Pushing Crates

TBD

Designer(s): elara Match Type: MM (for 12 players)
Featured in: The Genius Puzzler

Main Match 4: Pushing Crates

In Pushing Crates, players help others move their crates past checkpoints--but only when they request it.


RULES

This Main Match consists of one pregame round, and six main rounds. During the pregame round, players must assign the point multipliers [-1, -1, 0, 1, 1, 2] to the six rounds, one to each round. These point multipliers are not revealed publicly.


Each player owns a single crate, situated on a number line. Initially, each crate is located at 0. The location of a crate will never move leftwards.

Each round of the game, all players may push crates up to three times. You may push any crate, including your own, and may push a crate multiple times. When pushing a crate, you choose whether to push it rightwards (towards positive infinity) or leftwards (towards negative infinity).

You may also spend garnets for extra pushes, at the rate of 1 Garnet : 1 additional push.

In addition to pushing crates, players choose the material of ground they would like for their own crate; each one has its own movement multiplier. You may select rubber (x0 multiplier), stone (x1 multiplier), or ice (x3 multiplier). However, rubber can be selected at most once in total, and ice can be selected at most twice in total.


Afterwards, each crate moves according to how many times it was pushed, and the material of the ground. First, if there are as many or more left pushes than right pushes, the crate does not move. Otherwise, the crate moves a number of steps equal to the number of right pushes minus the number of left pushes, multiplied by the movement multiplier.

For instance, if a crate was pushed right 5 times and left 2 times over ice, it would move a total of 9 spaces to the right.


Finally, players earn points. For every multiple of 5 location that a player's crate crosses (or meets), that contributes a point to their score for that round. This round point total is multiplied by the assigned point multiplier for that round to yield the final the number of points the player earns in that round.

For instance, if a player starts at location 1, and moves 9 spaces to the right to location 10, then they crossed two multiples of 5. If they assigned a point multiplier of 2 for that round, then they would earn 4 points for the round.

At the end of each round, the remainder when each player's location is divided by 5 is revealed. In addition, each player is privately told their own score.


At the end of 6 rounds, the game ends.

Players are ranked by the number of points they earned. If there is a tie, it is broken as follows: First, the player who covered more distance (was more to the right at the end of round 6) wins the tie. If this is a tie, then the player who covered more distance at the end of round 5 wins the tie. This continues in decreasing round order. In the event that the players covered the same distance in each round, the tie is broken randomly.

This is a double elimination round. The top three players receive Tokens of Life, while the bottom two players are Elimination Candidates. The player who is second to last will pick their Death Match Opponent first.

Players earn 1 Garnet for every three points they have at the end of the game, rounded down. If their score is negative, they earn 0 Garnets.


ADMINISTRATION

Timing

The game lasts for 7 days. The first 24 hours is a pregame Round 0. Afterwards each of the 6 rounds also lasts for one day. (Note: This causes the game to end right around Christmas; the last deadline may end up slightly longer to account for this.)

Although the game is split into a Round 0 and a Round 1, you are allowed to submit your Round 0 submission up until the end of Round 1. This is to allow for extra time, but the rounds are split as such to make it clear that the pregame submission is separate from the rest of the game. (If you'd like, you may think of it as submitting both your point multiplier distribution and your Round 1 actions after 48 hours.)


Submissions

In Round 0, you submit a point multiplier distribution. It must be a permutation of [-1, -1, 0, 1, 1, 2], assigning one of these point multipliers to each round.

In later rounds, a submission consists of a list of all pushes you are making in that round (possibly more than three if you are spending Garnets), and your chosen ground material.


Information

Publicly announced, at the end of each round:

  • The modular remainder when each player's location is divided by five

Told to you, at the end of each round:

  • Your current score

Publicly announced, at the end of the game:

  • Each player's final score
  • The winners and losers of the Main Match. Note that this may give additional information than the above due to tiebreaking rules.

Known only to you:

  • Your submissions, including your point multiplier distribution as well as pushes and ground material chosen during each round.

Garnets

Garnets may be spent in the following way:

You may spend 1 Garnet to push one additional time in a round.


Garnets may be earned in the following way:

You earn 1 Garnet for every 3 points you earn at the end of the game, rounded down. (You cannot earn negative Garnets.)

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