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In the plane figure below, we have a regular octagon $abcdefgh$, and i belongs to the diagonal $cg$, so that $\angle gih = 30°$ Determine the locus of all midpoints of segments mn, where m is any point on segment ac and n any point on segment fh. Knowing this, determine in degrees the value of the angle indicated by x.
@jeanmarie if the coordinates of the cube are specified, i'd assume that the question considers rotational variants distinct A cube abcdefgh is given So the link doesn't answer the question
Also, this question wants us to count colourings with specific constraints (namely that if all neighbours of v are color c then so is v).
Can anybody please provide a solution that does not involve coordinate geometry? How many permutations of the letters abcdefghi contain a) the string cde B) the strings ac and cf C) the strings abc and ecg
For this problem, i understand how to find something like how many strings contain the string ba and gf I just look at the set of letters like this {ba, gf, c, d, e} and since i have 5 distinct How many permutations of the letters abcdefgh contain the string abc
Because the letters abc must occur as a block, we can find the answer by finding the number of permutations of six objects, namely, the block abc and the individual letters d, e, f , g, and h.
If $p$ is midpoint of $hg$ and $q$ midpoint of $fg$, and $r$ is midpoint of $pq$, and if $bs$ is the projection of $br. I found this problem very interesting and have an idea to solve it, but my method is very long. Cube $abcdefgh$ is cut into four pieces by cutting along planes $bche$ and $bdhf.$ find the fraction of the volume occupied by the piece containing the vertex $a.$
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