Grades 7-8 Video Solutions 2023-2023_7-8

Video Transcription

Question 21. Some beavers and some kangaroos are standing in a circle. There are three beavers in total, and no two beavers are standing next to each other.  There are exactly three kangaroos who are standing next to another kangaroo. What is the largest possible number of kangaroos in the circle? Let's draw out our circle.  And we know there are exactly three beavers, so let's draw them out. We also know that there are exactly three kangaroos standing next to another kangaroo.  We will have to set these kangaroos all next to each other. Because if instead we had a pair of kangaroos, that would be two kangaroos standing next to each other.  And then we would have to have another pair of kangaroos, and that would make four kangaroos standing next to each other.  So instead, we will have to have three kangaroos all standing next to each other to give us exactly three kangaroos next to another kangaroo.  Now, we also know that the beavers are not standing next to each other. So we need to spread out by adding kangaroos on either side. So we'll add a kangaroo here and here.  We can no longer add any more kangaroos without more than three kangaroos standing next to another kangaroo.  So when we add up our kangaroos, we get our answer, which will be B, five.

Video Summary

The problem involves arranging three beavers and some kangaroos in a circle where no two beavers stand next to each other and exactly three kangaroos are adjacent to one another. To meet these conditions, three kangaroos must stand together. The beavers are placed such that they are separated by at least one kangaroo. Additional kangaroos are placed between the beavers to prevent them from standing next to each other. By arranging the animals this way, the largest possible number of kangaroos in the circle is calculated to be five.

Keywords

beavers

kangaroos

circle

arrangement

puzzle