Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 12. Arpit moves from hexagon X to hexagon Y. He can only move from one hexagon to another if they have an edge in common.  How many different routes are there from X to Y that pass through each of the seven white hexagons exactly once?  Let's take a closer look at the hexagons.  The first thing that we know is that Arpit starts from hexagon X and ends on the hexagon Y. So these will be necessary paths to follow.  Next, it is up to us to diagram all of the possible paths. So let's start off with this one, marked by a blue line.  We can go like so, and with this we started at X and ended at Y, and pass through every hexagon at least once, or exactly once.  Next, we will go to the left side, following a similar path, but not exactly the same.  Now we can follow the same left path, but going downwards first, and then up, following this yellow path. Now with this purple path, we go around and to the center, and end up at Y.  With this red path, we go all the way around, and then into the center, and then meet at Y. Now we can count all of the numbers of different paths.  We had purple, yellow, green, red, and blue. And that means that there is a total of five. So the answer is D, five.

Video Summary

Arpit needs to move from hexagon X to hexagon Y, passing through each of the seven white hexagons exactly once. He can only move between hexagons that share an edge. The speaker diagrams multiple paths Arpit can take, each with a different color: blue, yellow, green, red, and purple. By following these distinct routes from X to Y, while ensuring that each white hexagon is visited exactly once, the total number of different possible paths is five. Thus, the solution to the problem is five distinct routes.

Keywords

hexagon

paths

distinct routes

puzzle solution

Arpit