Puzzles and Paradoxes have been popular since antiquity, and, in amusing themselves with these playthings men have sharpened their wits and whetted their ingenuity. But it was not for amusement alone that Kepler, Pascal, Fermat, Leibnitz, Euler, Lagrange, Hamilton, Cayley and many others devoted so much time to puzzles. Researches in Recreational Mathematics were guided by the same principles and required the same faculties as the researches leading to the most profound discoveries in mathematics or science.                                                                                (Edward Kasner & James R. Newman)  

There is not much difference between the delight a novice experiences in cracking a clever brain teaser and a delight a mathematician experiences in mastering an advanced problem. Both look on beauty bare-that clean, sharply defined, mysterious, entrancing order that underlies all structure. .                                                                                            (Martin Gardner)    

There is something about a puzzle which appeals to almost everyone, young and old. Perhaps it is a challenge to our thinking powers, the feeling that we must not be conquered by such a small thing.  One pleasant feature is that we do not have to know a great deal about mathematics to get amusement from it.                                                                                          (Helen A. Merill)

To most people "mathematics" is synonymous with "figuring". Actually this idea is far from truth. ...for mathematics is applied logic in its simplest and purest form               (Maurice Kraitchik)

The abstact aspect of mathematics attracts a large following of people who, weary of the complexities  of the human equation in everyday life, turn in their leisure times to the simplicities of recreational mathematics.                                                                            (Eugene E.Northop)

.... ..AND if this has not made a good case to  Solve and Enjoy Puzzles and Mind Games  there is the case of Euler who analysed  Latin Squares ( Leading to today's SUDUKU) and the puzzle about crossing bridges - the 7 bridges of  Konisberg - which in turn led the birth of Topology.. Leibnitz, Pascal and Fermat  were interested in Peg jumping problems and dice gambling problems that led to present day New Algebra . Lagrange, Laplace Poisson were all  engaged  into the coin tossing game and the Saint Peters Paradox , again leading to more knowledge in the field of Probability Theory. A deep analysis of the 15-Puzzle by A.M.Turing  led him to modern day  Computer theory. Besides our own Srinivasa Ramanajam was deeply interest in Magic Squares. And finally Albert Einstein's bookshelf was stacked with mathematical games & Puzzles.......So, it is  not difficult to see why all great mathematical minds thrived on  solving problems when they were elegantly posed.