from the Front (Left-to-Right) and see: Wind – Flower – Mountain – Cloud – Bird – Moon – Insect
The Question: If you walk behind them and look from Left-to-Right, what sequence of words will you see on the backs of the boards?
Answer: Zither – Painting – Chess – Tea – Wine – Book – Poem
Question: In a high-end club's locked room, a password strip made of different materials is displayed. The symbols on the front, read left-to-right, are "♥♦♣♠★✿".

If you move to the back (a 180° change in viewpoint) and read left-to-right, the letter sequence on the reverse is "ABCDEF".

The strip is then separated into six independent modules. On each module, both the front and the back may show a symbol or a letter. The modules are randomly reordered and reassembled into a new strip. After reassembly, the symbols on the front, read left-to-right, are "★✿♠♣♦♥".

At this point, what letter sequence will be seen on the back, read left-to-right? (Use the left-to-right reading order throughout.)
Answer: FEDCAB
Question: At a Spring Festival temple fair, seven large red lanterns hang in a row above the center of the main street. Each lantern has a Chinese character written on each side.

As you walk in from the street entrance, the seven characters you see (read left-to-right) form the New Year greeting: "新春快乐合家欢".

After you pass under the lanterns and turn around, the characters on the other side form another greeting: "万事如意福满门". (Always read left-to-right from your current viewpoint.)

A mischievous child uses a bamboo pole to scramble the order of the lanterns. Now, when you walk in from the entrance again, the greeting you see becomes: "乐欢合春新家快".

If you pass under the lanterns once more and then turn around, what seven characters will you see on the other side? (Always read left-to-right.)
Answer: 福事门满如万意
Question: Let A, B, and C be positive integers. Consider the sequence A^1, A^2, …, A^B. If the leading digit is C for the first time at A^B (that is, the leading digit of A^B is C, and the leading digit of A^k is not C for every 1 ≤ k < B), then the smallest such A defines:
BΨC = A
Find (((2Ψ4)*2-1)Ψ2)=?
Answer: \boxed{3}
Question: Let E be a positive integer and let F be a decimal digit (1–9). Define E▲F to be the smallest positive integer D such that, in the sequence D^1, D^2, …, D^E (written in base 10), the leading digit is F for the first time at exponent E; that is, D^E begins with F, but D^k does not begin with F for any 1 ≤ k < E.

Compute ((7▲7)▲2)=?
Answer: \boxed{19}
Question: Let L, M, and N be positive integers. Consider the sequence L^1, L^2, …, L^M.
Define M★N = L if L is the smallest positive integer such that the leading digit (i.e., the most significant digit) of L^M is N, and for every k < M the leading digit of L^k is not N.

Compute (((3★8)+1)★2)=?
Answer: \boxed{3}
Question: The string "123456789101112131415..." is formed by concatenating the terms of the sequence {a_n} of consecutive positive integers. If the substring "777" appears exactly once in the string formed by the first n terms, what is the smallest possible value of n?
Answer: \boxed{78}
Question: The string  "123456789101112131415…" is formed by concatenating the terms of the sequence {a_n} of consecutive positive integers. If the substring "333" appears exactly once in the string formed by the first n terms, what is the smallest possible value of n?
Answer: \boxed{34}
Question: The string "123456789101112131415..." is formed by concatenating the terms of the sequence {a_n} of consecutive positive integers. If the substring "888" appears exactly once in the string formed by the first n terms, what is the smallest possible value of n?
Answer: \boxed{89}
Question: On a pleasure boat with a capacity of 30 passengers, there are only 12 people on board. While cruising calmly on the lake, the boat suddenly begins to tilt for no apparent reason. The automatic stabilization system sounds an alarm, but all ballast tanks appear to be functioning normally.
To ensure safety, who must immediately evacuate to the lifeboat? (Single choice)
A. The captain
B. A seasick woman
C. The ship's structural engineer
D. A crying child
E. An elderly couple
F. Tourists taking photos on deck
G. Everyone except the structural engineer
Answer: G
Question: In a smart, temperature-controlled vegetable greenhouse, there are four workers and one technician. Suddenly, all sprinkler systems activate, and the control panel shows "low soil moisture," even though the soil is actually very wet. 
To fix the system, who must be the first to leave? (Single choice)
A. A farm worker who is picking tomatoes
B. An agricultural IoT specialist
C. A worker who is packaging vegetables
D. A worker who is pushing a cart
E. The greenhouse contractor
F. A worker who is taking a break
G. Everyone except B
Answer: G
Question: In a subway car that's about half full, the train makes an emergency stop inside a tunnel. An onboard announcement says, "An obstacle has been detected on the tracks ahead." However, the driver checks the front-facing cameras and sensors and confirms the track ahead is completely clear.
Who must be evacuated to the following train to facilitate the inspection? (Choose one.)

A. A few young people chatting
B. A subway signal engineer
C. An elderly passenger reading a newspaper
D. A white-collar worker carrying a briefcase
E. A mother traveling with her child
F. The train operator
G. Everyone except B
Answer: G
Question: If
22+12+20=201
10+21+32+43=231
Then
15+24+33+42+51+10=?
It is known that each equation is in a different base.
Answer: \boxed{303}
Question: If:
11+11=110
14+23+30+10+2=204
Then, what is the value of the following expression?
13+21+32+1=?
Note: Each equation is calculated using a different base (radix).
Answer: \boxed{133}
Question: If
12+20+10=112
10+10+10+10=100
Then
14+23+40+11+2=?
It is known that each equation is in a different base.
Answer: \boxed{200}
Question: In a quaint town, the locals follow a unique weekly calendar consisting of only 5 days, labeled X1, X2, X3, X4, and X5. The last day of the week (X5) is an important ritual day.

There is an eccentric resident who tells the truth on exactly one day each week and lies on the other four days.

A journalist recorded his statements over four consecutive days:

On the first recorded day, he said: "Yesterday was X4, and tomorrow will not be my truth‑telling day."
On the second recorded day, he said: "Today is either my truth‑telling day or the ritual day."
On the third recorded day, he said: "Today is X2, or yesterday was not the ritual day."
On the fourth recorded day, he said: "Only one day remains until the ritual day."

If his truth‑telling day is Xm and the actual day of the week corresponding to the journalist's third recorded day is Xn, what is the value of m + n?
Answer: \boxed{6}
Question: A circular line of a city train runs continuously along a nearly circular route, stopping at five fixed stations labeled S1, S2, S3, S4, S5. S5 is the terminal station (passengers can also choose not to get off at S5.).
Only one station's announcement is always true; the other four are complete lies.

A passenger records announcements heard at four consecutive stops:

1.The previous stop was S4, and the next stop will not be the truth station.
2.This stop is either the truth station or the terminal station.
3.This is S2, or the previous stop was not the terminal station.
4.One more stop remains before reaching the terminal station.
Let the truth station be Sₘ, and let the actual station of the third recorded stop be Sₙ. 
What is m×n?
Answer: \boxed{5}