1. Here's a table showing how many matches are needed for a few different numbers of players:
| Number of players |
Number of matches needed |
| 3 | 3 |
| 4 | 6 |
| 5 | 10 |
| 6 | 15 |
| N | $\frac{(N-1)N}{2}$ |
These numbers could be found adding up possible pairs. If we have N players A1, A2...An then the number of possible pairs is $(N - 1) + (N - 2) + (N - 3) + ... + 3 + 2 + 1 = \frac{(N-1)N}{2}$.
2. If we have three players A, B, C we need three rounds:
A - B
A - C
C - B
If we have four players A, B, C, D we still need three rounds:
A - B and C - D
A - C and B - D
A - D and B -C
If we have five players A, B, C, D, E we need five rounds:
A - B and C - D
A - D and C - E
A - E and B - D
A - C and B - E
B - C and D - E
3. A pentagon with arrows:
A hexagon with arrows:
4. Coloring using the trick:
