Set Theory

In this Death Match, submit numbers onto a grid to satisfy as many unknown sets as possible.

Designer(s): e_is_cool	Match Type: DM (for 2 players)
Featured in: Genius Game 4

Death Match 1: Set Theory

It wouldn't be an AoPS ORG without some advanced mathematics, would it?

Setup

In this game, you and your opponent alternate submitting distinct positive integers onto an 8x8 grid.

There are 10 infinite sets of numbers, labelled from A to J. All of the numbers in each set share some property. A number is said to belong to a set if it satisfies that set’s property. Each set will also have a worth of either 1, 2, or 3. All of the sets are independent from each other. The property and worth of each set is not made public.

Submissions

During your turn, you will submit a positive integer onto an empty cell of the grid. You may not submit a number that already exists on the grid.

Scoring

A submitted number earns n points for each set it belongs to, where n is the worth of the set.

Additionally, if the submitted number forms a 3-in-a-row (either orthogonal or diagonal) with other numbers on the grid such that all three numbers belong to the same set, it earns 3n points, where n is the worth of that set. Note that a submitted number may be part of multiple 3-in-a-rows and that 3-in-a-rows may belong to multiple sets.

Information

After each submission, it will be announced which sets the number belongs to. The amount of points gained is also announced, but not the origin of the points.

Endgame

The game ends when the entire grid has been filled. Whichever player has more points at the end of the game wins. If this is a tie, the player who had the highest scoring move wins. If this is still a tie, then the DMO wins.

Timing

Players have 2 minutes per turn. They are also given 5 minutes of reserve time, which is used in 1-minute increments named periods. Once the 2 minutes for a turn have passed, a period is used up, and the player has 1 minute to submit before the next period is used up. If a player runs out of time, the other player gets to submit instead while keeping their next turn as well.

Restrictions

You may take notes during the DM; however, the use of external tools such as calculators, programs, or spreadsheet formulas is prohibited.

Addendum: The DMO, @Simoz, will decide who goes first. He should make this decision before 24 hours before the DM.

Addendum: When the rules refer to "If a player runs out of time, the other player gets to submit instead while keeping their next turn as well," neither player will gain points for that turn. I do not expect players to run out of time.

Correction: Actually sure if you run out of time your turn is skipping and your opponent gets an extra move. This was what was intended in the ruleset, but if neither player run out of time this should not come into effect.

If there's something dumb that can happen with this and both players complain enough I can just make running out of time be an instant loss

Addendum: The numbers you submit must be less than one million. That means only integers in the range of ~~[1,999999]~~ [10, 999999] are allowed.

Addendum: For this DM, spectators are not allowed to host games.

Clarification: The sets being independent means that the contents of the set are static. Whether a number is in a set is purely determined by whether the number is in the set, and not on any other factors. For example, there won't be sets that are "Set of all numbers that are in no other sets," or "Set of all numbers that are a sum of two previous numbers," or "Set of all numbers in an even row on the grid."

Clarification: The internet counts as a tool.

Important Addendum: For each set, I will provide example numbers that fit into that set, revealed at the beginning of the DM. These numbers cannot be used in the DM. @Death Match Participant

Addendum: One digit numbers are banned. (I promise this is the last last minute rule change.)

Set Theory

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