3 papers
math.GM2026
How long is a game of Uno? A counting law for large hands and the Wild Draw Four hoard
Pragyaan Gaur
We study the length of one round of Uno under the official rules, for N players who each start with M cards. The fastest possible round takes at least M turns with two players and…
math.CO2026
The maximum area of the convex hull of a polyhex
Pragyaan Gaur
A polyhex is an edge-connected set of n cells of the regular hexagonal tiling, where each cell has area one. We prove that the convex hull of a polyhex has area at most (1/6)*ceili…
physics.class-ph2026
Exact turning invariants for projectile motion under quadratic drag and a vertical-axis Magnus force
Pragyaan Gaur
A ball spinning about a vertical axis is pushed sideways by the Magnus force, so its ground track curves. We show that when the lift and drag coefficients are constant, the horizon…