This interactive educational website is suitable for students of all ages
You are here:
Home
Algorithms
Free Downloads
Free Animations
Free Test Papers
Free Fun & Games
Products & Resources
The underlying ideas in many traditional recreational puzzles and challenging brainteasers can often be extended to areas much more than simple recreation. Indeed, they can find relevance in several branches of computing, engineering, management, mathematics and psychology. For example, the fundamentals of counting using ancient abaci have important applications in number systems in computer hardware, the arrangements of coloured blocks in Rubik’s cube have interesting applications in combinatorial problems, the connections in popular grid puzzles have important analogies in management science and finding paths through mazes can relate to algorithms used in both robotics and databases. Certainly, the history of puzzles, dating back thousands of years, plays an important role in the interdisciplinary approach of this text book.
In this first section, the nature of puzzles and their solutions are described with an objective to highlight algorithms encountered in later sections. Categories include abaci, blocks, boards, chance, grids, logical, matches, mazes, numbers and words. Most of them can be explored interactively in the puzzles and brainteasers sections at the Algana website www.algana.co.uk.
We will distinguish between a puzzle and a brainteaser as follows. A puzzle in its general sense tends to be an interesting solvable problem whose solution is normally achievable in a reasonable time and with reasonable effort. So examples could include playing tic tac toe, searching through a small maze or finding an anagram of a word. Often we can find appropriate solutions to puzzles such as these without the need for special aids such as a calculator, computer or machine. We will probably not count pencil and paper in this regard!
On the other hand, the term brainteaser is normally associated with a solvable problem whose solution might only be achievable in a relatively long time with significant effort, possibly with the support of a computer or machine. So examples could include playing multi-dimensional tic tac toe, searching through a very large maze or finding all of the anagrams of a long word.
Certainly, in either case, the problem in question is usually solvable and the step-by-step procedure for solving it is generally called a solution algorithm. However, it should be born in mind that there exist many interesting problems in computing and engineering for which we cannot say for sure if a solution exists or not, primarily because a solution has not yet been found . For instance, in number theory, the so-called twin primes include pairs such as (5,7) or (11,13) or (17,19) because each pair differs by precisely 2. However, to date no-one knows for sure if there exists a finite or infinite number of twin primes.
Most readers will recognise several of the puzzles included in this section as recreational. Many will have been encountered in school playgrounds or in toy stores. However, it is important to appreciate the development of strategies for solving them. These will probably be less recognizable. They can be generally defined in the context of game theory as one-person games or so-called games against nature. Also, the extension of the puzzles from the realms of recreation to a source of serious technical investigation needs to be thoroughly appreciated for an intrinsic understanding of subsequent sections.
Copyright © Algana 2000-2010. All rights reserved.
Contact Algana Associates: contact@algana.co.uk
BOOKS:
THEORIES:
Complexity Theory
Computability Theory
Graph Theory
Probability Theory
FUNCTIONS:
Ackermann Function
Beta Function
Dwyer Function
Gamma Function
Smarandache Function
Sudan Function
WEBSITES:
Mathworld
Enormath
Multifactorials
more
EXPERTS:
Mo Adda
Safa Alasad
Emma Dwyer
John Dwyer
Reza Joadat
Wathek Talebaoui
Hind Zantout
UNIVERSITIES:
Dubai
India
Japan
Kuwait
UK
USA
more
PUZZLES:
FREE ADVERTS:
advertize your educational link in this page
email:- contact@algana.com
Digital Environment