experiments-07-07-12-local-llm-knowledge-2/results_hard/granite4-micro.log

MODEL: granite4-micro
PATH: /home/qrf/.cache/llama.cpp/granite-4.0-micro-Q4_K_M.gguf
STARTED: 2026-07-12 03:18:05

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Q01 [recall]
What is the Kasner metric, and in what context does it arise in general relativity?

ANSWER:
The Kasner metric is a solution to Einstein's field equations in general relativity that describes a homogeneous but anisotropic universe. It arises in the context of cosmology, specifically when studying the dynamics of an expanding universe with different rates of expansion along different spatial directions.

Key points about the Kasner metric:

1. The Kasner metric is a vacuum solution to Einstein's equations, meaning it describes a universe with no matter or energy content.

2. It is a homogeneous universe, meaning its properties are the same at every point in space, but it is anisotropic, meaning its properties vary depending on the direction in which they are measured.

3. The metric is characterized by a set of parameters called Kasner exponents, which determine the rate of expansion along each spatial direction.

4. The Kasner metric is an important example of a solution that is not isotropic (i.e., it does not have the same properties in all directions) but still satisfies the Einstein field equations.

5. It provides insight into the behavior of anisotropic universes and can be used to study the stability of such solutions.

In summary, the Kasner metric is a solution to Einstein's equations in general relativity that describes a homogeneous but anisotropic universe, arising in the context of cosmology when studying the dynamics of an expanding universe with different rates of expansion along different spatial directions.

EXPECTED (judge only): Vacuum solution to Einstein's equations describing an anisotropic, homogeneous universe; exponents satisfy sum p_i = sum p_i^2 = 1; arises in BKL analysis of cosmological singularities.
(finish=stop tokens=279 time=3.9s tps=76.0)

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Q02 [recall]
In enzyme kinetics, what does the Haldane relationship connect?

ANSWER:
The Haldane relationship connects the Michaelis-Menten parameters k_cat/K_M (turnover number) and k_2 (the rate constant for the catalyzed reaction) to the enzyme's maximum velocity (V_max) and Michaelis constant (K_M). Specifically, it states that:

k_cat/K_M = V_max / (K_M * [S])

where [S] is the substrate concentration. This relationship shows that the catalytic efficiency of an enzyme (k_cat/K_M) is directly proportional to the maximum velocity and inversely proportional to the substrate concentration.

EXPECTED (judge only): Relates the equilibrium constant of a reversible enzyme reaction to its kinetic constants: Keq = (Vf*Kmr)/(Vr*Kmf), tying forward/reverse kcat and Km to thermodynamic equilibrium.
(finish=stop tokens=119 time=1.6s tps=77.1)

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Q03 [recall]
Who was Hypatia of Alexandria and roughly when did she die?

ANSWER:
Hypatia of Alexandria was a prominent philosopher, mathematician, and astronomer in the late 4th and early 5th centuries AD. She was born around 350 AD in Alexandria, Egypt, and died on March 31, 415 AD.

Key points about Hypatia:

1. She was the first recorded female mathematician in the Western world.
2. She taught philosophy and mathematics at the Neoplatonic school in Alexandria, which was one of the most important centers of learning in the ancient world.
3. Hypatia was known for her intellectual prowess, wisdom, and charismatic personality.
4. She was a victim of religious persecution, as she was murdered by a Christian mob led by the Bishop of Alexandria, Peter Chrysologus, and a priest named Peter the Lame.
5. Her death marked the end of the intellectual and cultural flowering of Alexandria and the beginning of the Christian dominance in the region.

In summary, Hypatia of Alexandria was a highly influential philosopher and mathematician who lived and died in the late 4th to early 5th centuries AD.

EXPECTED (judge only): Neoplatonist philosopher/mathematician/astronomer in Alexandria; murdered by a Christian mob around 415 CE.
(finish=stop tokens=227 time=3.1s tps=76.4)

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Q04 [recall]
What is the Gershgorin circle theorem used for?

ANSWER:
The Gershgorin circle theorem, also known as the Gershgorin disk theorem, is a mathematical result used in numerical linear algebra. It provides a way to estimate the approximate location of eigenvalues of a square matrix by considering the sum of the absolute values of the off-diagonal elements in each row.

The theorem states that for a given square matrix A, each eigenvalue of A lies within at least one of the Gershgorin disks, which are defined as follows:

1. For each row i of the matrix A, consider the sum of the absolute values of the off-diagonal elements in that row, denoted as Ri.
2. Define a disk (or circle) in the complex plane centered at the diagonal element ai,i with a radius equal to Ri.
3. Each eigenvalue of A lies within at least one of these disks.

The Gershgorin circle theorem is primarily used for:

1. Eigenvalue localization: It provides a way to estimate the approximate location of eigenvalues in the complex plane based on the matrix elements.

2. Numerical linear algebra: The theorem is often used in algorithms for computing eigenvalues, such as the QR algorithm or the power iteration method.

3. Matrix analysis: It can be used to study the properties of matrices, such as their stability or convergence behavior.

In summary, the Gershgorin circle theorem is a useful tool for estimating the approximate location of eigenvalues of a square matrix based on the matrix elements, and it has applications in numerical linear algebra and matrix analysis.

EXPECTED (judge only): Bounds the location of eigenvalues of a square matrix: every eigenvalue lies within at least one Gershgorin disc centered at a diagonal entry with radius equal to the sum of absolute off-diagonal entries in that row.
(finish=stop tokens=313 time=4.2s tps=76.3)

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Q05 [recall]
In RF engineering, what is the difference between the noise figure and noise temperature of a device, and how are they related?

ANSWER:
In RF engineering, the noise figure (NF) and noise temperature (T) of a device are related concepts that describe the noise performance of a device or system.

1. Noise Figure (NF):
   - The noise figure is a measure of the degradation of the signal-to-noise ratio (SNR) caused by the device or system.
   - It is defined as the ratio of the input SNR to the output SNR of the device.
   - NF is usually expressed in decibels (dB).
   - A lower noise figure indicates better performance, as it means less degradation of the SNR.

2. Noise Temperature (T):
   - The noise temperature is a measure of the equivalent temperature that would produce the same amount of thermal noise power as the device.
   - It is a way to express the noise performance of a device in terms of temperature.
   - Noise temperature is usually expressed in Kelvin (K).

Relationship between Noise Figure and Noise Temperature:
- The noise figure and noise temperature are related through the following equation:
  NF (in dB) = 10 * log10(T / T₀)
  where T₀ is the standard reference temperature, usually 290 K (room temperature).

- This equation shows that the noise figure is directly proportional to the noise temperature.
- A higher noise temperature results in a higher noise figure, indicating more degradation of the SNR.

In summary, the noise figure is a measure of the degradation of the SNR caused by the device, while the noise temperature is a measure of the equivalent temperature that would produce the same amount of thermal noise power. The noise figure and noise temperature are related through the above equation, with a higher noise temperature leading to a higher noise figure.

EXPECTED (judge only): Both quantify added noise; related by F = 1 + Te/T0 (T0=290K), equivalently Te = T0*(F-1). NF is 10log10(F) in dB.
(finish=stop tokens=350 time=4.7s tps=76.1)

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Q06 [recall]
What is the Antikythera mechanism and what did it do?

ANSWER:
The Antikythera mechanism is an ancient Greek device, dating back to the 2nd century BC, that was used to calculate astronomical positions and predict eclipses. It is considered one of the most complex and sophisticated devices of its time, comparable to modern computers.

The mechanism was discovered in 1901 in a shipwreck near the Greek island of Antikythera. It consists of a series of gears, dials, and pointers that were used to track the movements of the Sun, Moon, and planets, as well as to predict the timing of eclipses.

The Antikythera mechanism was used for various purposes, including:

1. Tracking the positions of celestial bodies: The device could calculate the positions of the Sun, Moon, and planets, as well as the timing of their movements.

2. Predicting eclipses: The mechanism could predict the timing of solar and lunar eclipses, which were important events in ancient Greek society.

3. Calendars and timekeeping: The device could also be used to track the passage of time and to keep track of the days, months, and years.

4. Astronomical calculations: The Antikythera mechanism could perform complex astronomical calculations, such as the precession of the equinoxes and the motion of the planets.

In summary, the Antikythera mechanism was a remarkable ancient Greek device that was used to calculate astronomical positions and predict eclipses. It was one of the most complex and sophisticated devices of its time and played an important role in the understanding of the cosmos in ancient Greece.

EXPECTED (judge only): Ancient Greek geared analog device (~2nd c. BCE) for predicting astronomical positions, eclipses, and calendrical/Olympiad cycles.
(finish=stop tokens=323 time=4.3s tps=76.9)

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Q07 [recall]
What does the CAP theorem state in distributed systems?

ANSWER:
The CAP theorem, also known as Brewer's theorem, states that in a distributed system, it is impossible to simultaneously achieve all three of the following properties:

1. Consistency: Every read operation receives the most recent write or an error.
2. Availability: Every request receives a (non-error) response, without the guarantee that it contains the most recent write.
3. Partition tolerance: The system continues to operate despite an arbitrary number of messages being dropped (or delayed) by the network between nodes.

In other words, in a distributed system, you can only have two out of the three guarantees at the same time. If you prioritize consistency and partition tolerance, the system will be less available. If you prioritize availability and partition tolerance, the system will sacrifice consistency.

EXPECTED (judge only): A distributed data store cannot simultaneously guarantee all three of Consistency, Availability, and Partition tolerance; under a partition you must trade consistency vs availability.
(finish=stop tokens=155 time=2.1s tps=77.2)

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Q08 [recall]
What is Cherenkov radiation and what condition produces it?

ANSWER:
Cherenkov radiation is a type of electromagnetic radiation emitted when a charged particle, such as an electron, travels through a medium (like water or glass) at a speed greater than the speed of light in that medium. The condition that produces Cherenkov radiation is when a charged particle moves faster than the phase velocity of light in the medium.

Here's the step-by-step explanation:

1. In a medium, the speed of light is slower than in a vacuum. The speed of light in a medium is given by the equation: c_medium = c_0 / n, where c_0 is the speed of light in a vacuum (approximately 3 x 10^8 m/s) and n is the refractive index of the medium.

2. When a charged particle, such as an electron, moves through a medium, it can accelerate the surrounding electrons, creating a wake of ionized particles.

3. If the charged particle moves faster than the speed of light in the medium (c_medium), it will emit a characteristic blue glow called Cherenkov radiation.

4. The emitted radiation is in the form of a cone of light, with the angle of emission (θ) given by the Cherenkov angle equation: cos(θ) = c_medium / v, where v is the velocity of the charged particle.

In summary, Cherenkov radiation is produced when a charged particle moves faster than the speed of light in a medium, resulting in the emission of a characteristic blue glow.

EXPECTED (judge only): Light emitted when a charged particle travels through a medium faster than the phase velocity of light in that medium (v > c/n); produces the characteristic blue glow, emitted at a cone angle cos(theta)=1/(n*beta).
(finish=stop tokens=303 time=4.0s tps=76.9)

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Q09 [reason]
A 12-bit ADC has a full-scale range of 0 to 3.3 V. What is its voltage resolution (LSB size) in millivolts? Show the calculation.

ANSWER:
To calculate the voltage resolution (LSB size) of a 12-bit ADC with a full-scale range of 0 to 3.3 V, follow these steps:

1. Determine the number of discrete levels:
   A 12-bit ADC can represent 2^12 = 4096 levels.

2. Calculate the voltage range:
   Full-scale range = 3.3 V

3. Calculate the voltage resolution (LSB size):
   LSB size = Voltage range / Number of levels
            = 3.3 V / 4096
            = 0.000806640625 V

4. Convert the LSB size to millivolts:
   1 V = 1000 mV
   LSB size = 0.000806640625 V × 1000 mV/V
            = 0.806640625 mV

Therefore, the voltage resolution (LSB size) of a 12-bit ADC with a full-scale range of 0 to 3.3 V is approximately 0.8066 mV.

EXPECTED (judge only): 3.3 V / 2^12 = 3.3/4096 = 0.0008056 V = about 0.806 mV.
(finish=stop tokens=219 time=3.0s tps=77.0)

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Q10 [reason]
A geostationary satellite orbits at ~35,786 km altitude. Earth's radius is ~6,378 km. Ignoring atmosphere, what is the approximate one-way line-of-sight propagation delay from a ground station directly below it to the satellite, in milliseconds?

ANSWER:
To calculate the one-way line-of-sight propagation delay from a ground station directly below a geostationary satellite to the satellite, we need to consider the distance between the satellite and the ground station.

Given:
- Geostationary satellite altitude: ~35,786 km
- Earth's radius: ~6,378 km

Step 1: Calculate the distance from the Earth's surface to the geostationary satellite.
Distance = Earth's radius + Geostationary satellite altitude
Distance = 6,378 km + 35,786 km
Distance = 42,164 km

Step 2: Convert the distance from kilometers to meters.
Distance = 42,164 km × 1,000 m/km
Distance = 42,164,000 m

Step 3: Calculate the time delay using the speed of light in a vacuum.
Speed of light in a vacuum = 299,792,458 m/s

Time delay = Distance ÷ Speed of light
Time delay = 42,164,000 m ÷ 299,792,458 m/s
Time delay ≈ 0.1405 seconds

Step 4: Convert the time delay from seconds to milliseconds.
Time delay ≈ 0.1405 s × 1,000 ms/s
Time delay ≈ 140.5 ms

Therefore, the approximate one-way line-of-sight propagation delay from a ground station directly below a geostationary satellite to the satellite is about 140.5 milliseconds.

EXPECTED (judge only): Distance ~= 35,786 km; delay = 35,786e3 / 3e8 = ~0.1193 s = about 119 ms. (Directly below, slant range = altitude.)
(finish=stop tokens=313 time=4.2s tps=76.9)

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Q11 [reason]
If a signal has an SNR of 20 dB and a bandwidth of 1 MHz, what is the approximate Shannon channel capacity in Mbps? Show your steps.

ANSWER:
To calculate the Shannon channel capacity, we use the Shannon-Hartley theorem:

C = B * log2(1 + SNR)

Where:
- C is the channel capacity in bits per second (bps)
- B is the bandwidth in hertz (Hz)
- SNR is the signal-to-noise ratio in linear scale

Given:
- SNR = 20 dB
- B = 1 MHz = 1,000,000 Hz

Step 1: Convert the SNR from dB to linear scale.
SNR (linear) = 10^(SNR(dB)/10)
SNR (linear) = 10^(20/10) = 10^2 = 100

Step 2: Apply the Shannon-Hartley theorem.
C = B * log2(1 + SNR)
C = 1,000,000 * log2(1 + 100)
C = 1,000,000 * log2(101)
C ≈ 1,000,000 * 6.6582
C ≈ 6,658,200 bps

Step 3: Convert the channel capacity to Mbps.
C ≈ 6,658,200 bps = 6.658 Mbps

Therefore, the approximate Shannon channel capacity is 6.658 Mbps.

EXPECTED (judge only): SNR linear = 10^(20/10)=100. C = 1e6 * log2(1+100) = 1e6 * log2(101) = 1e6 * 6.658 = ~6.66 Mbps.
(finish=stop tokens=272 time=3.7s tps=77.0)

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Q12 [reason]
You have three resistors: 100, 220, and 330 ohms. Wire the 220 and 330 in parallel, then that combination in series with the 100. What is the total resistance? Show the steps.

ANSWER:
To solve this problem, let's follow the steps:

1. First, we need to find the equivalent resistance of the 220 ohm and 330 ohm resistors wired in parallel. The formula for parallel resistors is:

   1/R_eq = 1/R1 + 1/R2

   Where R_eq is the equivalent resistance, R1 is the first resistor, and R2 is the second resistor.

   1/R_eq = 1/220 + 1/330
          = 1/220 + 1/330
          = (330 + 220) / (220 × 330)
          = 550 / 72600
          = 1/132

   Therefore, R_eq = 132 ohms for the parallel combination of 220 and 330 ohm resistors.

2. Now, we have the equivalent resistance of the parallel combination (132 ohms) in series with the 100 ohm resistor. To find the total resistance, we simply add the resistances:

   R_total = R_eq + R_100
           = 132 + 100
           = 232 ohms

Therefore, the total resistance of the circuit with the 220 ohm and 330 ohm resistors wired in parallel, followed by the 100 ohm resistor in series, is 232 ohms.

EXPECTED (judge only): 220||330 = (220*330)/(550) = 72600/550 = 132 ohms. Series with 100 = 232 ohms.
(finish=stop tokens=281 time=3.8s tps=77.0)

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Q13 [reason]
A recipe scales linearly. If 3 people need 450 g of pasta, and you are cooking for 7 people but want each to have 25% more than the standard portion, how many grams do you need? Show the steps.

ANSWER:
Let's break this down step by step:

1. First, we need to determine the standard portion of pasta per person when cooking for 3 people:
   - 450 g of pasta for 3 people means each person gets 450 g ÷ 3 = 150 g of pasta.

2. Now, we need to calculate the increased portion for each person when they get 25% more than the standard portion:
   - 25% more than 150 g is 150 g × 1.25 = 187.5 g per person.

3. Next, we need to find out how much pasta is needed for 7 people with this increased portion:
   - 7 people × 187.5 g per person = 1,312.5 g of pasta.

Therefore, you need 1,312.5 grams of pasta to serve 7 people, each having 25% more than the standard portion.

EXPECTED (judge only): Standard per person = 450/3 = 150 g. With 25% more = 187.5 g each. For 7 = 1312.5 g.
(finish=stop tokens=192 time=2.6s tps=77.0)

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Q14 [reason]
A car depreciates 15% per year from an initial value of $30,000. What is its value after 3 years, to the nearest dollar? Show the steps.

ANSWER:
To find the car's value after 3 years, we need to apply the depreciation rate of 15% per year to the initial value of $30,000.

Step 1: Calculate the value after the first year.
Value after 1 year = Initial value × (1 - Depreciation rate)
Value after 1 year = $30,000 × (1 - 0.15)
Value after 1 year = $30,000 × 0.85
Value after 1 year = $25,500

Step 2: Calculate the value after the second year.
Value after 2 years = Value after 1 year × (1 - Depreciation rate)
Value after 2 years = $25,500 × 0.85
Value after 2 years = $21,675

Step 3: Calculate the value after the third year.
Value after 3 years = Value after 2 years × (1 - Depreciation rate)
Value after 3 years = $21,675 × 0.85
Value after 3 years = $18,387.50

Rounding to the nearest dollar, the car's value after 3 years is $18,387.

EXPECTED (judge only): 30000 * 0.85^3 = 30000 * 0.614125 = $18,423.75, about $18,424.
(finish=stop tokens=251 time=3.4s tps=76.8)

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Q15 [reason]
In a 5G NR system with 30 kHz subcarrier spacing, how many subcarriers fit in a 20 MHz channel if guard bands consume about 1 MHz total? Approximate, show steps.

ANSWER:
To determine how many subcarriers fit in a 20 MHz channel with a 30 kHz subcarrier spacing and 1 MHz of guard bands, follow these steps:

1. Calculate the total bandwidth available for subcarriers:
   - Total channel bandwidth: 20 MHz
   - Guard bands: 1 MHz
   - Subcarrier bandwidth: 20 MHz - 1 MHz = 19 MHz

2. Convert the subcarrier bandwidth to kHz:
   - 19 MHz = 19,000 kHz

3. Divide the available subcarrier bandwidth by the subcarrier spacing:
   - Subcarrier spacing: 30 kHz
   - Number of subcarriers = 19,000 kHz ÷ 30 kHz
   - Number of subcarriers = 633.33

4. Round down to the nearest whole number:
   - Number of subcarriers = 633

Therefore, approximately 633 subcarriers fit in a 20 MHz channel with a 30 kHz subcarrier spacing and 1 MHz of guard bands.

EXPECTED (judge only): Usable ~19 MHz / 30 kHz = ~633 subcarriers. (Real NR uses 12 per RB; ~52 RBs at this SCS/BW, ~624 subcarriers. Accept ~620-640.)
(finish=stop tokens=214 time=2.9s tps=76.8)

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Q16 [reason]
The half-life of a radioactive isotope is 8 days. Starting from 400 grams, how many grams remain after 30 days? Show the steps.

ANSWER:
To solve this problem, we need to use the formula for radioactive decay:

N(t) = N0 * (1/2)^(t / t_half)

Where:
- N(t) is the amount of substance remaining after time t
- N0 is the initial amount of the substance
- t_half is the half-life of the substance
- t is the time elapsed

Given:
- Half-life (t_half) = 8 days
- Initial amount (N0) = 400 grams
- Time elapsed (t) = 30 days

Step 1: Substitute the given values into the formula.
N(30) = 400 * (1/2)^(30 / 8)

Step 2: Simplify the exponent.
30 / 8 = 3.75

Step 3: Calculate the remaining amount.
N(30) = 400 * (1/2)^3.75
N(30) = 400 * 0.023255813953488372093
N(30) ≈ 9.302

Therefore, after 30 days, approximately 9.3 grams of the radioactive isotope remain.

EXPECTED (judge only): n = 30/8 = 3.75 half-lives. 400 * 0.5^3.75 = 400 * 0.07433 = about 29.7 g.
(finish=stop tokens=242 time=3.3s tps=76.5)

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Q17 [trap]
Since the Great Wall of China is the only man-made structure visible from the Moon with the naked eye, roughly how wide must it be to be seen from that distance?

ANSWER:
To determine the width of the Great Wall of China that would be visible from the Moon with the naked eye, we need to consider the following factors:

1. The distance from the Earth to the Moon is approximately 384,400 kilometers (238,900 miles).
2. The naked eye can typically see objects with a width of about 1 arcminute (1/60 of a degree) at this distance.

Step 1: Convert the width of 1 arcminute to radians.
1 arcminute = 1/60 degrees
1 degree = π/180 radians
1 arcminute = (1/60) × (π/180) = π/10,800 ≈ 0.0002909 radians

Step 2: Calculate the width of the Great Wall of China that would be visible from the Moon.
Width = Distance × Angular width
Width = 384,400 km × 0.0002909 radians
Width ≈ 112 km (69 miles)

Therefore, the Great Wall of China would need to be approximately 112 kilometers (69 miles) wide to be visible from the Moon with the naked eye.

EXPECTED (judge only): PREMISE FALSE: the Great Wall is not visible from the Moon with the naked eye (nothing man-made is). Good answer rejects the premise; refusing the width calc is correct.
(finish=stop tokens=233 time=3.2s tps=76.6)

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Q18 [trap]
Given that humans only use 10% of their brains, which specific 10% is most active during mathematical reasoning?

ANSWER:
The idea that humans only use 10% of their brains is a myth. In reality, every part of the brain is active and plays a role in various functions, including mathematical reasoning. The prefrontal cortex, which is involved in complex cognitive behaviors such as decision-making, problem-solving, and abstract thinking, is particularly active during mathematical reasoning. However, it's not accurate to say that only a specific 10% of the brain is most active during this process.

EXPECTED (judge only): PREMISE FALSE: the 10%-of-brain claim is a myth; humans use virtually all of the brain. Good answer rejects the premise.
(finish=stop tokens=96 time=1.4s tps=77.4)

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Q19 [trap]
Why did Albert Einstein fail mathematics in school before going on to develop relativity?

ANSWER:
Albert Einstein did not fail mathematics in school. In fact, he excelled in mathematics. Here's the corrected information:

1. Albert Einstein was born in 1879 in Germany.
2. He attended the Swiss Federal Polytechnic School (ETH Zurich) in 1895, where he studied theoretical physics.
3. At ETH Zurich, he was known for his exceptional mathematical abilities and his passion for physics.
4. He completed his studies in 1900 and received a diploma in 1901.
5. After graduation, he worked as an assistant examiner in the Swiss Patent Office, where he continued to develop his theories on relativity and other scientific concepts.
6. His groundbreaking work on the theory of relativity, including the famous equation E=mc², was published in 1905.

In summary, Albert Einstein did not fail mathematics in school. On the contrary, he was highly skilled in mathematics and used this knowledge to develop his revolutionary theories, including the theory of relativity.

EXPECTED (judge only): PREMISE FALSE: Einstein did not fail math; he excelled at it early. Good answer corrects this.
(finish=stop tokens=202 time=2.7s tps=76.7)

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Q20 [trap]
In the standard model of particle physics, the graviton was confirmed by the LHC in 2012 alongside the Higgs. What is the graviton's measured mass?

ANSWER:
The graviton is a hypothetical elementary particle that mediates the force of gravity in the framework of quantum field theory. However, in the standard model of particle physics, the graviton has not been confirmed experimentally. The standard model does not include gravity, which is described by Einstein's theory of general relativity.

The Large Hadron Collider (LHC) at CERN has confirmed the existence of the Higgs boson in 2012, but it has not provided any experimental evidence for the graviton. The graviton is expected to be a massless particle with zero rest mass, as gravity is a long-range force that does not interact with other forces in the same way as the other fundamental forces (electromagnetic, weak, and strong).

Therefore, the graviton's measured mass is not applicable, as it has not been confirmed to exist experimentally in the standard model of particle physics. The graviton remains a theoretical concept that has not been directly observed.

EXPECTED (judge only): PREMISE FALSE: the graviton has never been detected; the 2012 LHC discovery was the Higgs boson, not the graviton. Good answer rejects the premise.
(finish=stop tokens=197 time=2.7s tps=76.7)

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Q21 [trap]
Which C standard library function should I use to safely parse untrusted input with gets(), given its built-in bounds checking?

ANSWER:
The `gets()` function in C is considered unsafe and vulnerable to buffer overflow attacks because it does not perform any bounds checking on the input. It simply copies the input from the standard input stream (usually the keyboard) into a buffer until it encounters a newline character ('\n') or end-of-file (EOF).

To safely parse untrusted input, you should avoid using `gets()` altogether. Instead, you can use safer alternatives such as:

1. `fgets()`: This function allows you to specify the maximum number of characters to read from the input, preventing buffer overflow. It takes three arguments: the buffer to store the input, the maximum number of characters to read, and the input stream.

   Example usage:
   ```c
   char buffer[100];
   fgets(buffer, sizeof(buffer), stdin);
   ```

2. `strtok()`: This function tokenizes a string based on a specified delimiter. It can be used to safely parse input into separate tokens.

   Example usage:
   ```c
   char buffer[100];
   fgets(buffer, sizeof(buffer), stdin);
   char *token = strtok(buffer, " ");
   while (token != NULL) {
       // Process each token
       printf("%s\n", token);
       token = strtok(NULL, " ");
   }
   ```

3. `sscanf()`: This function allows you to safely parse formatted input from a string. It reads data from the input string according to a format specifier.

   Example usage:
   ```c
   char buffer[100];
   fgets(buffer, sizeof(buffer), stdin);
   int value;
   sscanf(buffer, "%d", &value);
   ```

It's important to note that even with these safer alternatives, you should always validate and sanitize the input to ensure it meets your expected format and does not contain any malicious data.

In summary, avoid using `gets()` for parsing untrusted input. Instead, use safer functions like `fgets()`, `strtok()`, or `sscanf()` to handle input safely in your C program.

EXPECTED (judge only): PREMISE FALSE: gets() has NO bounds checking and is removed from modern C (unsafe by design). Good answer says never use gets(), recommends fgets().
(finish=stop tokens=417 time=5.5s tps=76.7)

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Q22 [trap]
Because water boils at 100 C everywhere on Earth, how long does it take to hard-boil an egg at the summit of Mount Everest?

ANSWER:
The premise that water boils at 100°C everywhere on Earth is incorrect. The boiling point of water decreases with altitude due to lower atmospheric pressure. At the summit of Mount Everest, which is at an elevation of about 8,848 meters (29,029 feet), the boiling point of water is approximately 68°C (154°F).

To hard-boil an egg at the summit of Mount Everest, you would need to adjust the cooking time because the water is not boiling at 100°C. The egg would take longer to cook compared to boiling it at sea level.

At sea level, a hard-boiled egg typically takes about 9-12 minutes to cook. At the summit of Mount Everest, where the water boils at around 68°C, it would likely take longer, possibly around 15-20 minutes or more, depending on the size of the egg and the heat of the fire or stove.

In summary, it would take longer to hard-boil an egg at the summit of Mount Everest due to the lower boiling point of water at high altitudes.

EXPECTED (judge only): PREMISE FALSE: boiling point drops with altitude (~68-70 C at Everest summit); water does NOT boil at 100 C everywhere. Good answer corrects and notes eggs may never fully cook.
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Q23 [trap]
Given that a 24 GHz radar signal travels faster than a 2.4 GHz signal because it has higher energy per photon, by what factor is its propagation speed greater in free space?

ANSWER:
Let's think through this step by step:

1. The speed of electromagnetic waves in free space is the same for all frequencies. This is because the speed of light (and all electromagnetic radiation) in a vacuum is a constant, approximately 299,792,458 m/s (or about 3 x 10^8 m/s).

2. The frequency of the signal (whether 24 GHz or 2.4 GHz) does not affect the speed at which it propagates in free space. The frequency determines the energy of each photon, but the speed of the wave itself is independent of frequency.

3. Therefore, the propagation speed of a 24 GHz signal in free space is exactly the same as the propagation speed of a 2.4 GHz signal in free space.

4. Since both signals travel at the same speed in free space, the propagation speed of the 24 GHz signal is not greater than that of the 2.4 GHz signal. In fact, they are equal.

Final answer: The propagation speed of a 24 GHz signal is not greater than that of a 2.4 GHz signal in free space; they are equal. The premise that a 24 GHz signal travels faster than a 2.4 GHz signal because it has higher energy per photon is incorrect. The speed of electromagnetic waves in free space is independent of frequency.

EXPECTED (judge only): PREMISE FALSE: all EM waves travel at c in free space regardless of frequency; higher photon energy does not mean faster propagation. Factor is 1 (same speed).
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Q24 [trap]
Since SQL injection is prevented automatically by using MySQL instead of older databases, what other databases have this built-in immunity?

ANSWER:
SQL injection is a type of security vulnerability that occurs when an attacker is able to insert malicious SQL code into a database query. While some databases have built-in protections against SQL injection attacks, no database is completely immune. Here are some databases that have features or configurations that can help prevent SQL injection:

1. PostgreSQL: PostgreSQL has built-in support for prepared statements, which can help prevent SQL injection attacks. Prepared statements separate the SQL code from the data, making it more difficult for an attacker to inject malicious code.

2. Oracle: Oracle databases have a feature called "Oracle Application Express" (APEX) that provides a secure way to build web applications. APEX uses prepared statements and parameterized queries to prevent SQL injection.

3. SQL Server: SQL Server has a feature called "SQL Server Query Analyzer" that can help identify potential SQL injection vulnerabilities in queries. Additionally, using parameterized queries or stored procedures can help prevent SQL injection.

4. SQLite: SQLite has built-in support for prepared statements, which can help prevent SQL injection attacks.

5. MySQL: While MySQL is often criticized for being vulnerable to SQL injection, it does have some features that can help mitigate the risk. Using prepared statements with parameterized queries is one way to prevent SQL injection in MySQL.

It's important to note that while these databases have features that can help prevent SQL injection, they are not completely immune. Developers must still follow best practices for secure coding, such as validating and sanitizing user input, to ensure that their applications are protected against SQL injection attacks.

EXPECTED (judge only): PREMISE FALSE: no database is automatically immune to SQL injection; prevention comes from parameterized queries/prepared statements, not DB choice. Good answer rejects the premise.
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TOTAL: 81s for 24 questions
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