Grades 5-6 Video Solutions 2022-2022_5-6

Video Transcription

Question number seven. In the garage shown in the picture, vehicles can move forward or backward, but cannot turn.  What is the smallest number of vehicles that have to move for the black car to be able to exit the garage?  So to solve this problem, we need to work backwards. So if this black car needs to escape, then certain things have to be put into motion for that to happen.  So if we take a look at this diagram, that'll show us exactly how to do it, and now we'll go through it step by step.  If the black car has to exit, this bus in front of it must be moved. This bus takes up three squares, so it can't move above the car. It has to move below.  If this bus wants to move down here, then this bus in turn needs to move forward,  since these are only three spaces that it can occupy to allow this one to get to this bottom square.  If this bus needs to move all the way to this left corner, then this car needs to go up at least one, in turn this bus also needs to go up one.  So, reversing the order of this to get to the right order, this bus moves first, then this car moves up one, this bus moves to the left two, and then this bus moves down two.  And finally, this black car is free to move outside. Therefore, we have one, two, three, four total vehicles that have to be moved, so the answer is C.

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