Grades 7-8 Video Solutions 2022-2022_7-8

Video Transcription

Question 12. On a standard die, the sum of the numbers of dots on opposite faces is always 7. Four standard dice are glued together as shown.  What is the minimum number of dots that can lie on the whole surface?  We look at the four dies glued together. We know that two opposite faces have to equal 7. So if we look at the top and the bottom of this one die, the total will be 7.  If we look at the front and the back of this die, again, it will be 7. Now, there are four dies together. So we get 14, and we have to multiply this by 4.  And this gives us 56 as a total.  Now we are left with the two faces on either side of the dies. These do not have to equal 7, since they are far apart from each other.  Since we are trying to minimize the number of dots on the whole surface, we will choose the smallest number on a standard die, which will be 1.  So we add 1, and then we add another 1 for both faces. And with this, we will get our answer, which is D, 58.

Video Summary

The problem involves finding the minimum number of dots on the surface of four standard dice glued together. Opposite faces on a standard die sum to 7. After calculating the sums for multiple pairs of opposite faces, the solution involves understanding that non-opposite, exposed faces provide the opportunity to minimize the total dot count. By assigning the minimum value of 1 dot to these exposed sides, the total minimum number of dots on the surface of the glued dice is calculated to be 58.

Keywords

minimum dots

standard dice

opposite faces

glued together

surface calculation