The games for the main tournament of the Game Tournament competition will be chosen from the following games and announced at the start of the tournament.
The game starts with a 5 x 5, 6 x 6, or 7 x 7 grid of dots, with some horizontal and/or vertical segments connecting adjacent dots pre-filled. The dimensions of the grid and the number and location of the pre-filled segments will be chosen in advance by the tournament organizers and will be the same for all competitors in each round.
On each turn, a player draws a horizontal or vertical segment connecting two adjacent dots. If as a result of this move a unit square is created, it is marked with the player's initial (or number or any other mark) and the same player goes again. When no new square is created, the turn passes to the other player.
The game ends when all possible segments have been drawn and thus all unit squares are marked. Each player counts how many squares they have marked. This is their score.
The total possible score per game for an n x n grid (n = 5, 6, or 7) is (n-1)^2 points, equal to the number of boxes to be claimed.
The game pieces are round plastic chips, colored red on one side and yellow on the other.
The game starts with a 4 x 4, 5 x 5, or 6 x 6 square board with chips pre-set in some of the squares, with 8-16 empty squares. The dimensions of the board and the number, locations, and orientations (yellow/red) of the pre-set chips will be chosen in advance by the tournament organizers and will be the same for all competitors in each round.
In each game the player who plays first will be yellow and the other player will be red, regardless of who is choosing whether to go first or second.
On each turn, a player can place their chip in any square so that in at least one row or column or diagonally there are chips of the opposite color consecutively adjacent to the chip being placed, followed, consecutively, by at least one chip of their color. When the new chip is placed, the chips of the opposite color surrounded by this new chip and another one of the same color are turned over, so that the whole stretch becomes the color of the new chip.
The game ends when the player whose turn it is has no available moves. Each player counts how many chips of their color are currently on the board. This is their score.
The total possible score per game for an n x n board (n = 4, 5, or 6) is n^2 points.
Competitors who qualify for the final game will play Math Horseshoes to determine their final score and placement. Paper and pencils will be provided, but competitors are not allowed to consult calculators, reference materials, the internet, or other people during the game.
At the start of the game, a set of four, five, or six computing numbers, all whole numbers between 1 and 20 inclusive, and a target number (somewhere between 100 and 2000), will be given.
The participants have three minutes to make an expression using the given computing numbers, exactly once each, and any of the operations of
Addition
Subtraction
Multiplication
Division
Exponentiation
Square root
Parentheses.
The object is to create a value that is as close to the target number as possible. Participants do not have to calculate the exact value of the expression in the allotted time.
Participants must write, on the provided answer sheet, exactly one expression for consideration before time is called.
When the time is called, each participant evaluates their expression (calculators and/or help from proctors are allowed) and computes the positive difference between their value and the target number.
The game is called "Horseshoes" because the closer you are, the better your score!
If the value E of the participant's expression is less than 2 units away from the target number T, i.e. |T-E| < 2, then the participant receives 10 points. Otherwise the score for a valid expression is 10-N where 2^N ≤ |T-E| < 2^(N+1), or 0 if |T-E| is greater than or equal to 1024 = 2^(10). For example:
If the target number is T = 782 and the value of the participant's expression is E = 793, then |T-E| = 11. 2^3 ≤ 11 < 2^4, so the score is 10 - 3 = 7 points.
If the target number is T = 1836 and the value of the participant's expression is E = 1833.345, then |T-E| = 2.655. 2^1 ≤ 2.655 < 2^2, so the score is 10 - 1 = 9 points.
If the target number is T = 127 and the value of the participant's expression is E = 1182.8, then |T-E| = 1055.8 ≥ 1024, so the score is 0 points.
If the expression is not a valid expression, the participant receives 0 points.
The raw score out of 10 points will be scaled based on the main tournament scores in order to minimize ties.
Suppose the computing numbers are 1, 3, 4, and 17 and the target number is 341.
The expression √((17+3)^4) - 1 = 399 would earn a score of 10 - 5 = 5 points since 399 - 341 = 58 is between 32 = 2^5 and 64 = 2^6.
The expression (4/3)^(17+1) ≈ 177.377 would earn a score of 10 - 7 = 3 points since 341 - 177.377 = 163.623 is between 128 = 2^7 and 256 = 2^8.
The expression ((17+1)^3)/17 - 4 ≈ 339.059 would earn a score of 0 since the computing number 17 was used twice.
The expression 4^(√(17+1)) ≈ 358.364 would earn a score of 0 since the computing number 3 was not used.
The square root, like the other symbols, can be used "for free" since it does not require a number to be written. This can help you adjust your expression without using any computing numbers. For example, √((17+3)^4) - 1 = 399.