Arranging an invertible matrix
Arrange any n² distinct real numbers in a square matrix with nonzero determinant.
linear algebradeterminantsinduction
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Problems to solve and ideas to explore.
Hex: a game with no middle ground
Build a connection, challenge the computer, and walk a coastline to discover why Hex can never end in a draw.
gamestopologygraph theory
Three utilities: from the plane to a mug
Connect three houses to gas, water, and electricity. The plane refuses—but a mug, a donut, and a square with joined edges reveal a way through.
topologygraph theorypuzzles
Lights Out: every light can be flipped
Play on a grid or a graph, reveal a solution, and discover why every pattern can be complemented—and why successful routes agree on parity.
combinatoricsgraph theoryparity
How big can a cevian triangle be?
Three lines meet. Three side points make a triangle. Move the meeting point—and discover why a quarter is the most you can get.
geometryinequalitiessimplexes