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The city, originally named Kaiping (开平; 開平; Kāipíng; 'open and flat'), was designed by Chinese architect Liu Bingzhong from 1252 to 1256, [4] and Liu implemented a "profoundly Chinese scheme for the city's architecture". [5] In 1264 it was renamed Shangdu by Kublai Khan. At its zenith, over 100,000 people lived within its walls.
Unlike other puzzle books, each page is involved in solving the book's riddle. Specifically, each page represents a room or space in a hypothetical house, and each room leads to other "rooms" in this "house". Part of the puzzle involves reaching the center of the house, Room #45 (page 45 in the book), and back to Room #1 in only sixteen steps.
It is impossible to solve in half of the starting positions. [1] Five room puzzle – Cross each wall of a diagram exactly once with a continuous line. [2] MU puzzle – Transform the string MI to MU according to a set of rules. [3] Mutilated chessboard problem – Place 31 dominoes of size 2×1 on a chessboard with two opposite corners removed ...
Famous Trick Donkeys is a puzzle invented by Sam Loyd in 1858, [1] first printed on a card supposed to promote P.T. Barnum's circus. At that time, the puzzle was first called "P.T. Barnum's trick mules". [2] Millions of cards were sold, with an estimated income for Sam Loyd of $10,000 from 1871 [3] —more than $200,000 in 2023 dollars. [4]
The search time required for the 4-list algorithm to find an optimal solution is considerably longer compared to Kociemba's or Feather's algorithm. Bidirectional search works by searching forward from the scrambled state, and backward from the solved state simultaneously, until a common state is reached from both directions.
The missionaries and cannibals problem, and the closely related jealous husbands problem, are classic river-crossing logic puzzles. [1] The missionaries and cannibals problem is a well-known toy problem in artificial intelligence , where it was used by Saul Amarel as an example of problem representation.
The puzzle is known to have appeared as early as 1981, in the book Super Strategies For Puzzles and Games. In this version of the puzzle, A, B, C and D take 5, 10, 20, and 25 minutes, respectively, to cross, and the time limit is 60 minutes. [6] [7] In all these variations, the structure and solution of the puzzle remain the same.
A common and simple version of this problem asks to measure a time of 45 seconds using only two fuses that each burn for a minute. The assumptions of the problem are usually specified in a way that prevents measuring out 3/4 of the length of one fuse and burning it end-to-end, for instance by stating that the fuses burn unevenly along their length.