SOLUTION: A 3 by 5 grid of dots is set out. How many straight line segments can be drawn that join two of these dots and pass through exactly one other dot?

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Question 1178570: A 3 by 5 grid of dots is set out. How many straight line segments can be drawn that join two of these dots and pass through exactly one other dot?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


13.

Draw the (rectangular) grid and count them.

There are 5 of one kind, 6 of another kind, and 2 of a third kind.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

Let think that the grid is 3 points vertically and 5 points horizontally.


Then there are THESE families of straight line segments satisfying imposed conditions


    3 x 3 = 9 horizontal segments of the length 2

            3 horizontal segments of the length 4


            5 vertical segments of the length   2


            1 sloped segment    of the slope   2/4 = 1/2

            3 sloped segments   of the slope     1

            3 sloped segments   of the slope    -1

            1 sloped segment    of the slope  -2/4 = -1/2


Counting this way, there are  9 + 3 + 5 + 1 + 3 + 3 + 1 = 25 segments satisfying the posed condition.

Solved.



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