This is a list of puzzles that cannot be solved. An impossible puzzle is a puzzle that cannot be resolved, either due to lack of sufficient information, or any number of

logical Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

impossibilities. *

15 puzzle The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others) is a sliding puzzle having 15 square tiles numbered 1–15 in a frame that is 4 tiles high and 4 tiles wide, leaving one unoccupied tile position ...

– Slide fifteen numbered tiles into numerical order. Impossible for half of the starting positions. *

Five room puzzle The five room puzzle is a classical, popular puzzle involving a large rectangle divided into five "rooms". The objective of the puzzle is to cross each "wall" of the diagram with a continuous line only once. Solutions As with the Seven Bridg ...

– Cross each wall of a diagram exactly once with a continuous line. * MU puzzle – Transform the string to according to a set of rules. * Mutilated chessboard problem – Place 31 dominoes of size 2×1 on a chessboard with two opposite corners removed. * Coloring the edges of the

Petersen graph In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is n ...

with three colors. *

Seven Bridges of Königsberg The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology. The city of Königsberg in Prussia (n ...

– Walk through a city while crossing each of seven bridges exactly once. * Three cups problem – Turn three cups right-side up after starting with one wrong and turning two at a time. *

Three utilities problem The classical mathematical puzzle known as the three utilities problem or sometimes water, gas and electricity asks for non-crossing connections to be drawn between three houses and three utility companies in the plane. When posing it in the ea ...

– Connect three cottages to gas, water, and electricity without crossing lines. *

Thirty-six officers problem In combinatorics, two Latin squares of the same size (''order'') are said to be ''orthogonal'' if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are ...

– Arrange six regiments consisting of six officers each of different ranks in a 6 × 6 square so that no rank or regiment is repeated in any row or column.

See also