question_id stringlengths 3 4 | cot_question stringlengths 15.1k 44.8k | cot_images images listlengths 11 17 | final_answer sequencelengths 1 2 | solution sequencelengths 1 4 | is_multiple_answer bool 2
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1020 | Context Example 1:
Question:
The arrangement of numbers known as Pascal's Triangle has fascinated mathematicians for centuries. In fact, about 700 years before Pascal, the Indian mathematician Halayudha wrote about it in his commentaries to a then-1000-year-old treatise on verse structure by the Indian poet and mathem... | [
"$E_{p}=\\frac{2 p}{4 \\pi \\varepsilon_{0} r^{3}}$"
] | [
"Using Coulomb's Law, we write the electric field at a distance $r$ is given by\n\n$$\n\\begin{aligned}\n& E_{p}=\\frac{q}{4 \\pi \\varepsilon_{0}(r-a)^{2}}-\\frac{q}{4 \\pi \\varepsilon_{0}(r+a)^{2}} \\\\\n& E_{p}=\\frac{q}{4 \\pi \\varepsilon_{0} r^{2}}\\left(\\frac{1}{\\left(1-\\frac{a}{r}\\right)^{2}}-\\frac{1}... | false | null | Expression | null | OE_MM_physics_en_COMP | Modern Physics | 3. To Commemorate the Centenary of Rutherford's Atomic Nucleus: the Scattering of an Ion by a Neutral Atom
<img_4421>
An ion of mass $m$, charge $Q$, is moving with an initial non-relativistic speed $v_{0}$ from a great distance towards the vicinity of a neutral atom of mass $M>>m$ and of electrical polarisability $... | |
1028 | Context Example 1:
Question:
- Proton mass, $m_{p}=1.67 \cdot 10^{-27} \mathrm{~kg}$
- Neutron mass, $m_{n}=1.67 \cdot 10^{-27} \mathrm{~kg}$
- Electron mass, $m_{e}=9.11 \cdot 10^{-31} \mathrm{~kg}$
- Avogadro's constant, $N_{0}=6.02 \cdot 10^{23} \mathrm{~mol}^{-1}$
- Universal gas constant, $R=8.31 \mathrm{~J} /(\ma... | [
"$\\frac{\\pi L}{\\sqrt{3 h}}$"
] | [
"In the coordinate system of the figure, we have for the centre of mass coordinates of the two triangular parts of the water\n\n$$\n\\left(x_{1}, y_{1}\\right)=(L / 3, h / 2+\\xi / 3) \\quad\\left(x_{2}, y_{2}\\right)=(-L / 3, h / 2-\\xi / 3) .\n$$\n\nFor the entire water mass the centre of mass coordinates will th... | false | null | Expression | null | OE_MM_physics_en_COMP | Optics | ||
1082 | Context Example 1:
Question:
The parabola $y=-x^{2}+4$ has vertex $P$ and intersects the $x$-axis at $A$ and $B$. The parabola is translated from its original position so that its vertex moves along the line $y=x+4$ to the point $Q$. In this position, the parabola intersects the $x$-axis at $B$ and $C$. Determine the ... | [
"$\\Delta \\phi_{C D}=0$"
] | [
"<img_4442>\n\nConsider the extreme trajectories $O C P$ and $O D P$ of $(\\mathrm{C} 1)$\n\nThe geometrical path difference is $E D$ in region I and $C F$ in region II.\n\nThis implies (note: $d \\ll\\left(x_{0}-x_{1}\\right)$ and $d \\ll x_{1}$ )\n\n$$\n\\begin{gathered}\n\\Delta \\phi_{C D}=\\frac{2 \\pi d \\sin... | false | null | Numerical | 0 | OE_MM_physics_en_COMP | Mechanics | A The Extremum Principle in Mechanics
Consider a horizontal frictionless $x-y$ plane shown in Fig. 1. It is divided into two regions, I and II, by a line $\mathrm{AB}$ satisfying the equation $x=x_{1}$. The potential energy of a point particle of mass $m$ in region I is $V=0$ while it is $V=V_{0}$ in region II. The pa... | |
1100 | Context Example 1:
Question:
An $\boldsymbol{n}$-label is a permutation of the numbers 1 through $n$. For example, $J=35214$ is a 5 -label and $K=132$ is a 3 -label. For a fixed positive integer $p$, where $p \leq n$, consider consecutive blocks of $p$ numbers in an $n$-label. For example, when $p=3$ and $L=263415$, t... | [
"$I_{\\max }=\\frac{q_{0}}{\\sqrt{2 L C}}$"
] | [
"At the moment when the current in the coils is a maximum, the total voltage across the coils is equal to zero, so the capacitor voltages must be equal in magnitude and opposite in polarity. Let $U$ be a voltage on the capacitors at the time moment just mentioned and $I_{0}$ be that maximum current. According to th... | false | null | Expression | null | OE_MM_physics_en_COMP | Electromagnetism | ||
1155 | "Context Example 1:\nQuestion:\n- Proton mass, $m_{p}=1.67 \\cdot 10^{-27} \\mathrm{~kg}$\n- Neutron(...TRUNCATED) | [{"src":"https://datasets-server.huggingface.co/assets/yuanshengni/OlympiadBench-OE-CoT-num10/--/{da(...TRUNCATED) | [
"10.8633, 10.925"
] | ["For gamma-emission from the static nucleus, laws of conservation of energy and momentum give:\n$$\(...TRUNCATED) | true | MeV | Numerical | 1e-3 | OE_MM_physics_en_COMP | Modern Physics | "3. Simple model of an atomic nucleus \n\nIntroduction\n\nAlthough atomic nuclei are quantum objects(...TRUNCATED) |
1164 | "Context Example 1:\nQuestion:\n\nA triangle has vertices $A(0,3), B(4,0)$, $C(k, 5)$, where $0<k<4$(...TRUNCATED) | [{"src":"https://datasets-server.huggingface.co/assets/yuanshengni/OlympiadBench-OE-CoT-num10/--/{da(...TRUNCATED) | [
"$v_{\\min }=3 \\sqrt{\\frac{g R}{2}}$"
] | ["The brute force approach would be writing down the condition that the optimal trajectory intersect(...TRUNCATED) | false | null | Expression | null | OE_MM_physics_en_COMP | Mechanics | "Problem T1. Focus on sketches\n\nPart A. Ballistics\n\nA ball, thrown with an initial speed $v_{0}$(...TRUNCATED) |
1166 | "Context Example 1:\nQuestion:\n## String Cheese\nContext question:\na. When a faucet is turned on, (...TRUNCATED) | [{"src":"https://datasets-server.huggingface.co/assets/yuanshengni/OlympiadBench-OE-CoT-num10/--/{da(...TRUNCATED) | [
"$F=\\frac{4-\\sqrt{2}}{8 \\pi \\mu_{0}} \\frac{\\Phi^{2}}{l^{2}}$"
] | ["Let us analyse, what would be the change of the magnetic energy when one of the straws is displace(...TRUNCATED) | false | null | Expression | null | OE_MM_physics_en_COMP | Electromagnetism | "Part C. Magnetic straws\n\nConsider a cylindrical tube made of a superconducting material. The leng(...TRUNCATED) |
1218 | "Context Example 1:\nQuestion:\n\nThe arrangement of numbers known as Pascal's Triangle has fascinat(...TRUNCATED) | [{"src":"https://datasets-server.huggingface.co/assets/yuanshengni/OlympiadBench-OE-CoT-num10/--/{da(...TRUNCATED) | [
"218"
] | ["2nd Newton's law\n\n$$\n\\begin{gathered}\nF=\\frac{d p}{d t} \\quad \\text { leads to } \\\\\n\\f(...TRUNCATED) | false | ns | Numerical | 2e0 | OE_MM_physics_en_COMP | Modern Physics | "Large Hadron Collider\n\nPlease read the general instructions in the separate envelope before you s(...TRUNCATED) |
1322 | "Context Example 1:\nQuestion:\n\n$\\quad$ Let $T=12$. As shown, three circles are mutually external(...TRUNCATED) | [{"src":"https://datasets-server.huggingface.co/assets/yuanshengni/OlympiadBench-OE-CoT-num10/--/{da(...TRUNCATED) | [
"$67$ , $100$"
] | ["PART B\n\nAs the liquids are in thermal contact with each other, their temperatures increase in ti(...TRUNCATED) | true | $^{\circ}\mathrm{C}$ | Numerical | 1e0 | OE_MM_physics_en_COMP | Thermodynamics | "Consider two liquids A and B insoluble in each other. The pressures $p_{i}(i=\\mathrm{A}$ or $\\mat(...TRUNCATED) |
1398 | "Context Example 1:\nQuestion:\n\nIn the diagram, $\\triangle P Q R$ has $P Q=a, Q R=b, P R=21$, and(...TRUNCATED) | [{"src":"https://datasets-server.huggingface.co/assets/yuanshengni/OlympiadBench-OE-CoT-num10/--/{da(...TRUNCATED) | ["$\\frac{2 m \\theta}{M}\\left(\\left(1-\\frac{h}{R}\\right)^{2}-1\\right)$","$-\\frac{4 m}{M} \\fr(...TRUNCATED) | ["During the first leg of the trip, the disk has angular velocity\n\n\n\n$$\n\n\\omega=-\\frac{2 m v(...TRUNCATED) | false | null | Expression | null | OE_MM_physics_en_COMP | Mechanics | "## Disk Jockey\n\n\n\nA disk of uniform mass density, mass $M$, and radius $R$ sits at rest on a fr(...TRUNCATED) |
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