Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theory

angles answer Antm arrangements balls bills bishops called cards chessboard chosen circle coefficient color column Combining compute Consequently consider consists contain controlled corresponding customers denote determine diagonals digits divided divisible draw equal equation equidistant equivalence event exactly example experiment expression fact factors favorable outcomes Finally five follows formula four given gives Hence intersection joining kings knights least length letters lies marked means multiple n-gon Note obtain occupied occurs pairs partition pass passengers paths pieces placed plane points polygons positive integers possible outcomes powers prime probability problem prove queens random reasoning rectangle relation remaining Remark result rooks satisfy segment selected sequence shown side Similarly solution solved sphere squares Suppose third total number triangle values vertex vertices