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P.V.Rama Brahmam ,M.Sc.Maths DEPARTMENT OF MATHEMATICSRB IIT/NEET ACADEMY. “ Mathematics is the only truly Universal language ”- Carl SaganThe inherent beauty and the University of Mathematics have been appreciated by the humans since origin of man kind in many ways. The importance and the unique position of mathematics also have been well respected since ages. The ancient Indian mathematician Lagdha in his composition ‘Vedanga Jyotisha’ has remarked that “Like the crest of a peacock and the head jewel of a cobra, so does Mathematics stand at the top of the Vedic sciences.” Mathematics has always been a powerful language to explain the beauty of both the earth and the nature.Many have found it difficult to differentiate some branches of Mathematics as to whether it is a form of art or science. Bertrand Russell has remarked that Mathematics is the greatest form of art!Despite all these traditional grandeur many have felt Mathematics , a hand nut to crack and the learning of mathematics , quite boring. Many of us feel that it is due to lack of inspiring teachers. At the same time, all over the world, attempts have been made to popularise mathematics at all levels by organizing contests and awarding prizes to honour one’s contributions to the cause of mathematics. The concept of organizing competitions to spot mathematically talented students.To face such competitions one need of good mathematical treasures at lower level. After 20 years of teaching Mathematics for all kinds of students, I realized the importance and need of a good book for Math enrichment. The idea to write this book, and more important the desire to do so is the scarcity in the field of book treasure of foundation in Mathematics towards olympiads. This book is organized into six parts and solution to the problem present in each part is one strategy.First part deals with tricky problems. What is tricky problem? Concept clarity students and even teachers put lot of efforts to get the solution for problems. Even after tireless efforts a few fail to solve the problem, few are able problems. Even after tireless efforts a few fail to solve the problem, few are able to solve the problems in lengthy way and very few come out with elegant methods with minimum number of steps. Start enjoying by putting your head into this topic by observing stunning solving methods present in this.Second part deals with math beauties. Critical insight, good concepts, control over all topics, good solving strategies and little efforts give path to get desired answers for the questions present in this topic. Before putting your head into the solutions you put tireless efforts and perceive the real mathematical beauty involved in it.Third part deals with problem solving strategies where I adopted many solving strategies for variety of problems which can’t be solved directly. Multiple approaches to solve problems also discussed for giving a message that the solution to the problem is not only unique but also to create intention among student community to come out with their own better solving strategies.To solve hard problems present in fourth part one need good concept, control over all basics, solving capabilities in addition to typical efforts, more concentration and lot of patience is required to break the logic .Worthy hard working teaching -student community will observe the lot of mathematical beauty, who ever put efforts in solving these problems with out seeing the solutions.As the author I hope this topic ‘non-routine problems fulfils the complete desires of students or teachers whoever is hungry of mathematical logical food, whose interest and eager - ness continues after seeing all the above parts and further in search of more brain ticklers.Major intention of writing this book is I feel my self extraordinary in obtaining the solutions to typical problem collection after tire less efforts and the strategies of solving which I collected from several sources stunned me for a moment giving a feeling that this can be solved in this way being always logically hungry person. After perceiving the beauty I feel why don’t I explore to the ideas to needy segment that are in search of them. Which result in the form of book named “Mathematical Marvels”.Parents and students are behind IITJEE admission and they are unaware of preparation methods but interested to invest their maximum earnings for their children comfortable settlement in the coming future. Almost all Olympiad IIT top rankers are IIT toppers. Is it not sure test of