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For many algorithmic problems found in practical systems, the best solutions are usually the elegant combinations of both efficient algorithms and advanced programming techniques. They are the results of some exciting blend of programming, mathematics and problem solving. ?The course introduces an interesting variety of subjects in programming, algorithms, and discrete mathematics through puzzles and practical problems so that students will have the chance to perform original discovery of new programming challenges and devise new ideas on solving the problems in an innovative way in terms of algorithms and programming techniques. ?After learning the course, the students will be able to develop advanced algorithmic and programming skills that are required to solve sophisticated problems in the real world. Due to the practicality of the problems which appear in many collegiate programming contests, we expect that the best students from this course will also be competent to solve competition-style programming problems and may be able to represent City University of Hong Kong at ACM Collegiate Programming contests.