Grades 1-2 Video Solutions 2022-2022_1-2

Video Transcription

Step. What is the smallest number of steps needed to place the cards in increasing order?  A1, B2, C3, D4, or E5.  The numbers we have here are 3, 4, 1, 5, and 2.  In increasing order, they should be 1, 2, 3, 4, 5.  If we compare the order we want with what we have here, we see that none of the cards are in the right place.  The problem is that we can swap two cards in each step. If we swap them, we are changing their places.  So at most, in each swap, we can put two cards in the correct place.  Since we have five cards that are out of place, there's no way that we can fix it with just switching two cards by making one swap.  And there's no way that we can fix it even with two swaps, because that would only fix the places of four cards at most.  Let's see if we can do it if we swap the cards three times.  Let's start by putting the 1 where it belongs. So let's do this swap.  So we swap 1. The 1 and the 3 changes places.  Now the 1 and the 3 are where they belong.  In the second swap, let's switch the 2 and the 4.  We will have the 2 in the correct place, but the order in the end is 5 and 4.  Well, that's easily fixed, because we just need to swap the 4 and 5 at this point to have them in order. So that will be the third swap.  And if we do that, we have the order we need.  1, 2, 3, 4, 5.  So in these three swaps, 1, 2, and then switching to 4 and 5, we can put the cards in the correct order.  So three swaps will work. The answer is C, 3.

Video Summary

Summary Not Available