Contents
Foreword vi i
Preface t o the Russia n Editio n i x
Part I . Th e Firs t Yea r o f Educatio n
Chapter 0 . Chapte r Zer o 1
Chapter 1. Parit y 5
Chapter 2 . Combinatorics- 1 1
Chapter 3 . Divisibilit y an d Remainder s 19
Chapter 4 . Th e Pigeo n Hol e Principle 3 1
Chapter 5 . Graphs- 1 3 9
Chapter 6 . Th e Triangl e Inequalit y 5 1
Chapter 7 . Game s 5 7
Chapter 8 . Problem s fo r th e Firs t Yea r 6 5
Part II . Th e Secon d Yea r o f Educatio n
Chapter 9 . Inductio n (b y I. S. Rubanov) 7 7
Chapter 10. Divisibility-2 : Congruenc e an d Diophantin e Equation s 9 5
Chapter 11. Combinatorics- 2 107
Chapter 12. Invariant s 123
Chapter 13. Graphs- 2 135
Chapter 14. Geometr y 153
Chapter 15. Numbe r Base s 167
Chapter 16. Inequalitie s 175
Chapter 17. Problem s fo r th e Secon d Yea r 187
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