The "MOAB" Problem
Source: 2016 BAMO-12 #5
February 25, 2016
B8Perspectivecombinatorial geometry
Problem Statement
The corners of a fixed convex (but not necessarily regular) -gon are labeled with distinct letters. If an observer stands at a point in the plane of the polygon, but outside the polygon, they see the letters in some order from left to right, and they spell a "word" (that is, a string of letters; it doesn't need to be a word in any language). For example, in the diagram below (where ), an observer at point would read "," while an observer at point would read "."Diagram to be added soonDetermine, as a formula in terms of , the maximum number of distinct -letter words which may be read in this manner from a single -gon. Do not count words in which some letter is missing because it is directly behind another letter from the viewer's position.