k pupils move on a 3x3 grid only up and right , at least 2 same path
Source: 2009 Greek Junior p4
March 17, 2020
combinatoricsgridsquare gridpaths
Problem Statement
In the figure we see the paths connecting the square of a city (point ) with the school (point ). In the square there are pupils starting to go to the school. They have the ability to move only to the right and up. If the pupils are free to choose any allowed path (in order to get to school), determine the minimum value of so that in any case at least two pupils follow the same path.
https://cdn.artofproblemsolving.com/attachments/e/2/b5d6c6db5942cb706428cb63af3ca15590727f.png