Chess tournament streaks
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On lichess.org, they use a points system for keeping track of who is winning in the 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.
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.
mathematics combinatorics chess
asked 9 mins ago
Brandon_JBrandon_J
1,794230
$endgroup$
add a comment |
$begingroup$
On lichess.org, they use a points system for keeping track of who is winning in the 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.
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.
mathematics combinatorics chess
asked 9 mins ago
Brandon_JBrandon_J
1,794230
$endgroup$
$begingroup$
I'm not sure if the combinatorics tag is correct. If you have any insight into this, please let me know and drop an edit if necessary.
$endgroup$
– Brandon_J
8 mins ago
add a comment |
$begingroup$
On lichess.org, they use a points system for keeping track of who is winning in the 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.
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.
mathematics combinatorics chess
asked 9 mins ago
Brandon_JBrandon_J
1,794230
$endgroup$
On lichess.org, they use a points system for keeping track of who is winning in the 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.
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.
mathematics combinatorics chess
mathematics combinatorics chess
asked 9 mins ago
Brandon_JBrandon_J
1,794230
asked 9 mins ago
Brandon_JBrandon_J
1,794230
edited 3 mins ago
Brandon_J
asked 9 mins ago
Brandon_JBrandon_J
1,794230
asked 9 mins ago
Brandon_JBrandon_J
1,794230
asked 9 mins ago
Brandon_JBrandon_J
1,794230
1,794230
$begingroup$
I'm not sure if the combinatorics tag is correct. If you have any insight into this, please let me know and drop an edit if necessary.
$endgroup$
– Brandon_J
8 mins ago
add a comment |
$begingroup$
I'm not sure if the combinatorics tag is correct. If you have any insight into this, please let me know and drop an edit if necessary.
$endgroup$
– Brandon_J
8 mins ago
$begingroup$
I'm not sure if the combinatorics tag is correct. If you have any insight into this, please let me know and drop an edit if necessary.
$endgroup$
– Brandon_J
8 mins ago
$begingroup$
I'm not sure if the combinatorics tag is correct. If you have any insight into this, please let me know and drop an edit if necessary.
$endgroup$
– Brandon_J
8 mins ago
add a comment |
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$begingroup$
I'm not sure if the combinatorics tag is correct. If you have any insight into this, please let me know and drop an edit if necessary.
$endgroup$
– Brandon_J
8 mins ago