MikaStars39/nano-eval huggingface dataset:
The indicator that needs to be directly measured through experiments among the three-phase ratio indicators of soil is ( ).

Options:
A. Water content, void ratio, saturation
B. Soil fertility, water content, compressibility
C. Soil structure, water content, texture
D. Particle size distribution, water content, porosity
E. Soil moisture, water content, conductivity
F. Density, water content, void ratio
G. Density, water content, porosity
H. Soil texture, water content, permeability
I. Compaction, water content, organic content
J. Soil particle specific gravity, water content, density
Answer: J
For a strip foundation with a width of 3m, a vertical load acting on the foundation base $\mathrm{N=1,000 kN/m}$, and an eccentricity $\mathrm{e} = 0.7m$, the maximum base pressure is ( ).

Options:
A. 950 kPa
B. 417 kPa
C. 400 kPa
D. 800 kPa
E. 650 kPa
F. 720 kPa
G. 300 kPa
H. 570 kPa
I. 500 kPa
J. 833 kPa
Answer: J
What are the main advantages of cross-linked polyethylene (XLPE) insulation for high-voltage cables?

Options:
A. Increased conductivity and mechanical stability
B. Reduced flexibility and enhanced durability
C. Greater material cost and environmental impact
D. Reduced water permeability and electrical stability
E. Higher thermal conductivity and heat resistance
F. Lower electrical stability and heat resistance
G. Lower thermal stability and fire resistance
H. Greater electrical losses and heat resistance
I. Lower water permeability and heat resistance
J. Higher water absorption and chemical resistance
Answer: H
What is the key factor in the selection of insulating materials for high voltage DC transmission?

Options:
A. optical transmittance
B. magnetic permeability
C. mechanical durability
D. corona resistance
E. dielectric strength
F. reflectivity index
G. seismic stability
H. electrical conductivity
I. thermal conductivity
J. chemical reactivity
Answer: D
In the relay protection of the power system, what characteristics of overcurrent protection can effectively prevent unnecessary tripping?

Options:
A. Endurance time characteristic and current limit characteristic; the current limit characteristic minimizes damage.
B. Definite time characteristic and inverse time characteristic; the inverse time characteristic can prevent maloperation.
C. Operating time characteristic and recovery characteristic; the recovery characteristic is more important for protection.
D. Error margin characteristic and fallback characteristic; the error margin characteristic improves precision.
E. Energization characteristic and phase shift characteristic; the phase shift characteristic aids in detection.
F. Delay time characteristic and directional characteristic; the directional characteristic is used to reduce maloperation.
G. Equipment fault characteristic and load shedding characteristic; the load shedding characteristic handles emergencies.
H. Execution speed characteristic and isolation characteristic; the isolation characteristic is crucial for accuracy.
I. Setting time characteristic and instantaneous action characteristic; the setting time characteristic is more reliable.
J. External fault characteristic and voltage stability characteristic; the external fault characteristic reduces risks.
Answer: B
The materials, cross-sectional areas, and forces applied to two rods are identical, but the length of one rod is twice that of the other. Compare their axial force, normal stress on the cross-section, axial normal strain, and axial deformation. Which of the following answers is correct?

Options:
A. The axial force and normal stress in both rods are the same, but the longer rod has greater normal strain and axial deformation than the shorter rod.
B. The longer rod has greater axial force, normal stress, normal strain, and axial deformation than the shorter rod.
C. The axial force in both rods is the same, but the longer rod has greater normal stress, normal strain, and axial deformation than the shorter rod.
D. The axial force in both rods is the same, but the shorter rod has greater normal stress and axial deformation than the longer rod.
E. The longer rod has the same axial force and normal strain as the shorter rod, but greater axial deformation and normal stress.
F. The axial force and normal stress in both rods are the same, but the longer rod has less normal strain and axial deformation than the shorter rod.
G. The axial force, normal stress, normal strain, and axial deformation of both rods are the same.
H. The axial force, normal stress, and normal strain in both rods are the same, but the longer rod has greater axial deformation than the shorter rod.
I. The axial force and axial deformation in both rods are the same, but the longer rod has greater normal stress and normal strain than the shorter rod.
J. The axial force and normal stress in both rods are the same, but the shorter rod has greater axial deformation than the longer rod.
Answer: H
A small ball under the pressure of still water, which of the following conclusions is incorrect?

Options:
A. The volumetric strain of the small ball should be zero.
B. There is no shear stress at any point within the ball.
C. The stress state at all points within the ball is isotropic.
D. The strain energy due to shape change of the small ball is zero.
Answer: A
What is the "Slip Angle" in vehicle dynamics?

Options:
A. The tilting angle of the vehicle's suspension system
B. Angle of the Vehicle's Center of Gravity Shift
C. The angle between the vehicle's frame and the ground
D. The inclination angle of the vehicle's chassis
E. The Angle of Wheel Rotation
F. The angle difference between the vehicle frame and the ground contact points in the direction of travel
G. The angular displacement of the vehicle's steering wheel
H. The angle difference between the contact points of the wheels and the ground along the direction of travel.
I. The angle of the wheel's rollover
Answer: H
According to the principles of the inclined plate (tube) sedimentation tank, if the tank depth $H$ is equally divided into three layers, then:

Options:
A. without changing the flow velocity $v$ and the minimum settling velocity $u_0$, the tank width $W$ will be reduced by 1/3
B. without altering the flow velocity $v$ and the minimum settling velocity $u_0$, the tank length $L$ will be increased by 2/3
C. without changing the flow velocity $v$ and the minimum settling velocity $u_0$, the tank capacity $C$ will be reduced by 2/3
D. without changing the flow velocity $v$ and the minimum settling velocity $u_0$, the tank length $L$ will be increased by 2/3
E. without changing the flow velocity $v$ and the minimum settling velocity $u_0$, the tank width $W$ will be reduced by 2/3
F. without changing the flow velocity $v$ and the minimum settling velocity $u_0$, the tank length $L$ will be increased by 1/3
G. without altering the flow velocity $v$ and the minimum settling velocity $u_0$, the tank depth $H$ will be reduced by 2/3
H. without changing the flow velocity $v$ and the minimum settling velocity $u_0$, the tank length $L$ will be reduced by 1/3
I. without changing the flow velocity $v$ and the minimum settling velocity $u_0$, the tank length $L$ will be reduced by 2/3
J. without changing the flow velocity $v$ and the minimum settling velocity $u_0$, the tank height $H$ will be reduced by 2/3
Answer: I
Bourdon tube pressure gauges generally have the best accuracy at ( ) of their dial.

Options:
A. 2/3
B. 1/3
C. 4/5
D. 1/5
E. 5/6
F. 3/4
G. 1/4
H. 3/5
I. 1/2
J. 7/8
Answer: A
Which of the following is a rate-based separation process?

Options:
A. Centrifugal Separation
B. Absorption
C. Membrane Separation
D. Chromatography
E. Precipitation
F. Sublimation
G. Filtration
H. Distillation
I. Sedimentation
J. Crystallization
Answer: C
In optical fiber communication systems, which modulation format can enhance the system's dispersion tolerance?

Options:
A. Return-to-Zero (RZ)
B. Non-Return-to-Zero (NRZ)
C. Inverse Frequency Modulation (IFM)
D. Quadrature Frequency Division Multiplexing (QFDM)
E. Continuous Wave Modulation (CWM)
F. Orthogonal Frequency Division Multiplexing (OFDM)
G. Amplitude Modulation (AM)
H. Differential Phase-Shift Keying (DPSK)
I. Pulse Amplitude Modulation (PAM)
J. Frequency-Shift Keying (FSK)
Answer: H
In a photonic integrated circuit, assuming the effective refractive index of the waveguide is 3.5 and the Bragg grating period is 500 nm, calculate the reflection wavelength.

Options:
A. 1450 nm
B. 1429 nm
C. 1550 nm
D. 1350 nm
E. 1900 nm
F. 1800 nm
G. 1700 nm
H. 1200 nm
I. 1625 nm
J. 1675 nm
Answer: C
In a fiber optic communication system using coherent detection technology, if the phase noise of the signal is $1 \times 10^{-4}$ radians and the carrier frequency is 200 THz, calculate the phase error caused by the phase noise (radians).

Options:
A. $$4 \times 10^{-10}$$
B. $$1 \times 10^{-10}$$
C. $$3 \times 10^{-10}$$
D. $$8 \times 10^{-10}$$
E. $$2 \times 10^{-12}$$
F. $$2 \times 10^{-10}$$
G. $$2 \times 10^{-14}$$
H. $$6 \times 10^{-10}$$
I. $$2 \times 10^{-13}$$
J. $$5 \times 10^{-10}$$
Answer: F
In a fiber optic communication system, the signal's state of polarization changes due to the polarization mode dispersion (PMD) of the fiber. If the maximum phase delay induced by PMD is 0.2 radians, find the change in the signal's state of polarization in the worst-case scenario (in radians).

Options:
A. 0.25
B. 0.15
C. 0.2
D. 0.05
E. 0.35
F. 0.3
G. 0.1
H. 0.45
I. 0.4
J. 0.6
Answer: I
In a fiber optic communication system, the signal's optical pulse width is 2 ps. It passes through a fiber with a dispersion parameter of 3000 ps/nm, and the spectral width of the signal is 0.3 nm. Calculate the pulse broadening of the signal (in ps).

Options:
A. 0.18
B. 0.36
C. 18.0
D. 180
E. 0.9
F. 9.0
G. 3.6
H. 1.8
I. 18
J. 180.0
Answer: H
In photonics, for a photonic crystal fiber laser, how can mode stability be ensured?

Options:
A. use single-mode fiber
B. integrate a total reflection coating
C. use multimode optical amplifiers
D. increase the intracavity loss
E. deploy a dual-frequency beam
F. decrease the fiber core diameter
G. apply a Polarization-Maintaining Fiber
H. incorporate a Long-Period Grating (LPG)
I. use highly nonlinear fiber
J. introduce a Fiber Bragg Grating (FBG)
Answer: J
In photonics, the temperature sensitivity of a Fiber Bragg Grating (FBG) can be compensated by:

Options:
A. using shorter fiber lengths
B. employing special grating design
C. increasing ambient humidity
D. increasing the bending of the fiber
E. applying a thermal coating
F. using an electronic feedback system
G. modifying the core diameter
H. using temperature-insensitive fiber
I. utilizing different light sources
J. adjusting the refractive index
Answer: B
Which of the following is a love song from the time of Yu the Great, expressing the longing of Yu's wife, the daughter of Tushan, for him?

Options:
A. Waiting for someone
B. When will the days fade? Both you and I
C. Great Xia
D. Fading Sun
E. Spring Blossom
F. Silent Dawn
G. Departed Heart
H. Mountain Song
I. River's Lament
J. Big Crossing
Answer: A
Which of the following works is a representative piece by Mao Minzhong?

Options:
A. Wangji Tune
B. Melody of Spring
C. Sunset over River
D. The Water and Clouds of Xiaoxiang
E. Autumn Moonlight
F. Zepan Chant
G. Sky Resonance
H. Song of the Mountains
I. Fisherman's Song
J. Night Whisperings
Answer: F
Which of the following warehousing methods can minimize the risk of goods being lost to the greatest extent?

Options:
A. Centralized
B. Distributed
C. Isolated
D. Virtual
E. Decentralized
F. Hierarchical
G. Fragmented
H. Condensed
I. Segregated
J. Rotational
Answer: A
What is meant by "asymmetrical beats"?

Options:
A. the notes have different values
B. the tempo changes sporadically
C. the melody skips random notes
D. the pitch varies unexpectedly
E. the accents shift unpredictably
F. the beats are at irregular intervals
G. the chords are randomly played
H. the bars are not of the same length
I. the rhythm is inconsistently timed
J. the harmony is unevenly spaced
Answer: H
Which of the following fractures is the most serious type of skull fracture?

Options:
A. zygomatic cranial fossa fracture
B. middle cranial fossa fracture
C. parietal cranial lobe fracture
D. lateral cranial ridge fracture
E. posterior cranial fossa fracture
F. basal cranial fossa fracture
G. temporal cranial fissure fracture
H. anterior cranial fossa fracture
I. occipital cranial joint fracture
J. frontal cranial fossa fracture
Answer: E
What is the most effective method for controlling bovine tuberculosis?

Options:
A. Conduct regular blood tests
B. Rotate grazing pastures
C. Enhance genetic selection
D. Improve ventilation systems
E. Implement hygiene protocols
F. Increase cattle exercise
G. Change feed
H. Isolate infected cattle
I. Use antibiotics
J. Vaccinate
Answer: H
The on-site mixed concrete is found to have poor cohesiveness. What is the most feasible improvement measure?

Options:
A. Increase the admixture proportion
B. Increase the amount of cement used
C. Add cement slurry (without changing W/C)
D. Reduce the cementitious content
E. Add CaSO4
F. Adjust water content for consistency
G. Add lime to the concrete mix
H. Use a different type of aggregate
I. Decrease aggregate size for better mix
J. Increase the sand ratio appropriately
Answer: J
The most effective medication for treating Trichodina (wheelworm) disease is ().

Options:
A. Hydrogen peroxide
B. Quicklime
C. Bleaching powder
D. Methanol
E. Potassium permanganate
F. Copper sulfate
G. Sodium chloride
H. Vinegar
I. Formaldehyde
J. Salt
Answer: F
In the application of game theory, which economist first introduced the method for the study of defense economics?

Options:
A. Zhang Wei
B. Yu Shang
C. Peter Long
D. Liu Ming
E. Du Weigong
F. Eric Hung
G. Hartley
H. Karl Bene
I. Xie Lin
J. Nash
Answer: I
In cases of otogenic peripheral facial paralysis, which segment of the facial nerve is most likely to be affected?

Options:
A. Labyrinthine segment
B. Intracranial segment
C. Geniculate ganglion
D. Vertical segment
E. Tympanic segment
F. Extracranial segment
G. Mastoid segment
H. Facial canal segment
I. Petrotympanic segment
J. Stylomastoid foramen
Answer: E
Regarding petrositis, which of the following statements is incorrect?

Options:
A. Petrosal apex syndrome is often marked by ear discharge, severe ear pain, and dizziness with nausea
B. Petrosal apex syndrome typically presents with facial numbness, severe headache, and visual disturbances
C. Petrosal apex syndrome manifests through scalp tenderness, unilateral hearing loss, and impaired balance
D. It is mostly caused by purulent infection of the air cells in the petrous part of the temporal bone
E. For pus accumulation in the petrous apex, especially when multiple abscesses cannot be cured, a petrous apex resection is required
F. After mastoid surgery, if there is no more ear discharge and then suddenly a large amount of pus is discharged, accompanied by trigeminal neuralgia and a rise in body temperature, this condition should be considered
G. Petrosal apex syndrome may involve symptoms like vertigo, hearing loss, and absence of pupil reflex
H. Petrosal apex syndrome may occur with symptoms including jaw pain, neck stiffness, and altered mental status
I. Petrosal apex syndrome may occur, characterized by paralysis of the medial rectus muscle, pain in the distribution of the abducens nerve, and localized meningeal symptoms
J. Pain is experienced in the frontal region on the affected side, often felt around the eye, and may radiate to the forehead, temple, cheek, and teeth
Answer: I
Most otosclerotic lesions originate from ()

Options:
A. Lateral to the cochlear base
B. Oval window
C. Internal auditory canal
D. Superior to the auditory canal
E. Inferior to the oval window
F. Anterior to the vestibular window
G. Semicircular canals
H. Base of the cochlea
I. Medial to the semicircular canal
J. Posterior to the vestibular window
Answer: F
In what year was the Scripps Press founded?

Options:
A. 1890
B. 1876
C. 1895
D. 1879
E. 1885
F. 1903
G. 1898
H. 1889
I. 1892
J. 1901
Answer: H
Considering the refractive index of an optical fiber, what is the usual refractive index distribution of a single-mode fiber?

Options:
A. Variable
B. Gradient
C. Spiral
D. Concentric
E. Symmetric
F. Alternating
G. Helical
H. Radial
I. Fluctuating
Answer: B
In amplification circuits, what is the most effective method to reduce input impedance?

Options:
A. Decreasing the Gain Factor
B. Changing the Feedback Loop
C. Modifying Input Capacitor
D. Using a Source Follower
E. Using a Voltage Divider
F. Reducing the Power Supply
G. Altering the Load Resistor
H. Adding an Emitter Follower
I. Increasing the Bias Voltage
J. Employing a Darlington Pair
Answer: D
Which two minerals are the most important for the health of pigs?

Options:
A. Magnesium, Calcium
B. Zinc, Calcium
C. Manganese, Molybdenum
D. Iron, Zinc
E. Cobalt, Phosphorus
F. Copper, Zinc
G. Phosphorus, Cobalt
H. Molybdenum, Selenium
I. Manganese, Selenium
J. Calcium, Phosphorus
Answer: D
A rotary vacuum filter is used to filter a suspension. 2.36 m³ of filtrate can be obtained per hour. The operating vacuum is 53000 Pa. The filtration constant K = 5.15×10⁻⁶ m²/s. If you want to use a BMS30/635-25 type (the length and width of the filter frame are both 635 mm, the thickness is 25 mm, and the total number of frames is 38) plate and frame filter press to complete the same task, what is the filtration pressure difference of this plate and frame filter press? Known: The filter cake is incompressible, the medium resistance can be ignored, and the filter cake obtained by sending out 1 m³ of filtrate contains 273 kg of solid phase, the solid phase density is 1500 kg/m³, and the solid phase fraction in the filter cake is 0.56. The filter cake does not need to be washed, and the auxiliary operation time of each cycle of the plate and frame filter press is 15 minutes.

Options:
A. 118246 Pa
B. 112675 Pa
C. 134256 Pa
D. 120315 Pa
E. 110582 Pa
F. 102489 Pa
G. 98352 Pa
H. 117524 Pa
I. 125847 Pa
J. 96124 Pa
Answer: A
A certain flow of liquid is turbulently flowing in a $\phi25$ mm$\times2.5$ mm straight tube, and its convective heat transfer coefficient $\alpha = 1000$ W/(m²·°C); if the flow rate and physical properties remain unchanged, and a $\phi19$ mm$\times2$ mm straight tube is used instead, then its $\alpha$ will become ().

Options:
A. 1800
B. 1200
C. 2100
D. 750
E. 1100
F. 1678
G. 1600
H. 850
I. 1900
J. 1450
Answer: F
What is the equivalent diameter of a fluid flowing in a rectangular pipe with a height of $2*3m$?

Options:
A. 3.6m
B. 3.2m
C. 4.0m
D. 1.5m
E. 2.0m
F. 2.4m
G. 1.8m
H. 3.0m
I. 2.5m
J. 2.7m
Answer: F
When a centrifugal pump works in a certain pipeline system, the head is independent of the density of the liquid being transported. What is the condition?

Options:
A. The velocity gradient along the pipe is constant.
B. The temperature gradient along the pipeline is zero.
C. The static pressure increases linearly with distance.
D. The pump's impeller diameter remains unchanged.
E. The flow rate is inversely proportional to pipe length.
F. The pressure difference between the two sections is zero.
G. The volumetric flow rate varies with liquid density.
H. The friction factor within the pipe is uniform.
I. The liquid's viscosity changes at constant intervals.
J. The cross-sectional area of the pipeline fluctuates.
Answer: F
Calculate the number of combinations \( n \) and the combination distance \(\delta X\), given that the apparent wavelength of the reflected wave \(\lambda_s\) is 244m, and the maximum and minimum apparent wavelengths of the interference wave are \(\lambda_{max} = 43m\) and \(\lambda_{min} = 18m\). What is the value of \( n \)?

Options:
A. 0
B. 4
C. 9
D. 2
E. 8
F. 1
G. 6
H. 5
I. 3
J. 7
Answer: I
Which of the following factors will most significantly affect the mechanical properties of wood?

Options:
A. soil type
B. color
C. leaf size
D. tree height
E. sap content
F. moisture content
G. annual ring width
H. bark texture
I. density
J. growth environment
Answer: I
What is the most important consideration when selecting an irrigation system?

Options:
A. ease of installation process
B. cost of initial investment
C. suitability for local crops
D. availability and quality of water
E. maintenance and repair needs
F. need for advanced technology
G. compatibility with soil type
H. impact on local wildlife
Answer: D
Which of the following is not part of the "Figaro Trilogy"?

Options:
A. The School for Wives
B. Eugenie
C. The Barber of Seville
D. The Marriage of Figaro
E. The Miraculous Mandarin
F. The Flying Dutchman
G. The Guilty Mother
H. The Magic Flute
I. The Misanthrope
J. The Imaginary Invalid
Answer: B
A tenant was broke and needed money to pay her rent.
The tenant recalled that one of her neighbor's had admired a painting she owned. The tenant asked the neighbor if he would be interested in buying the painting. The painting was worth $10,000, but the neighbor offered her only \$2,000, saying, "take it or leave it." The tenant was so desperate that she accepted his offer. The tenant and the neighbor agreed that the neighbor would bring the tenant a check the next day, at which time she would give him the painting. There was no written agreement. The next day, the tenant had second thoughts and refused to sell the painting to the neighbor. The neighbor sued the tenant to force the tenant to sell the painting, but the court refused to force the tenant to go forward with the sale.
Which of the following states the most likely ground(s) for the court's refusal to enforce the sale contract?

Options:
A. Only the statute of frauds and duress.
B. The statute of frauds, coercion, and inadequate consideration.
C. Only the statute of frauds.
D. The statute of frauds, unconscionability, and coercion.
E. Only the statute of frauds and unconscionability.
F. The statute of frauds, undue influence, and duress.
G. Only the statute of frauds and undue influence.
H. The statute of frauds, duress, and inadequate consideration.
I. Only the statute of frauds and equitable estoppel.
J. Only the statute of frauds and inadequate consideration.
Answer: C
In which of the following systems, is encryption slower than decryption?

Options:
A. antisymmetric cryptography
B. polynomial key cryptography
C. quantum cryptographic algorithms
D. parabolic curve cryptography
E. elliptic curve cryptography
F. direct point cryptography
G. reversible key algorithms
H. elliptic quantum cryptography
I. symmetric cryptography
J. asymmetric curve decryption
Answer: D
Which of the following statements about the purpose of radiation protection is incorrect?

Options:
A. Protecting Humanity
B. Restrict all practices related to radiation exposure.
C. Avoid the occurrence of deterministic effects and reduce the probability of stochastic effects to a reasonably achievable minimum level.
D. Protecting the Environment
Answer: B
Given 1 kg of propane ( $\mathrm{C_{3}H_{8}}$), when compressed to 10,132.5 kPa, its volume becomes $7.81 \ \mathrm{dm}^{3}$. Determine the temperature of this compressed gas. (Known: the molar mass of propane $M=44.09 \ \ \mathrm{g/mol} \,, \ T_{c} =$ 369.82 $\mathrm{K} \,, p_{\mathrm{c}}=4247 \ \mathrm{kPa}$.)

Options:
A. $580K$
B. $350K$
C. $520K$
D. $560K$
E. $600K$
F. $460K$
G. $540K$
H. $430K$
I. $620K$
J. $490K$
Answer: G
The vertical force on the top surface of the rectangular foundation of plain concrete under the column $( F_{k} )$ is 570 kN, with the foundation width set at 2.0 m and the column base width at 0.40 m. Within a depth of 6 m below the indoor floor, there is a homogeneous silt layer with $\gamma=\gamma_{\mathrm{m}}=20 \mathrm{kN/m^3}$, $f_{\mathrm{a k}}=150 \mathrm{kPa}$, and a clay content of $\boldsymbol{\rho}_{\mathrm{c}}=7\%$. Based on the above conditions and China's 'Code for Design of Building Foundation' (GB 50007-2002), the burial depth of the column foundation should not be less than which of the following options (taking the average weight density of the foundation and the soil above the foundation $\gamma$ as 20 kN/m³)?

Options:
A. 1.05m
B. 1.00m
C. 0.80m
D. 1.20m
E. 0.90m
F. 1.30m
G. 1.15m
H. 1.10m
I. 1.40m
J. 1.25m
Answer: C
We now define an algorithm: The definition of a(n) is: Conjectured upper bound on the area of the convex hull of any edge-to-edge connected system of n regular unit hexagons (n-polyhexes). Given the input x_list (a series of values): [47, 48, 49, 50, 51, 52, 53, 54, 55, 56], determine the corresponding output sequence y_list.

Options:
A. [406, 423, 440, 457, 475, 492, 511, 529, 547, 566]
B. [407, 425, 443, 458, 476, 493, 512, 530, 549, 568]
C. [409, 427, 444, 461, 479, 497, 516, 534, 553, 572]
D. [402, 418, 435, 452, 470, 487, 506, 523, 542, 561]
E. [405, 422, 437, 454, 471, 489, 508, 525, 544, 563]
F. [404, 421, 438, 455, 473, 491, 509, 528, 547, 566]
G. [408, 426, 442, 459, 478, 496, 514, 533, 552, 571]
H. [403, 419, 436, 451, 469, 488, 507, 526, 545, 564]
I. [410, 428, 446, 462, 481, 498, 517, 536, 555, 574]
J. [401, 417, 434, 450, 467, 485, 504, 522, 540, 559]
Answer: F
We now define an algorithm: The definition of a(n) is: Minimal total number of edges in a polyhex consisting of n hexagonal cells, where a polyhex is a plane figure composed of hexagonal cells that share sides. Given the input x_list (a series of values): [52, 53, 54, 55, 56, 57, 58, 59, 60, 61], determine the corresponding output sequence y_list.

Options:
A. [178, 182, 185, 188, 191, 195, 198, 201, 204, 207]
B. [179, 183, 186, 188, 192, 195, 198, 202, 205, 209]
C. [180, 184, 186, 190, 193, 197, 200, 203, 206, 209]
D. [182, 186, 189, 192, 195, 199, 202, 205, 208, 211]
E. [181, 185, 188, 191, 194, 198, 201, 204, 207, 210]
F. [182, 186, 188, 191, 194, 198, 200, 203, 206, 210]
G. [180, 184, 187, 190, 193, 197, 200, 203, 206, 209]
H. [183, 187, 189, 193, 196, 200, 202, 205, 208, 212]
I. [179, 183, 187, 189, 192, 196, 199, 202, 205, 208]
J. [184, 188, 190, 194, 197, 201, 203, 206, 209, 213]
Answer: E
We now define an algorithm: The definition of a(n) is the number of unique polyominoes that can be formed using 3 regular unit n-gons. Given the input x_list (a series of values): [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], determine the corresponding output sequence y_list.

Options:
A. [24, 25, 24, 25, 25, 27, 26, 27, 26, 27]
B. [23, 24, 24, 25, 25, 25, 26, 27, 26, 26]
C. [24, 25, 24, 25, 25, 26, 26, 27, 26, 27]
D. [23, 25, 23, 25, 25, 26, 27, 27, 26, 27]
E. [24, 25, 24, 26, 25, 26, 26, 26, 26, 27]
F. [24, 25, 25, 25, 25, 26, 27, 27, 26, 27]
G. [24, 25, 24, 25, 24, 26, 26, 27, 27, 27]
H. [23, 25, 23, 25, 25, 26, 25, 27, 27, 27]
I. [24, 24, 24, 25, 26, 26, 26, 26, 27, 27]
J. [24, 24, 24, 25, 25, 26, 26, 27, 26, 26]
Answer: C
We now define an algorithm: The definition of a(n) is the coordination sequence for a node of type V1 in the "krs" 2-dimensional tiling (or net). Given the input x_list (a series of values): [47, 48, 49, 50, 51, 52, 53, 54, 55, 56], determine the corresponding output sequence y_list.

Options:
A. [226, 194, 233, 236, 210, 243, 254, 218, 262, 264]
B. [221, 189, 229, 231, 205, 239, 249, 213, 257, 259]
C. [220, 188, 227, 230, 204, 237, 248, 212, 256, 258]
D. [224, 191, 228, 234, 208, 238, 252, 216, 260, 262]
E. [219, 187, 226, 229, 203, 236, 247, 211, 255, 257]
F. [225, 193, 232, 235, 209, 242, 253, 217, 261, 263]
G. [218, 186, 225, 228, 202, 235, 246, 210, 254, 256]
H. [223, 192, 231, 233, 207, 241, 251, 215, 259, 261]
I. [227, 195, 234, 237, 211, 244, 255, 219, 263, 265]
J. [222, 190, 230, 232, 206, 240, 250, 214, 258, 260]
Answer: J
We now define an algorithm: The definition of a(n) is the crystal ball sequence for a two-dimensional net known as the 4.8.8 tiling in mathematical crystallography. Given the input x_list (a series of values): [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], determine the corresponding output sequence y_list.

Options:
A. [2201, 2310, 2422, 2537, 2654, 2774, 2897, 3022, 3150, 3281]
B. [2160, 2270, 2383, 2499, 2617, 2738, 2861, 2986, 3114, 3245]
C. [2170, 2280, 2393, 2509, 2627, 2748, 2871, 2996, 3124, 3255]
D. [2175, 2284, 2397, 2512, 2630, 2750, 2873, 2998, 3126, 3257]
E. [2215, 2325, 2438, 2553, 2671, 2792, 2915, 3040, 3168, 3299]
F. [2188, 2297, 2409, 2524, 2641, 2761, 2884, 3009, 3137, 3268]
G. [2205, 2314, 2427, 2542, 2660, 2780, 2903, 3028, 3156, 3287]
H. [2195, 2304, 2417, 2532, 2650, 2770, 2893, 3018, 3146, 3277]
I. [2180, 2289, 2401, 2516, 2633, 2753, 2876, 3001, 3129, 3260]
J. [2192, 2302, 2415, 2530, 2648, 2769, 2892, 3017, 3145, 3276]
Answer: F
We now define an algorithm: The definition of a(n) is a(2n) and a(2n+1) are side lengths of a Beentjes sequence of perfect squared rectangles, starting with a 33 X 32 rectangle. Given the input x_list (a series of values): [13, 14, 15, 16, 17, 18, 19, 20, 21, 22], determine the corresponding output sequence y_list.

Options:
A. [4399793634, 86445553381, 98563095573, 1936532042761, 2207986245072, 43381714920931, 49462765251501, 971826516645091, 1108052711738430, 21770618800480141]
B. [4399793630, 86445553377, 98563095569, 1936532042757, 2207986245068, 43381714920927, 49462765251497, 971826516645087, 1108052711738426, 21770618800480137]
C. [4399793629, 86445553376, 98563095568, 1936532042756, 2207986245067, 43381714920926, 49462765251496, 971826516645086, 1108052711738425, 21770618800480136]
D. [4399793627, 86445553374, 98563095566, 1936532042754, 2207986245065, 43381714920924, 49462765251494, 971826516645084, 1108052711738423, 21770618800480134]
E. [4399793628, 86445553375, 98563095567, 1936532042755, 2207986245066, 43381714920925, 49462765251495, 971826516645085, 1108052711738424, 21770618800480135]
F. [4399793631, 86445553378, 98563095570, 1936532042758, 2207986245069, 43381714920928, 49462765251498, 971826516645088, 1108052711738427, 21770618800480138]
G. [4399793633, 86445553380, 98563095572, 1936532042760, 2207986245071, 43381714920930, 49462765251500, 971826516645090, 1108052711738429, 21770618800480140]
H. [4399793625, 86445553372, 98563095564, 1936532042752, 2207986245063, 43381714920922, 49462765251492, 971826516645082, 1108052711738421, 21770618800480132]
I. [4399793632, 86445553379, 98563095571, 1936532042759, 2207986245070, 43381714920929, 49462765251499, 971826516645089, 1108052711738428, 21770618800480139]
J. [4399793626, 86445553373, 98563095565, 1936532042753, 2207986245064, 43381714920923, 49462765251493, 971826516645083, 1108052711738422, 21770618800480133]
Answer: J
We now define an algorithm: The definition of a(n) is: Array read by antidiagonals: number of antichains (or order ideals) in the poset 3*m*n or plane partitions with rows <= m, columns <= n, and entries <= 3, where m and n are dimensions of the grid and entries are constrained by the value 3. Given the input x_list (a series of values): [45, 46, 47, 48, 49, 50, 51, 52, 53, 54], determine the corresponding output sequence y_list.

Options:
A. [2, 166, 4951, 41581, 116425, 116425, 41581, 4951, 166, 2]
B. [1, 165, 4950, 41580, 116425, 116423, 41580, 4950, 165, 2]
C. [1, 165, 4950, 41580, 116424, 116424, 41580, 4950, 165, 1]
D. [1, 166, 4950, 41579, 116424, 116424, 41579, 4950, 166, 1]
E. [3, 165, 4948, 41580, 116424, 116426, 41580, 4948, 165, 3]
F. [1, 165, 4951, 41581, 116425, 116425, 41581, 4951, 165, 1]
G. [1, 164, 4950, 41580, 116425, 116425, 41580, 4950, 164, 1]
H. [0, 164, 4949, 41579, 116423, 116423, 41579, 4949, 164, 0]
I. [1, 166, 4950, 41580, 116424, 116423, 41580, 4950, 166, 1]
J. [1, 165, 4951, 41582, 116426, 116424, 41579, 4949, 165, 1]
Answer: C
We now define an algorithm: The definition of a(n) is: Number of matched parentheses and brackets of length n, where a closing bracket will close any remaining open parentheses back to the matching open bracket (as in some versions of LISP). Given the input x_list (a series of values): [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], determine the corresponding output sequence y_list.

Options:
A. [332366533, 1075228780, 3513373376, 11456961542, 37590603304, 123327267523, 406246177503, 1339274997443, 4427777075489, 14655559052678]
B. [332366531, 1075228777, 3513373378, 11456961544, 37590603306, 123327267525, 406246177505, 1339274997445, 4427777075491, 14655559052680]
C. [332366527, 1075228771, 3513373372, 11456961548, 37590603310, 123327267529, 406246177509, 1339274997449, 4427777075495, 14655559052684]
D. [332365524, 1075228772, 3513373373, 11456961549, 37590603311, 123327267530, 406246177510, 1339274997450, 4427777075496, 14655559052685]
E. [332366530, 1075228776, 3513373379, 11456961545, 37590603307, 123327267526, 406246177506, 1339274997446, 4427777075492, 14655559052681]
F. [332366524, 1075228770, 3513373371, 11456961547, 37590603309, 123327267528, 406246177508, 1339274997448, 4427777075494, 14655559052683]
G. [332366526, 1075228773, 3513373374, 11456961550, 37590603312, 123327267531, 406246177511, 1339274997451, 4427777075497, 14655559052686]
H. [332366532, 1075228779, 3513373377, 11456961543, 37590603305, 123327267524, 406246177504, 1339274997444, 4427777075490, 14655559052679]
I. [332366525, 1075228774, 3513373375, 11456961551, 37590603313, 123327267532, 406246177512, 1339274997452, 4427777075498, 14655559052687]
J. [332366529, 1075228775, 3513373370, 11456961546, 37590603308, 123327267527, 406246177507, 1339274997447, 4427777075493, 14655559052682]
Answer: G
We now define an algorithm: The definition of a(n) is Catalan's triangle with right border removed, for n > 0 and 0 <= k < n. Given the input x_list (a series of values): [57, 58, 59, 60, 61, 62, 63, 64, 65, 66], determine the corresponding output sequence y_list.

Options:
A. [15, 69, 277, 914, 2552, 6192, 13264, 25198, 41994, 58790]
B. [13, 67, 275, 912, 2550, 6190, 13262, 25196, 41992, 58788]
C. [12, 66, 274, 911, 2549, 6189, 13261, 25195, 41991, 58787]
D. [14, 68, 276, 913, 2551, 6191, 13263, 25197, 41993, 58789]
E. [11, 65, 273, 910, 2548, 6188, 13260, 25194, 41990, 58786]
F. [20, 74, 282, 919, 2557, 6197, 13269, 25203, 41999, 58795]
G. [19, 73, 281, 918, 2556, 6196, 13268, 25202, 41998, 58794]
H. [18, 72, 280, 917, 2555, 6195, 13267, 25201, 41997, 58793]
I. [17, 71, 279, 916, 2554, 6194, 13266, 25200, 41996, 58792]
J. [16, 70, 278, 915, 2553, 6193, 13265, 25199, 41995, 58791]
Answer: E
We now define an algorithm: The definition of a(n) is: For n>=2, the number of (s(0), s(1), ..., s(n-1)) such that 0 < s(i) < 5 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n-1, s(0) = 2, s(n-1) = 2. Given the input x_list (a series of values): [19, 20, 21, 22, 23, 24, 25, 26, 27, 28], determine the corresponding output sequence y_list.

Options:
A. [12079787, 31624365, 82792241, 216750691, 567457148, 1485616472, 3889385433, 10182528791, 26658183179, 69791991999]
B. [12079707, 31624285, 82792161, 216750601, 567457058, 1485616392, 3889385353, 10182528721, 26658183099, 69791991919]
C. [12079717, 31624295, 82792171, 216750621, 567457078, 1485616402, 3889385363, 10182528711, 26658183109, 69791991929]
D. [12079747, 31624325, 82792201, 216750651, 567457108, 1485616432, 3889385393, 10182528751, 26658183139, 69791991959]
E. [12079737, 31624315, 82792191, 216750641, 567457098, 1485616422, 3889385383, 10182528741, 26658183129, 69791991949]
F. [12079607, 31624275, 82792151, 216750611, 567457068, 1485616382, 3889385343, 10182528731, 26658183089, 69791991909]
G. [12079757, 31624335, 82792211, 216750661, 567457118, 1485616442, 3889385403, 10182528761, 26658183149, 69791991969]
H. [12079777, 31624355, 82792231, 216750681, 567457138, 1485616462, 3889385423, 10182528781, 26658183169, 69791991989]
I. [12079767, 31624345, 82792221, 216750671, 567457128, 1485616452, 3889385413, 10182528771, 26658183159, 69791991979]
J. [12079727, 31624305, 82792181, 216750631, 567457088, 1485616412, 3889385373, 10182528701, 26658183119, 69791991939]
Answer: B
We now define an algorithm: The definition of a(n) is the number of partitions of 2*n into at most 4 parts, where each part is a non-negative integer. Given the input x_list (a series of values): [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], determine the corresponding output sequence y_list.

Options:
A. [4272, 4579, 4890, 5241, 5589, 5962, 6343, 6739, 7157, 7589]
B. [4268, 4574, 4892, 5232, 5582, 5953, 6337, 6732, 7154, 7581]
C. [4260, 4568, 4891, 5238, 5579, 5956, 6333, 6729, 7148, 7582]
D. [4269, 4575, 4899, 5240, 5585, 5960, 6338, 6737, 7159, 7590]
E. [4265, 4570, 4895, 5233, 5583, 5951, 6331, 6735, 7152, 7583]
F. [4271, 4578, 4896, 5239, 5588, 5959, 6341, 6738, 7161, 7587]
G. [4263, 4571, 4894, 5231, 5584, 5952, 6336, 6736, 7153, 7586]
H. [4270, 4577, 4893, 5236, 5586, 5958, 6332, 6740, 7155, 7591]
I. [4267, 4576, 4898, 5235, 5587, 5957, 6340, 6733, 7156, 7588]
J. [4264, 4573, 4897, 5230, 5581, 5954, 6335, 6734, 7158, 7585]
Answer: G
We now define an algorithm: The definition of a(n) is: Triangle T(n,k) of number of minimal 2-covers of a labeled n-set that cover k points of that set uniquely (k=2,..,n). A 2-cover of a set is a collection of pairs of elements from the set such that each element is included in at least one pair. Minimal means that no proper subset of the 2-cover still covers all elements. Given the input x_list (a series of values): [45, 46, 47, 48, 49, 50, 51, 52, 53, 54], determine the corresponding output sequence y_list.

Options:
A. [2548, 509, 59, 496, 2307, 6931, 14335, 20784, 20956, 14027]
B. [2560, 515, 58, 500, 2315, 6935, 14325, 20780, 20950, 14030]
C. [2559, 512, 54, 492, 2318, 6934, 14308, 20779, 20958, 14022]
D. [2550, 511, 55, 495, 2310, 6930, 14322, 20790, 20955, 14025]
E. [2555, 520, 50, 490, 2300, 6920, 14320, 20795, 20950, 14020]
F. [2561, 513, 52, 494, 2302, 6932, 14328, 20789, 20953, 14028]
G. [2545, 511, 65, 500, 2310, 6925, 14315, 20775, 20945, 14015]
H. [2552, 517, 51, 499, 2325, 6919, 14329, 20791, 20957, 14022]
I. [2540, 510, 60, 490, 2305, 6935, 14330, 20785, 20965, 14035]
J. [2550, 505, 53, 485, 2320, 6940, 14310, 20785, 20960, 14040]
Answer: D
We now define an algorithm: The definition of a(n) is: Sequence contains no 3-term arithmetic progression, other than its initial terms 1, 2, 3. The sequence is constructed such that after the terms 1, 2, 3, each additional term is chosen to avoid forming any new 3-term arithmetic progression with the previous terms. Given the input x_list (a series of values): [48, 49, 50, 51, 52, 53, 54, 55, 56, 57], determine the corresponding output sequence y_list.

Options:
A. [316, 317, 354, 355, 359, 362, 364, 365, 371, 372]
B. [317, 318, 358, 362, 363, 364, 367, 368, 371, 373]
C. [314, 317, 355, 359, 362, 363, 368, 369, 370, 372]
D. [313, 315, 353, 356, 363, 364, 365, 368, 372, 373]
E. [315, 316, 357, 358, 360, 361, 366, 367, 369, 370]
F. [312, 319, 355, 361, 365, 367, 369, 370, 372, 374]
G. [311, 320, 356, 357, 363, 366, 368, 369, 371, 375]
H. [313, 319, 357, 359, 364, 365, 368, 369, 370, 375]
I. [318, 319, 360, 361, 362, 365, 367, 368, 370, 371]
J. [316, 318, 356, 359, 360, 364, 365, 368, 371, 374]
Answer: E
We now define an algorithm: The definition of a(n) is: Reversed binary words of length up to n in reversed lexicographic order. Given the input x_list (a series of values): [55, 56, 57, 58, 59, 60, 61, 62, 63, 64], determine the corresponding output sequence y_list.

Options:
A. [62, 63, 58, 61, 60, 57, 54, 46, 35, 69]
B. [64, 61, 59, 62, 58, 56, 52, 44, 37, 71]
C. [63, 59, 64, 58, 60, 62, 53, 45, 36, 70]
D. [58, 59, 60, 62, 63, 61, 57, 49, 31, 64]
E. [55, 62, 61, 57, 63, 59, 51, 43, 38, 72]
F. [60, 57, 62, 61, 64, 56, 55, 47, 33, 66]
G. [61, 56, 62, 60, 59, 58, 56, 51, 30, 68]
H. [59, 58, 61, 63, 62, 60, 56, 48, 32, 65]
I. [56, 58, 60, 63, 57, 61, 50, 42, 39, 73]
J. [57, 60, 63, 59, 61, 63, 55, 50, 34, 67]
Answer: H
We now define an algorithm: The definition of a(n) is the n-th letter of the infinite word generated from w(1)=1 inductively by w(n)=JUXTAPOSITION{w(n-1),w\'(n-1),w"(n-1)}, where w(k) becomes w\'(k) by the cyclic permutation 1->2->3->1 and w"(k) = (w\')\'(k), using the cyclic permutation rules. Given the input x_list (a series of values): [96, 97, 98, 99, 100, 101, 102, 103, 104, 105], determine the corresponding output sequence y_list.

Options:
A. [3, 3, 1, 2, 2, 1, 1, 2, 3, 2]
B. [2, 2, 1, 3, 1, 3, 2, 1, 2, 3]
C. [3, 1, 3, 2, 2, 1, 3, 1, 2, 2]
D. [2, 1, 2, 3, 3, 2, 1, 3, 1, 2]
E. [3, 2, 3, 1, 1, 2, 3, 2, 3, 1]
F. [2, 3, 1, 2, 3, 1, 2, 2, 1, 3]
G. [3, 1, 2, 2, 1, 2, 3, 1, 3, 1]
H. [1, 1, 2, 3, 2, 3, 1, 1, 2, 3]
I. [1, 2, 3, 1, 2, 3, 3, 1, 2, 1]
J. [2, 3, 1, 1, 3, 1, 2, 3, 1, 2]
Answer: E
We now define an algorithm: The definition of a(n) is: Number of ON cells at the n-th generation of a one-dimensional cellular automaton defined by Rule 150, starting with a single ON cell at generation 0, where Rule 150 follows the rules for updating cells based on their neighbors as described in elementary cellular automata. Given the input x_list (a series of values): [65, 66, 67, 68, 69, 70, 71, 72, 73, 74], determine the corresponding output sequence y_list.

Options:
A. [6, 6, 12, 6, 24, 12, 30, 6, 24, 24]
B. [7, 7, 13, 7, 25, 13, 31, 7, 25, 25]
C. [9, 9, 15, 9, 27, 15, 33, 9, 27, 27]
D. [8, 8, 14, 8, 26, 14, 32, 8, 26, 26]
E. [12, 12, 18, 12, 30, 18, 36, 12, 30, 30]
F. [5, 5, 11, 5, 23, 11, 29, 5, 23, 23]
G. [14, 14, 20, 14, 32, 20, 38, 14, 32, 32]
H. [13, 13, 19, 13, 31, 19, 37, 13, 31, 31]
I. [10, 10, 16, 10, 28, 16, 34, 10, 28, 28]
J. [11, 11, 17, 11, 29, 17, 35, 11, 29, 29]
Answer: C
We now define an algorithm: The definition of a(n) is the sequence generated by the regular paper-folding (or dragon curve) sequence, which is constructed by repetitively folding a strip of paper in half in the same direction and unfolding it to reveal a specific pattern of creases, interpreted as binary values with 'valley' folds denoted by 1 and 'mountain' folds denoted by 2. Given the input x_list (a series of values): [72, 73, 74, 75, 76, 77, 78, 79, 80, 81], determine the corresponding output sequence y_list.

Options:
A. [1, 2, 1, 1, 2, 2, 2, 1, 2, 1]
B. [1, 1, 2, 2, 1, 2, 2, 1, 1, 1]
C. [2, 1, 1, 2, 1, 2, 1, 2, 1, 2]
D. [2, 1, 2, 2, 1, 1, 1, 2, 1, 2]
E. [2, 2, 1, 1, 2, 1, 2, 2, 1, 1]
F. [1, 2, 2, 1, 2, 1, 1, 2, 1, 1]
G. [1, 1, 1, 2, 1, 2, 1, 1, 2, 2]
H. [1, 2, 1, 2, 1, 1, 2, 1, 2, 2]
I. [2, 2, 1, 1, 1, 2, 1, 1, 2, 1]
J. [2, 1, 1, 1, 2, 1, 2, 2, 1, 2]
Answer: B
We now define an algorithm: The definition of a(n) is the number of binary words of length n (beginning with 0) whose autocorrelation function is the indicator of a singleton. This means a binary sequence, starting with 0, where only one position (other than 0) overlaps with its own shifted version in exactly one place. Given the input x_list (a series of values): [27, 28, 29, 30, 31, 32, 33, 34, 35, 36], determine the corresponding output sequence y_list.

Options:
A. [17973078, 35943946, 71887894, 143771366, 287542734, 575076659, 1150153320, 2300289020, 4600578042, 9201120916]
B. [17973077, 35943945, 71887893, 143771365, 287542733, 575076658, 1150153319, 2300289019, 4600578041, 9201120915]
C. [17973085, 35943953, 71887901, 143771373, 287542741, 575076666, 1150153327, 2300289027, 4600578049, 9201120923]
D. [17973079, 35943947, 71887895, 143771367, 287542735, 575076660, 1150153321, 2300289021, 4600578043, 9201120917]
E. [17973081, 35943949, 71887897, 143771369, 287542737, 575076662, 1150153323, 2300289023, 4600578045, 9201120919]
F. [17973083, 35943951, 71887899, 143771371, 287542739, 575076664, 1150153325, 2300289025, 4600578047, 9201120921]
G. [17973080, 35943948, 71887896, 143771368, 287542736, 575076661, 1150153322, 2300289022, 4600578044, 9201120918]
H. [17973076, 35943944, 71887892, 143771364, 287542732, 575076657, 1150153318, 2300289018, 4600578040, 9201120914]
I. [17973084, 35943952, 71887900, 143771372, 287542740, 575076665, 1150153326, 2300289026, 4600578048, 9201120922]
J. [17973082, 35943950, 71887898, 143771370, 287542738, 575076663, 1150153324, 2300289024, 4600578046, 9201120920]
Answer: G
We now define an algorithm: The definition of a(n) is the number of possible decompositions of the polynomial $n * (x + x^2 + ... + x^q)$, where q > 1, into a sum of k polynomials, not necessarily all different; each of these polynomials is to be of the form $b_1 * x + b_2 * x^2 + ... + b_q * x^q$ where each b_i is one of the numbers 1, 2, 3, ..., q and no two b_i are equal, and the coefficients of $x, x^2, ..., x^q $in each polynomial are drawn from distinct elements of a set of integers from 1 to q. Given the input x_list (a series of values): [83, 84, 85, 86, 87, 88, 89, 90, 91, 92], determine the corresponding output sequence y_list.

Options:
A. [1, 12, 5, 3, 6, 7, 0, 15, 5, 5]
B. [2, 13, 5, 3, 5, 6, 1, 15, 5, 5]
C. [1, 13, 5, 3, 5, 7, 1, 15, 5, 5]
D. [0, 13, 6, 3, 5, 7, 2, 15, 5, 5]
E. [1, 13, 5, 3, 4, 7, 1, 15, 5, 5]
F. [1, 12, 5, 3, 5, 7, 1, 15, 5, 4]
G. [1, 13, 5, 3, 6, 7, 1, 15, 6, 5]
H. [1, 14, 5, 2, 5, 7, 1, 15, 4, 5]
I. [1, 13, 5, 4, 5, 7, 1, 16, 5, 5]
J. [2, 13, 4, 3, 5, 8, 1, 14, 5, 5]
Answer: C
We now define an algorithm: The definition of a(n) is from Apéry continued fraction for ζ(3): ζ(3)=6/(5-1^6/(117-2^6/(535-3^6/(1463...(continue the pattern))) where the coefficients {a(n)} are given by the values in the numerators of the continued fractions. Given the input x_list (a series of values): [22, 23, 24, 25, 26, 27, 28, 29, 30, 31], determine the corresponding output sequence y_list.

Options:
A. [387305, 441275, 500035, 563800, 632769, 707130, 787115, 872909, 964718, 1062750]
B. [387312, 441284, 500049, 563808, 632769, 707132, 787114, 872903, 964716, 1062746]
C. [387310, 441280, 500040, 563800, 632760, 707130, 787110, 872900, 964710, 1062740]
D. [387315, 441283, 500045, 563805, 632767, 707135, 787113, 872905, 964715, 1062747]
E. [387317, 441281, 500046, 563809, 632771, 707129, 787117, 872901, 964711, 1062742]
F. [387318, 441278, 500044, 563803, 632770, 707133, 787112, 872907, 964717, 1062749]
G. [387314, 441286, 500050, 563807, 632768, 707136, 787116, 872904, 964713, 1062743]
H. [387320, 441290, 500055, 563810, 632774, 707138, 787118, 872908, 964720, 1062745]
I. [387311, 441282, 500041, 563806, 632765, 707139, 787110, 872906, 964719, 1062739]
J. [387313, 441289, 500048, 563804, 632766, 707132, 787119, 872902, 964712, 1062748]
Answer: D
We now define an algorithm: The definition of a(n) is the number of n-step one-sided prudent walks on a 2D grid avoiding exactly three consecutive West steps. A prudent walk is a self-avoiding walk where each step is either up, down, left, or right, and does not lead the walker back to any previously visited position. Given the input x_list (a series of values): [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], determine the corresponding output sequence y_list.

Options:
A. [40386519, 96018828, 228284494, 542745738, 1290376450, 3067866320, 7293843431, 17341091933, 41228396594, 98020395241]
B. [40386516, 96018832, 228284498, 542745741, 1290376446, 3067866324, 7293843429, 17341091934, 41228396590, 98020395243]
C. [40386518, 96018831, 228284497, 542745740, 1290376448, 3067866323, 7293843428, 17341091936, 41228396592, 98020395245]
D. [40386512, 96018824, 228284490, 542745734, 1290376454, 3067866316, 7293843435, 17341091929, 41228396598, 98020395237]
E. [40386511, 96018823, 228284489, 542745733, 1290376455, 3067866315, 7293843436, 17341091928, 41228396599, 98020395236]
F. [40386514, 96018826, 228284492, 542745736, 1290376452, 3067866318, 7293843433, 17341091931, 41228396596, 98020395239]
G. [40386513, 96018825, 228284491, 542745735, 1290376453, 3067866317, 7293843434, 17341091930, 41228396597, 98020395238]
H. [40386517, 96018830, 228284496, 542745739, 1290376447, 3067866322, 7293843427, 17341091935, 41228396591, 98020395244]
I. [40386520, 96018829, 228284495, 542745742, 1290376449, 3067866321, 7293843430, 17341091937, 41228396593, 98020395242]
J. [40386515, 96018827, 228284493, 542745737, 1290376451, 3067866319, 7293843432, 17341091932, 41228396595, 98020395240]
Answer: C