Broken Prism

In this Death Match, create paths on the grid by making equations that satisfy the target numbers.

Designer(s): uriquack	Match Type: DM (for 2 players)
Featured in: The Genius: House of Larks

Broken Prism

In Broken Prism, players find expressions that evaluate to the Target Numbers. As expression chains are formed, the game takes on another dimension.

Board

This game takes place on a triangular board consisting of 49 smaller triangular units. For notation purposes, there will be a guide board for which each triangular unit has been labeled from A to w (A through Z, then a through w). Each side of a triangular unit will represent one single or double digit number. Any one triangular unit will have 3 unique sides, meaning no two sides will have the same number.

To prevent errors based on case sensitivity, A and a will not have any sides of the same value; B and b will not have any sides of the same value; C and c will not have any sides of the same value, and so on.

Guide Board

Example of a Game Board

Target Numbers

Each round, players are given Target Numbers. Players must find an expression that evaluates to the Target Number. Expressions are formed by sides of triangular units joined together by operations of the player’s choice. Each side of a triangular unit is represented by a number symbol to be used in expression chains. Expressions must be a contiguous chain of triangle sides, meaning that the sides must connect at a singular point on a triangular unit’s vertex. Players cannot retrace a side that has already been used in the expression or in previously formed solid chain.

The operations allowed in these expressions are:

addition (+),

subtraction (-),

multiplication (x)

and division (/).

Parentheses are not allowed. Evaluation of expressions will follow PEMDAS controls, meaning multiplication and division parse before addition and subtraction, and multiplication/division and addition/subtraction ties are evaluated in a left to right order within the expression (not to be confused with the board). Please use the lowercase x symbol for multiplication as opposed to the asterisk *, as Discord parses asterisks as applied formatting.

When a player claims a target number, both players are then given 60 seconds. If the other player can respond within these 60 seconds using the same target number with an expression that scores more points, their chain becomes the solid chain instead.

The highest scoring valid chain evaluating to the target number will be taken as the solid chain; the player whose chain is taken as the solid chain will receive points for the solid chain and the target number will no longer be available. If both players’ chains are of equal score, the player who originally claimed the target number will win the solid chain. If both submissions are invalid, the same target number cannot be claimed within the next 30 seconds. The last valid submission within this 60 second period will be taken as the final expression.

When a solid chain is made, neither player can “break” the chain by forming an expression that “breaks” an existing solid chain. Breaking a solid chain means to intersect with it. Below is an example of how a chain cannot be "broken".

The purple expression "breaks" the red chain at the EFGKLM vertex.

Format and Notation

There are seven rounds total and three target numbers per round. Each round will be played on a new board with new side values. The Guide Board will remain consistent for each board.

If 10 minutes have passed since the beginning of the round and not all target numbers have been found, the board will be disposed of, and the next round begins.

The notation for this game will be as follows:

[starting letter] [expression]

For example, in the following image, for the expression 5 + 3 + 6 + 12 x 22 - 35 + 42 + 33 / 20, the notation would be B 5+3+6x12x22-35+42+33/20. C 5+3+6x12x22-35+42+33/20 is also an acceptable submission for the same expression.

Point Scoring

A solid chain is a chain that earns points.

Each side (or number value) used in the expression is worth 1 point.

If a player completes an enclosed space, which is any polygon, out of their expression and potentially any existing solid chains, each enclosed space is worth 2 points.

In the above image, the scoring player earns 9 (number values) + 2 (one enclosed space) for a total of 11 points.

At the end of seven rounds, the player with the greatest number of total points wins the Death Match. If the score is a tie, the Death Match Opponent becomes the winner of the Death Match.

Addendum: Calculators and other external tools are disallowed. A writing utensil and paper are fine.

Writing utensils + writing surfaces are fine as long as they are acceptable replacements for pen & paper. To be safe, if you don't know if a tool is okay to use, I recommend that you check with me.

To claim a target number, send "claim [number]" as a message in #dm1-game-room. The 60 second timer will begin with that message.

Clarification: When a target number has been used for a solid chain, it may not be used again.

Clarification: For each target number, a solid chain can be made. After a target number is claimed, both players have 60s to privately submit an expression. The expression that scores more points becomes the solid chain for that target number.

Clarification: Edited wording - Each side (or number ~~symbol~~ value) used in the expression is worth 1 point. 10 contains two symbols and 1 contains one symbol, but both are considered 1 point each.

Clarification:

Each side of a triangular unit will represent one single or double digit number.

All values representing the sides of triangular units will be positive integers.

Clarification: The target number is guaranteed to be a rational number.

Clarification: During the time I am parsing/placing a solid chain, players may not claim target numbers. Also, this host downtime will not be included in the 10 minutes per board game time.

Clarification:

If a player completes an enclosed space, which is any polygon, out of their expression and potentially any existing solid chains, each enclosed space is worth 2 points.

For enclosed spaces, if there is a greater loop/polygon consisting of two sub-loops/sub-polygons, such as in the following image, only the sub-loops will be counted toward your score. In the example image provided below, the solid chain scores 17 points; only 2 x 3 = 6 points are earned through enclosed spaces. The U tetriamond highlighted in purple does not score.

The triangle enclosing C, the triangle enclosing K, and the trapezoid enclosing L, S and T each earn 2 points.

Broken Prism

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