Grades 5-6 Video Solutions 2023-2023_1-2

Video Transcription

Question 6. Anna has 5 circular disks of different sizes. She wants to build a tower of 4 disks  so that each disk in her tower is smaller than the disk immediately below it. How many different towers could Anna build?  Let's draw out the 5 disks and label them A to E, with A being the biggest and E the smallest. Let's start off with having A as the base of our tower. So Anna could build a tower  A, B, C, D. Next, she could switch out D for E, since this will follow her rules. And, if we want to remain A as our base, we could make A, B, D, E. Next, we can make a tower  A, C, D, E, omitting the B. And finally, we could make a tower B, C, D, E. There are no other towers that Anna could make that follow her rules. So when we total up the number  of towers we've built, we will get our answer, which will be B, 5.

Video Summary

Question 6. Anna has 5 circular disks of different sizes. She wants to build a tower of 4 disks so that each disk in her tower is smaller than the disk immediately below it. How many different towers could Anna build? Let's draw out the 5 disks and label them A to E, with A being the biggest and E the smallest. Let's start off with having A as the base of our tower. So Anna could build a tower A, B, C, D. Next, she could switch out D for E, since this will follow her rules. And, if we want to remain A as our base, we could make A, B, D, E. Next, we can make a tower A, C, D, E, omitting the B. And finally, we could make a tower B, C, D, E. There are no other towers that Anna could make that follow her rules. So when we total up the number of towers we've built, we will get our answer, which will be B, 5.

Keywords

tower

disks

combinations

size

arrangement