Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem8

Video Transcription

Question number 8. While in Verona, Maggie decided to walk each of the five famous bridges on the Adige River.  She began and ended her walk in the same place, passed through each of the five bridges at least once, and did not use any other bridge.  How many times could Maggie have crossed the Adige River?  So the piece of information that's important here is that the start and the end are in the same place. Meaning, at the same side of the river, on the same bank.  And so if Maggie starts here, she has to cross a bridge, so let's just cross them in order, like that.  She's walking across bridge 1, then has to cross again bridge 2, then crosses bridge number 3, moves on, comes back through bridge number 4,  and she has one bridge left, and what happens is she ends up on the opposite side of where she started, which is not allowed.  We know that her walk begins and ends in the same place. So five crossings is not enough. We need to cross again. At least once.  And if we do that, we will end up where we started, on the same bank of the river.  So this is not the end, we can cross that out, and then what happens is, from here, there has to be one more crossing.  And then if we have one more crossing like that, then Maggie can end up at exactly the same side where she started. So there has to be five plus one, at least six.  So at least six crossings. And possibly more, but a minimum of six crossings. So that is the answer to our question, how many times could Maggie have crossed the Adage River?  No less than six times, and so the answer here would be D, six.

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