Math Riddles and Puzzles

A puzzle is a problem that challenges one's ability to think out of the box and come up with original solutions. Puzzles can be thought provoking and entertaining. In recent times, puzzles have become the base for mathematical research. Arithmetic and logical puzzles have served this purpose.

A riddle can be defined as an interrogatory statement that has two meanings and is generally asked as a puzzle to be solved by the observant. Most of the riddles have a clue within themselves and it lies in the creativity and presence of mind of the observer to crack it. Let us look at various types of riddles and puzzles.

Types of Riddles

In general, riddles can be divided into two main sections, namely enigmas and conundrums. The former is a type of a question that is presented in a metaphorical language. These can be cracked or solved only after careful observation of the problem statement. Most of the ancient English poems had these kinds of enigmas embedded within them.

Conundrums are similar to enigmas but for the fact that the answer lies hidden in the question itself and application of the concept of punning can bring out the real answer hidden within the question. The usage of different meanings for the same word in the question with a common spelling too, can extract the hidden truth.

Types of Math Puzzles

Math puzzles can be divided into a number of types. They have been described in the following lines.

Arithmetic Puzzles
Arithmetic puzzles are those that involve simple calculus and general mathematics. The solution simply depends on the correct application of the optimal method and performing a set of simple calculations to arrive at the final answer.

Algebraic Puzzles
Algebraic puzzles can be defined as those that involve any type of algebra to arrive at the solution. The question generally contains a statement that depicts the conditions of a problem statement precisely. In order to arrive at the solution, it is necessary that you apply theorems and common sense. Algebra does not stop with general algebra alone. The list also includes modern algebra and Boolean algebra among others.

Combinatorial Puzzles
When a solution for a certain type of puzzle depends on the combinations or permutations of the entire input set, then the puzzle can be defined as a combinatorial puzzle. As stated earlier, the solution can only be arrived at, by using permutations and combinations of a valid set of required inputs. The solutions are relational within them and the change in one dataset affects the whole solution.

Graph Puzzles
Certain kinds of puzzles involve the direct application of graph theory concepts and hence, are known as graph puzzles. Well-known puzzles like the Konigsberg's bridge problem and the shortest path problem are best examples of graph puzzles.

Puzzles Based on Probability
A wide variety of puzzles are based on the concept of probability. Pure probabilistic theorems and pre-defined concepts related to probability can be used to arrive at the solution. Many arithmetic puzzles involve probabilistic puzzles within them and use probability to arrive at a part of the solution. The Monty Hall problem and Three Prisoners problem are well-known examples.

Puzzles Related to Packing and Dissecting
Most of the arithmetic problems come under this category of packing and dissecting. These are a set of trial and error kind of puzzles. The solutions to such puzzles are obtained by the method of induction. 'The eight queens problem' in a chessboard is a good example for these type of problems.

Puzzles and riddles not only serve to be a good pastime but also improves one's thinking capability and the pace of solving math problems. Just like your body muscles need exercise to develop, so do your brain require a mental challenge, to sharpen thinking abilities. Try out as many math riddles and puzzles as you can, but beware, after a point of time, it becomes addictive!