The Biggest Brain

⚔️ Final Match 1: The Biggest Brain ⚔️

Congratulations on making it this far. The ORG might have had hiccups here and there, but you two have persevered 'till the end. You have outwitted, outplayed, and outlasted the other twelve players; now, your only remaining opponent is each other. This game is the first roadblock of your final leg in the journey on becoming the champion. The player that can better use the full capacity of their mind under intense pressure will win the first point, getting one step closer to lifting the trophy. Do you have the biggest brain?

Your goal is to connect opposite sides of a board by drawing lines. However, in order to draw a line on the board, you must form mathematical equations using numbers obtained from solving puzzles. The first player to make the connection wins the first Final Match.

RULES

There are two channels, #fm1-puzzles and #fm1-game-room. However, #fm1-puzzles is read-only. The game will be played on #fm1-game-room.

Puzzles will be posted in #fm1-puzzles. At the start of the game, 4 puzzles will be released, and at regular intervals, one new puzzle will be released until there are 20. Each puzzle has a letter from A-T associated to it, and puzzles will be released in order from A to T (so the first 4 puzzles are A-D, then the next puzzle is E, and so on). The answer to each puzzle is a number.

The game will take place on the following board of interleaved grids of 5x6 dots, with X's marking spots between adjacent pairs of dots.

Danny will use the red dots and Uri will use the blue dots. Your goal is to connect the opposing marked sides of your dots: Danny connecting left to right, Uri connecting top to bottom. You can connect two adjacent dots of your color by a line, over a spot marked with X. Lines may not intersect, thus when you draw a line over a spot, your opponent cannot draw a line over the same spot.

There are 16 spots on the board marked yellow. These are also called "sideways" spots, because if you draw a line over one such spot, you are drawing a line sideways that does not directly help you connect your two sides closer. In the game, there is no difference between a sideways spot and a non-sideways spot; however, several items specifically refer to sideways spots.

In the actual game, each X is replaced by a number. In order to connect a line across a number, you must give a mathematical expression evaluating to that number. The precise rules are as follows.

The game is played in real-time; there are no turns, and you may make a move at any time. To make a move, you must name a number on the board, and give a mathematical expression evaluating to that number. The expression must follow these rules:

• It contains between 2 and 5 letters, among A-T.
• It may only use five arithmetic operations (+, -, x, /, % (modulus)) as well as parentheses. - may be used as a unary minus. (You can use either x or * for multiplication, but be careful of using * as it is a Discord formatting. I usually can read it if you mistakenly use *, but better be safe than sorry.)
• Letters may not be concatenated (put side by side).
• No letter may be used more than once in the expression.

For example, "Ax(B-C)" is a valid expression. These expressions are not valid: "D" (only one letter), "B+B" (reuses a letter), "CA" (concatenated), "Dx/A" (malformed expression).

The value of an expression is obtained by replacing each letter with the answer to the puzzle with that letter, and evaluating the resulting mathematical expression. To emphasize, there is no way for you to confirm an answer to a puzzle; you can only use it in expressions. While technically you can use any puzzle letter even before the puzzle shows up, it is probably not useful.

The result is not capped or rounded in any way; it is possible that the result is negative or fractional. If you attempt to divide by zero (using / or %), the result is the number NaN, and any operation on NaN produces another NaN. When using modulus (%), the result has the same sign as the divisor; for example, -5 % 3 = 1 and 5 % -3 = -1.

If your move is not legal (either because the expression is not valid, or the number you name is not on the board or already claimed), I will reject it, but there is no other penalty; you may make a new move right away. If your move is legal, you will enter a waiting period, during which you cannot submit any move; I will reject any move you attempt to make during your waiting period.

Once the waiting period is over, the result of the expression will be shown privately to your opponent. You will only know whether the result matches the number you're claiming or not. If the result matches, you will draw a line connecting your dots on the spot you're claiming. If it doesn't match, you don't draw any line, but there is no other penalty.

If your opponent is in the waiting period for a move, you may make a move that also claims the same spot; it's legal to do so. But if your opponent's move is correct and they claim the spot, you must still wait out your full waiting period, and even if your move is correct, you will not be able to claim the same spot (since lines may not cross). (The result of your expression will still be revealed to the opponent, and you will still know whether the result matches the number or not.)

The first player to connect their two opposite sides wins the Final Match.

ITEMS

The following items are available in this game. As per the item distribution, Danny has the Vary item, and Uriquack has the Veto and View items.

In addition, Uriquack has the global Copy item, and Danny has the global Delete item. You may only use Copy and Delete before the start of the game. Once the game has started, all items for this game are fixed.

As a reminder, the sideways spots are marked with yellow on the board.

Vary: Choose a sideways spot (by naming its number). That spot's number is changed to 492 for the rest of the game. (If this item is copied and as a result there are two 492s on the board, they will be distinguished in some manner.)

Veto: Your opponent's next (legal) move may not be on the sideways spots. If your opponent makes a move on a sideways spot, it is treated as an illegal move with the usual implications: I refuse the move, but the opponent may immediately make a new move, and as the opponent hasn't yet made a legal move, it still cannot be on a sideways spot. (If your opponent has a move in the waiting period, it may be on a sideways spot just fine. The restriction is for the opponent's next move.)

View: Before the start of the game, choose a puzzle letter (publicly). You will privately get the puzzle associated with that letter at the start of the game.

ADMINISTRATION

Make your moves in #fm1-game-room. To make a move, post the number you're attempting to claim and the expression you wish to use.

Use items by posting in #fm1-game-room in any reasonable format.

Information revealed in #fm1-game-room: current board; timestamps of when you submit an expression and when I update the board. (The timestamps are mostly for my convenience.)

Information revealed in #fm1-puzzles: the puzzles.

Information revealed in your private channel: results of your opponent's expressions. If you hold the View item, also the puzzle you decide to see.

Timing:

• Puzzles are posted at 2-minute intervals. Therefore, the fifth puzzle will be available 2 minutes into the game (remember, you start with four revealed). An unwilling spectator a volunteer will be the one posting the puzzles.
• The waiting period for a move is 1 minute. Since I'm going to do updates manually, allow a few seconds of delay.

CLARIFICATIONS

In general, you may use a four-function calculator and a spreadsheet, but not a special program that gives you mathematical expressions or helps you solve puzzles. You may also use the internet to look up stuff since some puzzles will require trivia. However, you may not talk to other people during the DM. You may bring prepared notes to the DM.

What kind of puzzles should you expect? Well, you might have known Zero's puzzles from his other ORGs, like Zero's Gauntlet and Master of All Trades. Expect more ridiculous puzzles from me. To quote my intro, by the end of this ORG you will know me. and fear me. a lot.

The following is an example puzzle to give you some idea how each puzzle will look like. It may or may not reflect the contents of the puzzles you will face during the game.