MathDB

There are

9

vertical columns in a row. In some places, horizontal sticks are inserted between adjacent columns, no two are at the same height. The beetle crawls from the bottom up; when he meets the wand, he crawls over it to the next column and continues to crawl up. It is known that if a beetle starts at the bottom of the first (leftmost) column, then it will end its journey on the ninth (rightmost) column. Is it always possible to remove one stick so that the beetle ends up at the top of the fifth column? (For example, if the sticks are arranged as in picture, the beetle will crawl along a solid line. If you remove the third one A stick in the path of the beetle, then it will crawl along the dotted line.) Proposed by G. Karavaev

Problem Statement