santa visits 13 houses in the same order
Source: 2020 Kürschák Competition P3
April 9, 2021
combinatorics
Problem Statement
There are houses in a city. Every Christmas, Santa visits these houses in some order. Show that if is large enough, then it holds that for three consecutive years there are always are houses such that they have been visited in the same order for two years (out of the three consecutive years). Determine the smallest for which this holds.