Contents
Chapter 1. Th e Fou r Number s Proble m 1
1. Introductio n 1
2. Th e Fou r Number s Gam e Rul e 2
3. Symmetr y an d th e Fou r Number s Gam e 5
4. Doe s Ever y Fou r Number s Gam e Hav e Finit e Length ? 11
5. Game s Wit h Lengt h Independen t o f th e Siz e o f th e Number s 15
6. Lon g Game s 17
6.1. Som e Forma l Notatio n 18
6.2. Constructin g Lon g Game s 19
7. Th e Tribonacc i Game s 2 2
7.1. Computatio n o f L(T n) 2 2
7.2. Uppe r Bound s fo r Length s o f Game s 2 3
8. Th e Lengt h o f th e Fou r Rea l Number s Gam e 2 6
8.1. Linea r Algebr a Come s Int o Pla y 2 6
8.2. Constructio n o f a Fou r Number s Gam e o f Infinit e Lengt h 2 7
8.3. Constructio n o f Al l Fou r Number s Game s o f Infinit e Lengt h 2 8
9. Th e Probabilit y tha t a Fou r Number s Gam e End s i n n Step s 3 2
10. Th e fc-Numbers Gam e 4 1
Bibliography 4 5
Chapter 2 . Rationa l Righ t Triangle s an d th e Congruen t Numbe r
Problem 4 7
1. Introductio n 4 7
2. Righ t Triangle s 4 8
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