# Rules

There are **three** different games that will be played, **two individual games and one team game.**

### Scoring for individuals and teams

Individuals:

All participants will participate in the first two individual games and accumulate the scores for individual award consideration.

Teams:

Team participants continue to participate in the team relay game. The team's score is the sum of all teammates individual scores from the first two games plus the team game score.

### Awards

Awards will be given to the** top **individuals and teams **for each grade**. If a team consists of various grade level students, its grade level is counted as the maximum grade level among the members of the team.

## Game 1: Hit the Target

*Adopted from ThinkFun's dice game*

- 8 rounds
**Time limit:**All players are given**What to do:**In each round two twelve-sided dice,**1-12**, will be rolled, and the product of the two numbers will be the target number. Then, four 12-sided dice will be rolled. Contestants will have to use those four numbers and any operations/functions to get as close as possible to the target.**Scoring:**If you hit the target directly, you will receive 10 points. If your result is one off of the target, you will receive 9 points, and so on. For example, if the target is 36 and you make 34, you receive 8 points.**Bonus score:**If you hit the target and there is still time, you can find another method to hit the target again, and each additional method will count as 10 extra points. You need to completely hit the target to get bonus points.

## Game 2: 24 Game

*A twist on the classic 24 game but with no limits on the operations/functions you can use*

- 8 rounds
**Time:**As with the last game, the players are given**What to do:**4 six-sided dice**1-6**will be rolled each round, and contestants will have to use these four numbers and any operations/functions to make 24*exactly*.**Scoring:**One correct method of making 24 be worth 10 points, with each distinct method awarding 10 more points.

## Game 3 (team relay): SMASH

*SMASH = Sprint + MAke + SHoot*

**Time:**10 minute game**Goal:**The goal is to use**three random numbers 1-10**to make numbers 1, 2, 3, ... and so on, in this order.**Before the game:**40 play cards (four sets of Ace through 10, Ace is considered as 1) will be shuffled by each team and placed on the opposite side of the room.**About the game:**- When game starts, each team will send a representative to sprint to the cards, take the top 3, and come back to their team. They will use those three numbers to make 1.
- The proctor will verify their method, and then one member will sprint back, place the 3 cards at the bottom of the deck and take the next three cards on top and sprint back to make the next number 2. The game continues in this fashion.
- A new set of 3 cards must be retrieved after successfully making each number.
- If they are stuck, they can sprint back to swap out for three new cards.

**After the game:**In addition, each correct method (written on a piece of paper) can be balled up, and used as a basketball. Each shot to the basket results in 10 bonus points.**Scoring**The team's score will be 10 multiplied by the highest number they successfully achieve plus the basket bonus. For example, if the team achieves up to 8 and out of the 8 balls they make 4 baskets, the score will be 8x10 + 4x10 = 120.

### Tiebreaker

In the rare case of a tie, whether it be between individuals or teams, they will be paired up against each other, and will play the target game for three minutes. Whichever side comes up with the most methods of hitting the target will win. In the case of multiple ties, each tiebreaker will eliminate one side, until there is one champion left.

# The Fine Print

- In all games, all given numbers must be used once and only once.
- Numbers cannot be concatenated to form a multi-digit number. For example, you cannot put together 1 and 2 to make 12.
- Besides + - x / and (), other functions are also allowed, such as exponent, root, factorial, double factorial, triangle numbers... the sky is the limit! However, defining and using your own functions is disallowed. For example, defining f(x)=4 with a target of 16 is strongly disallowed.
- When using exponents, the exponent (index) must be from the provided numbers.
- Use 1, 3, 4, 5 to make 24: 5^2 - 1 x (4-3); (This is not allowed as there is no 2 to be used as the exponent)
- Use 2, 3, 10, 12 to hit target 66: 10^2 - 3x12 = 64 (This is valid, and also very close to the target)

- Note that square roots can be done with or without a two. However, cube roots and further roots require the number on upper left of the radical sign.
- Numbers can be written as a subscript (ex. triangular number) or a superscript (ex. exponent).
- Order of operations is strictly enforced! Use parentheses if you are unsure.
- Use of the commutative and associative properties to write the expression differently does NOT count as another way. For example, 1+2 and 2+1 count as one way, and 3x4/2 and 3/2x4 count as one way. You need to use other methods to create a new way.
- Functions or
*recursive*functions that take*one*input and result in the*same*value does NOT count as another way. Ex. 1+2, sqrt(1) + 2, 1+2! and 1+(2!)! all count as one way because the square root and factorial do not change the input; but 5x1 and 5/1 count as two ways because of two different operations.

***In the event of ambiguity or dispute, the board of judges has the final say.**