Abstract
1. The Fibonacci sequence, generalized Fibonacci sequences, and related topics 2. Patterns of dots and partitions of integers 3. Patterns, related to rational numbers: periodic decimal fractions, repunits, and visible lattice points 4. Reflected light rays and real numbers: a theorem of Kronecker 5. The Chinese remainder theorem and invisible lattice points 6. Two famous inequalities and some related problems 7. Mysteries of the their dimension: on cubes, pyramids, and spheres 8. A Glimpse of higher-dimensional spaces: hypercubes, lattice paths, and related number patterns 9. Do it with groups 10. From puzzles to research topics: selected problems of combinatorics
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