August 6th, 2009

Math Puzzle Games

Mathematical puzzles games take the form of a range of problems, from simple to complex and deep problems, which are still unsolvec. The history of mathematics is strong connected to history of math games, which have led to the study of many fields in mathematics. Geometrical puzzles, network problems, number games are few of the most well known types of puzzles.

There is an old Egyptian papyrus, which shows that mathematical games were based on mathematical puzzles, since those early ages. Rhind papyrus dates from the 1850 BC. "Seven houses contain seven cats. Each cat kills seven mice. Each mouse had eaten seven ears of grain. Each ear of grain would have produced seven hekats of wheat. What is the total of all of these?"-this kind of riddles appeared in Fibonacci's "Liber Abaci" written in 1202, and many other problems like this are found in writings from that historical period, based, most of them, on the same number, seven.

Archimedes invented a division of a square into fourteen elements creating a game that is very similar to chinese Tangrams involving making figures from the 14 pieces; this requires little mathematical skill.The aim is to see how many convex shapes you can make from the tangram pieces.

The sequence 1, 1, 2, 3, 5, 8, 13, ... where each number is the sum of the previous two numbers, was invented by Fibonacci and he has many other puzzles, like the one with the rabbits. He say that he puts a pair of rabbits between 4 walls, and he asks how many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begins a new pair which from the second month on becomes productive?
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Magic squares are an interesting type of puzzles in which you have to use all the numbers from 1 to NxN, in a NxN board, so that each row, column and diagonal have the same sum. They go far back in time with their origins, and it seems they appeared in China, and that they were called lo-shu. Counting the magic squares of a given order we find out that there are 880 squares of size 4 and 275305224 squares of size 5.

The Thirty Six Officers Problem, first put by Euler in 1779, asks if it is possible to arrange 6 regiments consisting of 6 officers each of different ranks in a 6 × 6 square so that no rank or regiment will be repeated in any row or column. The problem is insoluble but it has led to important work in combinatorics.

The most recent puzzles is Rubik's cube invented by the Hungarian Ernö Rubik. It has an incredible fame. Invented in 1974 it was put on the market in Hungary in 1977. In 1982 10 million cubes had been sold in Hungary, more than the population of the country. It is estimated that 100 million were sold world-wide. It is really a group theory puzzle, although not many people realise this.

There are many math puzzle games which don't require specific mathematical skills or knowledge, but which can help you spend your free time is a pleasant or intelligent manner.