MathDB
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 PP) with the school (point SS). In the square there are kk 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 kk so that in any case at least two pupils follow the same path. https://cdn.artofproblemsolving.com/attachments/e/2/b5d6c6db5942cb706428cb63af3ca15590727f.png