B3. From 45 matches, we form a network (see the image). What is the minimum number of matches we need to remove so that the remaining matches do not form any regular hexagon?

![](https://cdn.mathpix.com/cropped/2024_06_07_8c7265975f2fda1205e1g-09.jpg?height=529&width=560&top_left_y=181&top_left_x=1359)

## 61st Mathematical Competition for High School Students in Slovenia  National Competition, April 22, 2017

## Problems for 3rd Year

Time for solving: 180 minutes. In section A, we will score a correct answer with two points, and deduct one point for an incorrect answer. Write the answers for section A in the left table, leave the right table blank.
![](https://cdn.mathpix.com/cropped/2024_06_07_8c7265975f2fda1205e1g-10.jpg?height=156&width=802&top_left_y=590&top_left_x=640)