Grades 1-2 Video Solutions 2020-2020Levels12prob10

Video Transcription

Problem number 10. A village with 12 houses has 4 straight roads and 4 circular roads.  The map shows 11 of the houses. On each straight road there are 3 houses. On each circular road there are also 3 houses.  Where on the map should the 12th house be put? A at A, B at B, C at C, D at D, E at E.  We know that there should be 4 circular roads with 3 houses each and 4 straight roads with 3 houses each.  Since one house is missing, we need to find a circular road that has only 2 houses on it, a straight road that only has 2 houses on it, and the place where they intersect.  To make the answer correct, this point should be marked with one of the letters.  Starting from the middle of the circle, we see that the first circular road has 3 houses on it. The next circular road, the one with A, also has 3 houses on it.  The circular road marked with B and D also already has 3 houses. But this outside circular road only has 2 houses, here and here.  So the last house will be at either E or C. Now if we look at the straight roads, we only need to look at these two, going through here and through here.  And we see that the road that goes through E already has 3 houses, here, here, and here. And the road that goes through C has 2 houses.  So C is placed on a circular road that only has 2 houses and on a straight road that only has 2 houses shown on our map. So the 12th house will have to be at C. So the answer is C.

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