Answer by Henry for How many hexagons can be constructed by joining the...
More generally drawing $n$-gons in a $k$-gon but not using any of the original sides, suppose you know one of the vertices: then you need to divide the $k$ gaps into $n$ parts with each part at least...
View ArticleAnswer by André Nicolas for How many hexagons can be constructed by joining...
Write down $9$ $\times$'s, like this$$ \times\qquad \times\qquad \times\qquad \times\qquad \times\qquad \times\qquad \times\qquad \times\qquad \times$$These determine $8$ gaps, plus $2$ "endgaps." We...
View ArticleHow many hexagons can be constructed by joining the vertices of a 15 sided...
How many hexagons can be constructed by joining the vertices of a 15 sided polygon if none of the sides of the hexagon is also the side of the 15-gon.My attemptFirst calculate in how many ways we can...
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