1. A telescoping sum -- 2. Lagrange's identity -- 3. Perfect squares -- 4. Lest common multiples -- 5. Trig substitutions -- Coffee break 1 -- 6. Popoviciu's theorem -- 7. Catalan's identity -- 8. Several inequalities -- 9. Vectors -- 10. Mathematical induction at work -- Coffee break 2 -- 11. A highly divisible determinant -- 12. Hermite's identity -- 13. Complete sequences -- 14. Three polynomials -- 15. More about induction -- Coffee break 3 -- 16. A classical identity -- 17. Multiplicative functions -- 18. The "arbitrary" Proizvolov -- 19. Hölder's inequality -- 20. Symmetry -- Coffee break 4 -- 21. He knows I know he knows -- 22. A special inequality -- 23. Two inductive constructions -- 24. Some old-fashioned geometry -- 25. Extremal arguments -- Coffee break 5 -- 26. The AMS inequality -- 27. Helly's theorem for one dimension -- 28. Two approaches -- 29. Radical axis -- 30. The pigeonhole principle -- Coffee break 6 -- 31. The three jug problem -- 32. Rectifying trajectories -- 33. Numerical systems -- 34. More on polynomials -- 35. Geometric transformations -- Coffee break 7 -- 36. The Game of life problem -- 37. Tetrahedra with a point in common -- 38. Should we count -- 39. Let's count now -- 40. Some elementary number theory -- Coffee break 8 -- 41. Euclid's game -- 42. Perfect powers -- 43. The 2n-1 problem -- 44. The 2n+1 problem -- 45. The 3n problem -- Coffee break -- 46. Pairwise sums -- 47. Integer progressions -- 48. Incomparable sets -- 49. Morse's sequence -- 50. A favorite of Erdös.