Oh My Stars!Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.
The following sequence has a geometric tint to it, with emphasis on the title. What are the next two numbers and why?
0, 0, 0, 0, 1, 0, 2, ...
Answer1 and 2.
These are the number of unique star configurations you can have with that many points (the first 0 meaning 1 point cannot have a star configuration, the 1 at 5 means you can draw a 5 point star, continuously). A 6 point star does not exist in continuous fashion (the star of David is 2 triangles, remember), and there are two ways to draw a 7 point star.
A star is to be defined as any number of points connected in continuous subsequent line segments without repetition, that cross over each other in the same size segments.
Obviously, you cannot have a star with one or two points (a dot and line, respectively), 3 points make only a triangle, 4 a square. Five, however, can be made into a pentagon, which is not a correct shape in this instance, but CAN be made into a star, as explained below.
(The following part of the explanation, relevantly, is taken from teaser #32838)
First let's examine the 5-point star and why there is only that one, described, way to draw it. Starting at A, you cannot go straight to point B, otherwise you will have a pentagon, not a star. Same with point E. AC and AD (and their progressions) yield identical pictures (notice that the last segment in the AB one is DA, literally reverse all the letters to get AD ending in BA).
Now, for a 6-point star, there are points A, B, C, D, E, and F. Starting at A, we cannot go to B or F, because then we have a hexagon. If we go AC, then we must go CE, then CA... making a triangle, not a 6-point star. Going backwards, AE, EC, EA; mirror image. If we skip 2 points, we go AD, then DA, a straight line, hardly a 6-point star.
For a 7-point star, A-G, AB and AG are not possible, as that's a heptagon. AC, CE, EG, GB, BD, DF, FA is one way to draw the star, skipping one point in between. Also, AD, DG, GC, CF, FB, BE, EA, skipping two points in between each, is the other way. The last two line possibilities, AF and AE are mirror images of the two working scenarios.
There is only 1 way to make an 8 point star and 2 ways to make a 9 point star.
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