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The Tower of Hanoi (also called The problem of Benares Temple, [1] Tower of Brahma or Lucas' Tower, [2] and sometimes pluralized as Towers, or simply pyramid puzzle [3]) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod.
Wire puzzles, or nail puzzles consist of two or more entangled pieces of more or less stiff wire, metal rods, or bent nails. The pieces may or may not be closed loops. The closed pieces might be simple rings or have more complex shapes. Normally the puzzle must be solved by disentangling the two pieces without bending or cutting the wires. [10]
There is even enough additional freedom on the torus to solve a version of the puzzle with four houses and four utilities. [21] [5] Similarly, if the three utilities puzzle is presented on a sheet of a transparent material, it may be solved after twisting and gluing the sheet to form a Möbius strip. [22]
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Although the puzzle is a disentanglement-type puzzle, it also has mechanical puzzle attributes, and the solution can be derived as a binary mathematical procedure. The Chinese rings are associated with the tale that in the Middle Ages , knights would give these to their wives as a present, so that in their absence they may fill their time.
The muddy children puzzle is the most frequently appearing induction puzzle in scientific literature on epistemic logic. [4] [5] [6] Muddy children puzzle is a variant of the well known wise men or cheating wives/husbands puzzles. [7] Hat puzzles are induction puzzle variations that date back to as early as 1961. [8]
A puzzle can be expressed as a graph coloring problem. [9] The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The Sudoku graph has 81 vertices, one vertex for each cell. The vertices are labeled with ordered pairs (x, y), where x and y are integers between 1 and 9.
After the player has correctly solved the crossword puzzle in the usual fashion, the solution forms the basis of a second puzzle. The designer usually includes a hint to the metapuzzle. For instance, the puzzle Eight Isn't Enough by Matt Gaffney gives the clue "This week's contest answer is a three-word phrase whose second word is 'or'."