MathDB

2

Part of 2022 Durer Math Competition Finals

Problems(2)

drawing X on 5x5 board

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 1 E2

11/29/2022
Anett is drawing XX-es on a 5×55 \times 5 grid. For each newly drawn XX she gets points in the following way: She checks how many XX-es there are in the same row (including the new one) that can be reached from the newly drawn XX with horizontal steps, moving only on fields that were previously marked with XX-es. For the vertical XX-es, she gets points the same way. a) What is the maximum number of points that she can get with drawing 2525 XX-es? b) What is the minimum number of points that she can get with drawing 2525 XX-es? For example, if Anett put the XX on the field that is marked with the circle, she would get 33 points for the horizontal fields and 11 point for the vertical ones. Thus, she would get 44 points in total. https://cdn.artofproblemsolving.com/attachments/5/c/662c2e4c3dea8d78e2f6397489b277daee0ad0.png
combinatorics
Csaba stands in the middle of a 15 x 15 m room

Source: (2021-) 2022 XV Dürer Math Competition Finals Day2 E2

12/1/2022
Csaba stands in the middle of a 1515 m ×15\times 15 m room at a workplace where everyone strictly adheres to 1,51,5 m social distancing. At least how many people are there other than Csaba in the room if Csaba cannot reach any wall without the others moving? The people are viewed as points.
geometry