Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

The number of the dots on opposite faces of a die add to 7. The vertex labeled p on the die  is formed by the faces which have 1, 2, and 3 dots on them. Its vertex sum is the sum of the  number of dots on those faces which meet at a given vertex. The vertex sum of p is 1 plus 2 plus 3 equals 6. What is the largest of the vertex sums of vertices q, r, and s?  For this problem, it's probably easiest to just find the vertex sums of each of q, r, and s.  Starting with q, we know that we have a 1 and a 3 already exposed and a 5 opposite 2. Therefore,  it has a vertex sum of 9. r, we can work out similarly, has a 2 and 3 exposed and a 6 on the bottom of the die, giving us a vertex sum of 11. And s will have a vertex sum of 1, 2,  and a 4 hidden on the backside, giving us 7. And thus, the maximum is 11.

Video Summary

In the video, they discuss finding the largest vertex sum of a die's vertices, given that opposite faces add up to 7. They identify the vertex sums for vertices q, r, and s by adding the dots on the faces meeting at each vertex. For q, the vertex sum is 9, calculated from faces with 1, 3, and 5 dots. For r, it's 11, with 2, 3, and 6 dot faces contributing. For s, the sum is 7, from 1, 2, and 4 dots. The largest vertex sum among these is 11.

Keywords

vertex sum

die

opposite faces

largest sum

dots