Grades 3-4 Video Solutions 2022-2022_3-4

Video Transcription

Problem number 20. Alma wants to put one of the pieces shown in the middle of the picture so a child in A is able to travel to B and to E but not to D. She can rotate the pieces.  Which two pieces could she use? A, 1 and 2. B, 2 and 3. C, 1 and 4. D, 4 and 5. E, 1 and 5. If we look at the pieces we see that all the roads connect in the middle.  The child starts in A so go from A to the middle and needs to be able to get to B  and to E. However, it cannot go to D which is here directly across from A.  So the piece has to have one road going straight across so that both E and B can be reached  but it cannot have two roads going across. So go from A but not to D and it doesn't matter whether there are more roads here.  Let's look at our pieces. In 1 there's a straight road. We can rotate it so it goes from B  to E and A would be at this point. There's no straight road so 1 works.  In 2 there's no straight road at all so that will not work.  In 3 there's no straight road so that doesn't work. In 4 we have two straight roads.  If we lay it down so that B is connected to E and A is here then D also would be connected.  If we rotated this one so that this end goes at B and this end goes at E then A  which is just a little counterclockwise from B would not be connected so 4 does not work.  In 5 we have one straight road. If we place it so that B is here and E is here  A would be connected here and there's no problem with D being connected so 5 works. So the answer is 1 and 5 which is answer E.

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