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The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of Alice's Adventures in Wonderland.In his book The Game of Logic he introduced a game to solve problems such as confirming the conclusion "Some greyhounds are not fat" from the statements "No fat creatures run well" and "Some greyhounds run well". [1]
One strategy for solving this version of the hat problem employs Hamming codes, which are commonly used to detect and correct errors in data transmission. The probability for winning will be much higher than 50%, depending on the number of players in the puzzle configuration: for example, a winning probability of 87.5% for 7 players.
Hermite's problem is an open problem in mathematics posed by Charles Hermite in 1848. He asked for a way of expressing real numbers as sequences of natural numbers , such that the sequence is eventually periodic precisely when the original number is a cubic irrational .
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.
Juggler sequences can reach very large values before descending to 1. For example, the juggler sequence starting at a 0 = 37 reaches a maximum value of 24906114455136. Harry J. Smith has determined that the juggler sequence starting at a 0 = 48443 reaches a maximum value at a 60 with 972,463 digits, before reaching 1 at a 157.
To solve this problem, Kociemba devised a lookup table that provides an exact heuristic for . [18] When the exact number of moves needed to reach G 1 {\displaystyle G_{1}} is available, the search becomes virtually instantaneous: one need only generate 18 cube states for each of the 12 moves and choose the one with the lowest heuristic each time.
In this variant of the problem, which allows for interesting applications in several contexts, it is possible to devise an optimal selection procedure that, given a random sample of size as input, will generate an increasing sequence with maximal expected length of size approximately . [11] The length of the increasing subsequence selected by ...
A method is formally called effective for a class of problems when it satisfies these criteria: It consists of a finite number of exact, finite instructions. When it is applied to a problem from its class: It always finishes (terminates) after a finite number of steps. It always produces a correct answer.
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