**On-Sets**

**A set is merely a fancy way of saying a**

group of objects that share a quality.

group of objects that share a quality.

**What is a "Set"?**

For example, examine the picture on the right. One set could be the boys. One could be the boys with black

hair. Another could be the girl. And yet another could be everyone with(out) glasses.

Naming Sets

On-Sets requires its own special language of symbols. Each of the four colors is indicated by its first letter: B(lue), R(ed), G(reen), and Y(ellow). These colors are linked via other symbols (known as operations) on the red cubes to name a set equal to the goal. There are four operations, with each acting in a special way to help you name different sets.

How do I play it?

So what exactly is On-Sets?

In On-Sets. a game (called a round) will

have two or three players. Within each "game

within the game" (called a shake), there will be

one player who sets a goal and a player that

deals a "universe". This universe is a group of

6-12 cards marked with various patterns of

four colors: blue, red, green, and yellow. The

object of On-Sets is to name a group or "set"

of cards that is equal to your goal.

The Operations - Part I

The first operation is Intersect a.k.a. And, represented by an underlined, upside down U: this operation names a set that has both qualities listed. For example, R U B (pretend its upside down) names the set of cards with both Red AND Blue on them. You can take it even further and say R U Y U B (again, pretend both U's are upside down) and name the cards with Red AND Yellow AND Blue on them. You could even go so far as to have R U G U B U Y which would name which card?

The Operations - Part II

The next operation is Union a.k.a. Or, represented by an underlined U: this operation names the set of cards that has both of the qualities linked by the operation. For example, G U Y would name the set of all cards with either Green OR Yellow on them. Again, one could take it even further and say G U Y U R which would name the set of all cards with either Green OR Yellow OR Red.

Let's review: What's a set?

Challenge: How could you combine both And & Or?

The Operations - Part III

The third operations is Minus, represented by the usual minus sign: this operation is used to name a set of cards that has one quality but NOT another. For example, R-G would name the set of cards that does have Red but is WITHOUT Green. If you wanted to get really complex, you could say R-(G U Y) which would name the set of Red cards WITHOUT Green OR Yellow.

Start thinking about how you use sets in your daily life. Like when you order a burger WITHOUT tomatoes or if you knew that you wanted to wear a blue OR green shirt today.

The Operations - Part IV:

The Wrath of Prime

The fourth and final operation is called prime and is represented by an apostrophe ('): this operation is used to name the set of cards that DO NOT have a quality. For example, B' refers to the set of cards which DO NOT have blue on them.

Try writing a "Set Name" that uses all

four operations. Think you can do it?

Now this is all fine and dandy, but how do I play an actual shake?

To begin a shake, all players each take one of the number cubes and rolls them. Whoever has the highest number is the player who sets the goal and rolls the cubes. If players tie for the highest number, then the cubes are rolled until there is a clear winner.

Continuing the Play

After you've figured out who is the goal setter, you begin the shake itself. This is done by rolling the cubes and dealing the universe. The player to the RIGHT of the goal setter deals a universe of 6-12 cards at RANDOM while the goal setter rolls all cubes.Both players are given one minute (using the one minute timer within the game bag), the SAME minute, to do these tasks.

Setting the Goal

After the cubes have been rolled and the universe is being set, the goal setter needs to set a goal. They have 2 minutes to set a goal. There are 3 number cubes which can be used to set a goal. A player may use either 1, 2, or 3 cubes to set a goal. One can set the goal in which the cubes used are horizontal, meaning that they are added. When all cubes are placed vertically, it means that they are multiplied.

Examples:

2

5

4

This equates to a

goal of 2+5+4

which equals 11.

2

4

1

This equates to a

goal of 2x1x4

which equals 8.

Setting the Goal: Part Dos

One can create even more complex goals

than just putting the cubes side by side or on top

shape. This formation means that you multiply the two

of one another. Cubes can be put together into an L

cubes on top of one another and then add the one on

the side to the result. The next formation is that of a

number with the result. Also, it is important to note

adding the cubes on bottom and then multiply the top

pyramid. In this one, the goal is interpreted by first

that negative numbers are indicated by placing the

number cube upside down.

OR 3 cubes to set a goal

Remember: You can use 1, 2,

Examples:

3

2

1

This equates to a

goal of (3x2)+1

which equals 7.

5

1

1

This equates to a

goal of (1+1)x5

which equals 10.

3

2

4

upside-down

This equates to a

goal of 3+(-2)+4

which equals 5.

Practice & Review:

1) Explain what

each of the

following means:

a. B-R

b. (G U Y)'

(B'-Y)U B

2) Figure out

the value of

each goal:

a. 46

b.

c.

2

43

23

1

Answers:

1a. (B)lue minus (R)ed

which names the set

of all Blue cards

without Red.

1b. ((G)reen or (R)ed) Prime which names the set of all cards without Green or Red.

1c. ((B)lue Prime minus Yellow) or Blue which names the set of all cards (without Blue or Yellow) or Blue

2a. 4+6=10

2b.(2x4)+3=11

2c. 1x(2+3)=5

The First Move

Once the goal has been set, the player to the LEFT of the goal-setter has TWO minutes to move a cube into one of three sections on the playing mat: Forbidden, Permitted, and Required. After the first move has been made, all movers after that have only ONE minute to make a move.

Forbidden

If a mover places a cube into

forbidden, that cube can not

be used to write your solution or "set name". Remember that the goal of On-Sets is to name a group, or "set", of cards that equals the goal. Thus, you are naming the set.

Permitted

If a cube is placed into permitted, then it may or may not be used while writing a selection. It is the choice of each player if they want to use that cube or not.

Required

If a cube is placed into required, then it MUST be used in all solutions that are presented.

Don't be afraid to ask questions if you need to!

Remember:

Challenging

In order for a shake to end, at least one solution must be presented. A challenge is the most common way that a solution is presented. There a two types of challenges: Now & Never. A player challenges Now when they have found that they can make a solution that contains all cubes in required, any number of cubes from permitted, none from forbidden, and at most one cube from resources (the cubes that have not been moved yet). A player challenges never when they believe that there is no solution that can be made which equals the goal

Challenging-Part II

Now, by the nature of what a challenge is, when a player challenges, he or she is challenging on the player who made the last move which allowed the challenge to be made.

Also, it is important to note

that a player can challenge

now only when his solution

will contain at least two cubes.

Challenging Now

When a challenge now is made, the player with the last move can't present or write a solution. The third player must decide whether or not they want to solve within two minutes. The challenger also has those same two minutes to write a correct solution. If the challenger is correct, then they score 6 points and the player challenged on scores 2. Furthermore, if the third player presents a solution and is correct, they score 4. If, however, the third player is correct and the challenger is not, then the third party scores 6. If the challenger is incorrect, they score 2 point; the person challenged on will score 6 as well as the third player if they chose not to solve.

Challenge Never

In a challenge never, the challenge

is issued on the last mover. The last mover has two minutes to present a correct solution. The third player has those same two minutes to decide whether or not they want to present a solution. All correct solutions presented score 6 points. All incorrect solutions presented score 2 points. The challenger scores 6 points if no correct solution is presented. The third player scores 4 points if he sides with the challenger and no correct solution is presented.

Last Cube Procedure

Like Equations, On-Sets also has a last

procedure rule. What this means is that when there is only one cube remaining in resources, the mover must either move cube into either permitted or required or there must be a challenge never. After the cube has been moved, all players must write a solution within 2 minutes. All correct solutions score 4 points and all incorrect score 2. However, a challenge never may be issued to the mover of the last cube within the first minute of the

procedure.

The

Blue

Cubes

In elementary division, the blue cubes are not rolled. Instead, the goal setter, when rolling the cubes, merely takes the cubes and will place either 2 V's and 1 upside-down V or 1 V and 2 upside down V's.

Universe

The universe, as mentioned earlier, refers to the set of all cards being used in the shake. It is also used to refer to a symbol on the blue cubes that looks like an underlined V. The V symbolizes the universe in a cube.

Examples:

V-R means the Universe minus red, naming all the cards in the universe without Red

V U Y means the Universe or Yellow, naming all the cards or the yellow ones. So really, all the cards.

Null-Set

The Null-Set refers to a cube that has an upside-down, underlined V. This cube is used to mean No cards. It is a "null set" because it refers to 0 cards.

Examples (just pretend the V is upside-down:

V U G means the null-set OR green, so this means the set of cards that are null (zero) added to the set of cards with Green

V' is null set prime, meaning the opposite of Null-Set, which is the Universe, or, all of the of cards.

V-G is the Null Set minus Green which names no cards since nothing minus something is nothing.

Variations

Variations are special rules called by each player at the beginning of the shake after the cubes are rolled and the universe is set. One is called by each player unless it is a two player match in which case the person who is not the goal setter will call two variations. Each player has 15 seconds to call each variation. The other players manually count down to time the player currently calling their variation.

Elementary Variations

7. Shift from Permitted On your turn you may transfer a cube in Permitted to either

Required or Forbidden. This move takes the place of your regular move.

6. Multiple operations Every operation sign in Required or Permitted may be used

many times in any Solution.

5. Two operations Each Solution must contain at least two operation symbols. The

operation symbols are U, Ω, –, and '.

4. V and /\ interchangeable Any V may represent V or /\, and any /\ may represent /\ or V.

3. U and Ω interchangeable Any U may represent U or Ω, and any Ω may represent Ω or U.

2. Wild cube The ___ cube may represent any symbol on the cubes except a digit.

The ___ cube must stand for the same symbol everywhere it occurs in the Solution. The player selecting this variation specifies which cube from the Resources is

wild. The wild cube may not be a digit. Each Solution-writer must specify in writing

the interpretation of the wild cube if it stands for anything other than itself in his

Solution.

1. Required cube The Solution must contain a ___ cube. The player selecting this

variation specifies which non-digit symbol from the Resources fills the blank in the

previous sentence.