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A domination (or covering) problem involves finding the minimum number of pieces of the given kind to place on a chessboard such that all vacant squares are attacked at least once. It is a special case of the vertex cover problem. The minimum number of dominating kings is 9, queens is 5, rooks is 8, bishops is 8, and knights is 12.
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The stated intent was to recruit "intelligent individuals" by presenting a series of puzzles to be solved; no new puzzles were published on January 4, 2015. A new clue was posted on Twitter on January 5, 2016. [5] [6] Cicada 3301 posted their last verified OpenPGP-signed message in April 2017, denying the validity of any unsigned puzzle. [7]
The 24 puzzle is an arithmetical puzzle in which the objective is to find a way to manipulate four integers so that the end result is 24. For example, for the numbers 4, 7, 8, 8, a possible solution is ( 7 − ( 8 ÷ 8 ) ) × 4 = 24 {\displaystyle (7-(8\div 8))\times 4=24} .
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Let G be a graph with n ≥ 1 vertices.Trivially, the eternal domination number is at least the domination number γ(G).In their paper, Goddard, Hedetniemi, and Hedetniemi proved the eternal domination number is at least the independence number of G and at most the clique covering number of G (the clique covering number of G is equal to the chromatic number of the complement of G).
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