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The roots of connecting dots to create pictures or help with calligraphy can be traced back to the 19th century. The Nine Dots Puzzle is the first known puzzle game where the player has to connect dots. But in this variant the goal is not to draw a picture, but to solve a logic puzzle. The emergence of connect the dots games in the printed ...
The puzzle is studied by D. E. Knuth in an article on estimating the running time of exhaustive search procedures with backtracking. [2] Every position of the puzzle can be solved in eight moves or less. [3] The first known patented version of the puzzle was created by Frederick Alvin Schossow in 1900, and marketed as the Katzenjammer puzzle. [4]
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 or retracing any lines.
Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle. Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set ...
Visual comparison may be used to solve the puzzle. The solution to the puzzle is often listed nearby or in an accompanying answer page of a puzzle book. Additionally, one can cross one's eyes and merge the two pictures into one, in the much the same way as when viewing an autostereogram picture. The differences will appear to blink in and out ...
Example grid for a cross-figure puzzle with some answers filled in. A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells.
In a puzzle, the solver is expected to put pieces together (or take them apart) in a logical way, in order to find the solution of the puzzle. There are different genres of puzzles, such as crossword puzzles, word-search puzzles, number puzzles, relational puzzles, and logic puzzles. The academic study of puzzles is called enigmatology.
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.