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Combinatorics and constellations

A Puzzle of Clever Connections Nears a Happy End

The three young friends who devised the “happy ending” problem would become some of the most influential mathematicians of the 20th century, but were never able to solve their own puzzle. Now it receives its first big breakthrough.


A New Path to Equal-Angle Lines

Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.


Simple Set Game Proof Stuns Mathematicians

A new series of papers has settled a long-standing question related to the popular game in which players seek patterned sets of three cards.


Sphere Packing Solved in Higher Dimensions

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.


Theorists Draw Closer to Perfect Coloring

A theorem for coloring a large class of “perfect” mathematical networks could ease the way for a long-sought general coloring proof.


The Connoisseur of Number Sequences

For more than 50 years, the mathematician Neil Sloane has curated the authoritative collection of interesting and important integer sequences.


The Nine Schoolgirls Challenge

Solve this variation of Thomas Kirkman’s famous 1850 puzzle by arranging girls in walking groups. And think fast — the clock is ticking.


A Design Dilemma Solved, Minus Designs

A 150-year-old conundrum about how to group people has been solved, but many puzzles remain.


For Persi Diaconis’ Next Magic Trick …

A mathematician who has analyzed card shuffling for decades is tackling one final nemesis: “smooshing.”