By Henry E. Dudeney, Martin Gardner

For 2 a long time, self-taught mathematician Henry E. Dudeney wrote a puzzle web page, "Perplexities," for *The Strand Magazine.* Martin Gardner, longtime editor of *Scientific American*'s mathematical video games column, hailed Dudeney as "England's maximum maker of puzzles," unsurpassed within the volume and caliber of his innovations. This compilation of Dudeney's long-inaccessible demanding situations attests to the puzzle-maker's reward for growing witty and compelling conundrums.

This treasury of interesting puzzles starts off with a variety of arithmetical and algebraical difficulties, together with demanding situations concerning funds, time, pace, and distance. Geometrical difficulties persist with, besides combinatorial and topological difficulties that characteristic magic squares and stars, direction and community puzzles, and map coloring puzzles. the gathering concludes with a chain of video game, domino, fit, and unclassified puzzles. suggestions for all 536 difficulties are integrated, and captivating drawings liven up the booklet.

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**Sample text**

It is extremely important in the worlds of biology, sociology, engineering, and computer science. Surprisingly, graph theory had its origins in a recreational problem now known universally as The Seven Bridges of Königsberg. The problem was eventually tackled and solved by using the basics of what is now known as graph theory by Leonard Euler (1707–1783), one of the greatest mathematicians who ever lived. Another example of the overlap between recreational mathematics and more serious mathematics is found when you consider the origins of probability theory.

It is my sincere hope that the contents of this book fulfill that aim. Magic squares have fascinated people of all ages through the centuries. A magic square is an array of numbers, usually distinct, arranged in square formation. Thus a magic square contains the same number of horizontal rows as vertical columns. The magic square derives its name from the fact that the sums of the numbers in each row, in each column, and across its two diagonals, are identical. Although no mathematical knowledge is imparted through the study of magic squares, nevertheless many have investigated these squares with the expectation of finding beautiful relationships between the integers within the squares.

Magic squares of order n, commencing with integer A, may be formed where the numbers within them are increasing in an arithmetic series with a difference of D between terms. The constant of such a magic square may be obtained by using the following simple formula: Thus in the simplest three-by-three magic square the smallest integer is 1, and the integers are increasing in an arithmetic series, with a common difference of 1 between terms. Thus, in the above expression A = 1, D = 1, and n = 3. The expression then produces a constant that equals This equals , which equals 15.