Webpages tagged with «Markov chains»

A Barcelona experience is not quite complete without having visited Sagrada Família, Antoni Gaudí's in several senses of the word monumental project (more or less needing the years from 1883 to 2026 to be completed). On the Passion façade there is an innocent and inconspicuous but magic 4 x 4 square, catching my attention, with sums of rows, columns, diagonals, and 2 x 2 subsquares all equal to 33. Can I make such a 4 x 4 square myself, using tools of probability theory and simulation?

The 数独 puzzles have a long history, with variations going back more than a hundred years, but its current and perhaps surprising world-wide prominence goes back to certain initiatives and then puzzle-generating computer programmes from just after 2000. To solve a sudoko puzzle, a statistician can put up a probability model on the enormous space of 9 x 9 matrix possibilities, constructed to favour "good attempts", and then engineer a Markov chain to sample a long enough chain of sudoku table realisations from that model, until the solution is found.