Shadow Math

Shadow Math

In Shadow Math, players try to reach target numbers by finding integers arranged on a board in specific shapes or "shadows" and then forming their own equations.

Goal

The game takes place over several rounds on various boards, 10 x 10 grids that contain integers ranging from 1 to 20. Each round, players will be given a target number and a "shadow," with the "shadow" being some shape of blocks. Players must search for an arrangement of numbers on the grid that are in the shadow's shape somewhere on the board, and that player will use any amount of addition, subtraction, multiplication, division, and parentheses symbols to manipulate those numbers into an equation that results in the target number.

After a target number is posted, players "buzz in" by saying at least one coordinate involved in the shape they've found, and then the equation they've created with the numbers in their shape.

They may use each math operation symbol any number of times in their equation, but they must use each block in a shape matching the shadow given exactly once. We will resolve an equation using PEMDAS/BODMAS/BIDMAS (Order of Operations). Remember to use parentheses in your answer if you'd like addition or subtraction to resolve before multiplication or division!

If their equation resolves to the target number, and the blocks of the numbers on the grid used in the equation form the "shadow's" shape or a rotation of the shadow's shape, then the player buzzing in earns 2 points. Otherwise, the other player earns 1 point and the round ends.

If neither player buzzes in after five minutes pass and time is called, we will move on to the next round. Each 10 x 10 grid of numbers will be used for three rounds before a new grid of numbers is used.

The game ends when one player reaches 20 points; that player is declared the victor and advances to the Final 5 of Genius One.

Constraints

⬛ A round's "shadow" will always be comprised of filled-in black blocks, but there is otherwise no restrictions on the shape that I give you - a shape can be any length or size, and it can even contain non-contiguous blocks (blocks that don't touch one another) in which case, the amount of spaces between each block must also be exactly correct. The shape of the blocks/numbers that a player submits must always match the shape of the shadow or a rotation of the shadow. Using numbers in "flipped" or reflected version of the shape is considered incorrect.

⬛ Additionally, there are no restrictions on target number. It could be an integer or a fraction, positive or negative, any length...

⬛ A round will always have at least one solution but might have multiple solutions instead.

⬛ When creating an equation, you may not use the minus as a negative symbol - if the numbers you are using are 3, 4, 5 for example, you cannot create the equation -3 + 4 + 5, though 4 + 5 - 3 would be acceptable.

⬛ If your submission is ambiguous (there are multiple ways to form shapes with the coordinate you gave and the numbers you used) then I will always assume the shape you are creating is the one that matches the "shadow"

⬛ You may not use a calculator or other automated methods for this match. You are, however, allowed to use a pencil/paper if you wish.

Example

An example of a "Shadow Math" problem is shown below.

Remember, when the shadow is overlayed over the board, number on the board that is covered by the "shadow" must be included in the final solution once, using addition, subtraction, multiplication, division and brackets. The shadow can be rotated, but not reflected, and given solutions will be checked using PEMDAS/BODMAS.

In the above board, the target number is 25. The "shadow" is the four-block shape shown below the target number. Note that the Shadows given will have no outlines, though they will be proportional to the board.

An incorrect answer might be G1 8+11+6, which results in 25, but the shape of the numbers involved doesn't fully form the "shadow."

Another incorrect answer might be E4 9+7-1+10 which results in 25, but the shape, again, doesn't match the "shadow" asked for.

A correct answer to the above board would be E1 20 + 4 + (12/12), which results in 25 and is a rotation of the shadow

Clarification

No Prewritten Notes

(Examples of prewritten notes: a 69 x 69 times table you wrote out before the dm)

(Example of not prewritten notes: memorising said 69 x 69 times table then writing it during the dm)

We will allow any notes you wish during the game.

Just don't have prewritten notes.