The magician’s problem
A coin, an audience, and a probability that seems to settle—until you magnify a ripple that never disappears.
probabilityoscillationslimits
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Problems to solve and ideas to explore.
Two expressions that cannot both be cubes
For a natural number n, prove that n + 2 and n² + n + 1 cannot both be perfect cubes.
number theoryperfect powers
Finding an invisible spaceship
Can a fixed collection of detectors distinguish every possible 2 × 2 spaceship position on a 7 × 7 board?
combinatoricspuzzles
The average distance across a circle
Choose two points uniformly on a unit circle. What is their expected straight-line distance?
probabilitygeometryexpectation
A three-variable inequality
Prove a symmetric inequality for arbitrary real x, y, and z.
algebrainequalities