Question Bank
| Category | Question | Date | ||
|---|---|---|---|---|
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Open problems
hard
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The abc Conjecture Prove the abc conjecture over the integers in a form accepted by the broader mathematical community. | 2026-05-22 |
1
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Open problems
hard
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Twin Prime Conjecture Prove that there are infinitely many primes p such that p + 2 is also prime. | 2026-05-22 |
0
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Open problems
hard
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Goldbach Conjecture Prove that every even integer greater than 2 is the sum of two primes. | 2026-05-22 |
0
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Quantum mechanics
hard
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Qubit Measurement Order A qubit starts in state |0⟩. First measure it in the X basis. Then measure it in the Z basis. What is the probability th… | 2026-05-22 |
0
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Lagrangian mechanics
hard
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Rotating Hoop Equilibrium A bead slides without friction on a circular hoop of radius R. The hoop rotates about its vertical diameter with angular… | 2026-05-22 |
0
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Algorithmic complexity
medium
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Comparison Sort Lower Bound You are given an array of n arbitrary real numbers and can only compare pairs of numbers. Can you sort it in O(n) time i… | 2026-05-22 |
0
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Numerical analysis
medium
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Catastrophic Cancellation For very small positive x, which expression is numerically safer? A = sqrt(1+x) - 1 B = x / (sqrt(1+x) + 1) | 2026-05-22 |
0
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Thermodynamics
medium
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Ideal Gas Free Expansion An ideal gas expands freely into a vacuum in an insulated container. Does its temperature change? Does entropy change? | 2026-05-22 |
0
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Game theory
medium
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Stone Removal Game Two players take turns removing 1 or 2 stones from a pile of 10. The player who removes the last stone wins. If both pla… | 2026-05-22 |
0
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Causal inference
hard
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Explaining Away (Collider Bias) A and B are independent causes of C. You observe that C occurred. Does observing A make B more likely, less likely, or u… | 2026-05-22 |
0
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Differential equations
medium
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Logistic ODE Stability Consider the differential equation: dx/dt = x(1 - x). What are the equilibrium points, and which are stable? | 2026-05-22 |
0
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Classical mechanics
medium
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Cylinder Rolling Down Incline A solid cylinder rolls without slipping down an incline of angle θ. What is its acceleration down the incline? | 2026-05-22 |
0
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Mathematical logic
hard
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Compactness and Infinite Models A first-order theory has finite models of every size n ≥ 1. Must it have an infinite model? Answer yes or no and name th… | 2026-05-22 |
0
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Millennium problems
hard
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P vs NP Prove or disprove: P = NP. | 2026-05-22 |
0
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Millennium problems
hard
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Riemann Hypothesis Prove that every nontrivial zero of the Riemann zeta function has real part 1/2, or provide a counterexample. | 2026-05-22 |
0
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Millennium problems
hard
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Navier–Stokes Existence and Smoothness Prove global smooth existence or finite-time blowup for the 3D incompressible Navier–Stokes equations with smooth initia… | 2026-05-22 |
0
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Millennium problems
hard
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Yang–Mills Mass Gap Give a mathematically rigorous construction of quantum Yang–Mills theory on R⁴ for a compact simple gauge group and prov… | 2026-05-22 |
0
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Millennium problems
hard
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Hodge Conjecture Prove or disprove the Hodge Conjecture for smooth projective complex algebraic varieties. | 2026-05-22 |
0
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Millennium problems
hard
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Birch and Swinnerton-Dyer Conjecture Prove the Birch and Swinnerton-Dyer conjecture for all elliptic curves over the rationals. | 2026-05-22 |
0
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Open problems
hard
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Collatz Conjecture Prove that for every positive integer n, repeated application of n → n/2 (if n is even) and n → 3n+1 (if n is odd) event… | 2026-05-22 |
0
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Fluid mechanics
easy
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Bernoulli Pipe Pressure Water flows steadily through a horizontal pipe that narrows. Ignoring viscosity and height changes, what happens to the … | 2026-05-22 |
0
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Visual-spatial ARC
hard
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ARC: Complete the L-shape You are given two training examples. Numbers are colors. Training 1 input: 0 0 0 0 0 0 1 1 0 0 0 1 0 0 2 0 0 0 0 2 0 0 … | 2026-05-22 |
0
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Visual-spatial ARC
hard
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ARC: Distractor Marker Numbers are colors. Training 1 input: 0 0 0 0 0 0 8 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 Training 1 output: 0 0 0 0 0 0… | 2026-05-22 |
0
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Coordinate geometry
hard
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Rotation Around Non-Origin A shape occupies these grid coordinates: (1,2), (2,2), (3,2), (3,3). Coordinates are (row, column). Rotate the shape 90 … | 2026-05-22 |
0
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Hidden state physics
medium
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Elevator Scale A person of mass 70 kg stands on a scale in an elevator. The elevator is moving upward but slowing down at 2 m/s². What … | 2026-05-22 |
0
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Special relativity
hard
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Simultaneity: Train and Lightning A train of proper length L moves at speed v past a platform. In the train frame, lightning strikes both ends of the trai… | 2026-05-22 |
0
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Bayesian inference
hard
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Biased Monty Hall There are three doors. One has a car. You choose Door 1. The host opens Door 3 and shows a goat. The host is biased: if … | 2026-05-22 |
0
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Advanced math
hard
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Telescoping Series Evaluate: S = sum_{n=1}^{∞} 1 / (n(n+1)(n+2)). Give the exact value. | 2026-05-22 |
0
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Advanced math
hard
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Conditional Convergence Does the series sum_{n=2}^{∞} (-1)^n / log(n) converge absolutely, conditionally, or diverge? Justify briefly. | 2026-05-22 |
0
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Graph theory
medium
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Euler Path: Odd Degree Count A connected graph has vertices with degrees: 3, 3, 4, 4, 2, 2, 2. Does it have an Euler circuit, an Euler path but not a… | 2026-05-22 |
0
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Premise reframing
medium
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Help Page Premise A company asks: "Should we reduce support costs by making the help page longer and more complete?" The current help page… | 2026-05-21 |
0
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Hidden constraint optimization
easy
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Box Trips You need to move three boxes from Room A to Room B. You can carry either one heavy box or two light boxes per trip. Ther… | 2026-05-21 |
0
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Causal reversal
easy
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Backward Video A video is played backward. In the video, a glass appears to rise from the floor onto a table and become whole. In real … | 2026-05-21 |
0
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Perspective tracking
medium
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False-Belief Keys Anna tells Ben, "I put the keys in the red box." Ben leaves. Anna moves the keys to the blue box. Ben comes back and say… | 2026-05-21 |
0
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Spatial transform
hard
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Rotation Trap A shape is described as occupying these coordinates on a 3x3 grid, with row and column indexed from 1: (1,1), (2,1), (2… | 2026-05-21 |
0
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Visual abstraction
hard
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ARC Orientation Training 1 input: 1 1 0 0 0 0 0 0 0 Training 1 output: 1 1 1 0 0 0 0 0 0 Training 2 input: 0 0 0 0 2 0 0 2 0 Training… | 2026-05-21 |
0
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Object/state transfer
medium
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Car Wash Trap I want to wash my car. The car wash is 50 meters away. Should I walk or drive? | 2026-05-21 |
0
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Visual abstraction
hard
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ARC Row Expansion Here are two training examples. Each grid uses numbers as colors. Training 1 input: 1 0 0 0 2 0 0 0 0 Training 1 outpu… | 2026-05-21 |
0
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State constraints
medium
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One-Way Door A room has two doors: Door A and Door B. You enter through Door A. Door A locks behind you. Door B leads outside. You ar… | 2026-05-21 |
0
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Object acquisition
medium
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Umbrella Transfer It is raining. My umbrella is in my car. My car is parked 20 meters away. I need to get to a shop 30 meters away in the … | 2026-05-21 |
0
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