Grades 3-4 Video Solutions 2023-2023_3-4

Video Transcription

Problem number seven. Anna has four disks of different sizes. She wants to build a tower of three disks so that each disk is smaller than the disk below it. How many  different towers can Anna make? Here are the four disks. I'm going to clean up our space a little bit here. Here's a copy of the disk so we can keep track. We have  the yellow disk which is the biggest, then this dark orange or reddish disk, blue, and the lighter orange. It makes sense to start with the yellow as the  biggest disk, and let's see how many towers we can make that way. If the biggest disk is the bottom one, then the next biggest could be on top of it, and  the next biggest one could be on top of that, and that's one tower. Also starting with the yellow, we can put the next biggest over it, and then put the  smallest one on top. Or, starting with the yellow, we can skip the orange one, do the blue, and then the smallest one on top. Next, we can start with the orange disk,  and since the tower has three disks in it, we need to use the remaining two on top of it. So that's only one option. We can't put the blue disk as the bottom disk  because there aren't two disks that are smaller than it. So we have exactly four options. This is answer C.

Video Summary

Anna wants to build a tower using three out of her four disks, with each disk smaller than the one below it. Starting with the largest disk, the yellow one, there are three possible combinations using the three smallest disks on top in different sequences. Starting with the second-largest disk, there is only one combination possible due to only having two smaller disks left. The smallest disk cannot be at the bottom as it requires two smaller disks above, which do not exist. Thus, there are four different towers Anna can make, which corresponds to option C.

Keywords

tower building

disk arrangement

combination possibilities

disk sizes

tower options