Let $ABCD$ be vertices of a convex quadrilateral. If $AC$ and $BD$ have mid-points $E$ and $F$ respectively, show that:
$$\overline{AB} + \overline{BC} +\overline{CD} + \overline{DA} \ge \overline{AC}+\overline{BD}+2\overline{EF}$$
where, $\overline{XY}$ denotes the length of the line segment $...
In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations. It is also called factorial base, although factorials do not function as base, but as place value of digits. By converting a number less than n! to factorial representation, one obtains a sequence of n digits that can be converted to a permutation of n in a straightforward way, either using them as Lehmer code or as inversion table representation; in the former case the resulting map from integers to permutations of n lists them in lexicographical order. General...
