On lichess.org, they use a points system for keeping track of who is winning in a tournament. A win is worth two points, a draw is worth one point, and a loss worth zero points. Once a player has amassed two wins in a row, the following games will be worth double of what they are normally worth until there is a draw or a loss to break the winning streak. Furthermore, a player may "berserk" and cut their time in a game in half in order to add one extra tournament point with a win.
Here's an example: loss=0, win=2, win(berserked)=3, win=4, win(berserked)=5, win=4, drawbreaking the streak=2, draw(berserked)=1, loss=0, draw=1, represented as 0234542101, for a grand total of 22 tournament points. You can also find the official lichess explanation here.
To see if you understand, find a simple way to score 15 points in 4 games as a warm-up:
Win all four games, and berserk any three of them - for example, all but the first one, for a pattern of 2355.
Part One: (easy)
A player played 18 games, won two-thirds of them, and "berserked" half of them.
What is the minimum and maximum number of tournament points he could have received?
Part Two: (Hard)
How many ways are there to score seven points in seven games?
Note that permutations of a "way" are not additional "ways": 0202021 is the exact same solution as 0022012 or 2020201, but not the same solution as 3020200.