Below are seven patterns in a sequence, 1 through 7.
Which of the patterns A through F would be number 8 in that sequence? enter image description here


I think it is



Composite positive integers are 4, 6, 8, 9, 10, 12, 14, 15, .... Each pattern contains figures with number of edges equal to factors of corresponding composite number (line represents number 2, triangle number 3, etc). The next one is 15, which is 3 * 5 (triangle and pentagon).


An alternative answer suggested by the sequence index numbers:



Each sequence number is represented by its prime factors, including unity where fewer than two factors are present. Factors are represented with this substitution: 1: a single line, 2: triangle, 3: pair of lines, 5: pentagon, 7: septagon. So 1 is represented as two single lines (1x1), 3 is a single line and a line pair (1x3), 4 is 2 triangles (2x2), 6 is a triangle and line pair (2x3), etc. The next number in the sequence is 8, and the corresponding symbol would be three triangles (2x2x2).

This scheme is maybe a bit less intuitive than the accepted answer, but could be an interesting alternative.


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