The new games revolve around forming Quads as well as using the biographies of the honorees. The original Quad Collector game was developed by Dr. Lauren Rose and Jeffrey Pereira.

Visit here for rules to the EvenQuads Beginner, Regular and Solitaire versions and here for rules to play EvenBetter.

A Quad consists of four cards that, simultaneously and for each attribute, must feature

• the same value of the attribute (example: all four cards have the same number of symbols), or
• distinct values of attributes (example: all cards have different symbols), or
• two cards with one value of an attribute and the other two cards with another value of the same attribute (example: two cards have green symbols and two cards have pink symbols).

## Flip to see why this is a quad

The four cards feature different colors, have the same number of symbols, and all have the same symbol.

## Flip to see why this is a quad

The four cards feature different colors, have two cards with one symbol and two other cards with another symbol, and have two cards with one symbol and another two cards with two symbols.

## Flip to see why this is a quad

The four cards feature the same color, different numbers of symbols, and different symbols.

## Flip to see why this is not a quad

The four cards fail to be a Quad because the number of symbols is not all the same, not all distinct, and not two-and-two.

## Flip to see why this is not a quad

The four cards fail to be a Quad because neither the number nor kind of symbols is all the same, all different, or two-and-two.

## Flip to see why this is not a quad

The four cards fail to be a Quad because the symbols are not all the same, not all distinct, and not two-and-two.

Use the online version of the QUADS app for more examples of Quads. The game was developed by Dr. Lauren Rose and Jeffrey Pereira.

Set-up: The dealer lays out ten cards on the table.

New Rule: An EvenQuad consists of four cards that, simultaneously and for each attribute, must feature an even number of cards of each value. That is, for each attribute (shape, number, color, and background style) no cards must have the same value, all four cards must have the same value, or two cards must have one value and the other two cards must have a different value.  (This differs from regular Quad Collector only in that the background style of the four cards must all be the same, or two must be one style and two the other style.)

Game Play: Proceeds as does regular Quad Collector.

Creator: Lauren Rose

Set-up:

• Shuffle the deck.
• Deal the top card, face up, to the top of the table. This is the match card.
• Deal 9 cards in a square below the match card.

Game Play:

• All players look for three cards from the square that form a Quad with the match card.
• Someone who finds a Quad Match yells “Quad!” and indicates the three cards completing the Quad to the other players.
• The player who correctly calls “Quad!” takes the three cards completing the Quad and the dealer deals three more cards.
• If no player finds a Quad Match, one additional card is dealt out.
• The game ends when the deck is depleted and no Quads can be completed using the match card.
• The winner is the player who collected the most matched Quads.

Challenge:  Noting that there are 63 active cards and that this is the same number of nonzero elements of $$\mathbb{Z}_2^6$$, can you construct an isomorphism to the game Projective Set?

Creator: Lauren Rose

Players: 2 – 4.

Set-up: Deal 7 cards to each player, and lay out 8 cards face-up in the center as the pool.

Game play is simultaneous.  A hand ends when a player has no cards left in their hand.

• Each player tries to form a Quad using 1–3 cards from the hand and the remaining cards from the pool.  (Note: a player may not form a Quad entirely from the pool or entirely from the hand.)
• Someone who finds a Quad yells “Quad!” and indicates the four cards in the Quad to the other players.
• The player who correctly calls “Quad!” takes the four Quad cards, and the dealer replaces removed pool cards. If a “Quad!” call is incorrect, the player must add all four cards to their hand.
• After a player declares “I can’t find a Quad,” if within the next minute no player can find a Quad, then the whole pool is replaced: Put the old pool on the bottom of the deck, deal 8 new cards, and shuffle the remaining deck.
• If the deck is exhausted a smaller pool can be used to continue play until everyone declares they can’t make any quads, at which point the hand ends.

Scoring: In each hand, a player gets as many points as Quads that player laid down. The player who goes out earns 3 additional points. The game ends when the first player earns 20 points, and that player is the winner.

Number of players: 1 to 5, one of whom is the searcher.

Set-up: Shuffle the deck and place it logo-side-up.

Phase 1: Proceed in rounds as follows.

• The searcher deals three cards to each other player. (If playing solo, do deal three cards to yourself.)
• Each player identifies the unique fourth card that will complete the three cards to a Quad.
• The searcher looks through the deck to find the identified cards and complete the Quads.
• If an identified card is not in the deck, because some player holds the unique fourth card needed by another player:
• Phase 1 ends (unless this happens in the first round of searching, in which case the players should restart Phase 1).
• Set aside all complete Quads and return remaining cards to the deck.
• If all identified cards were found in the deck, deal another round.

Phase 2: Players collaborate to try to form all remaining cards into Quads, with no cards left over.  The players collectively win if there are no cards left over after forming the maximal number of Quads.

Notes and questions:

• If it is possible to win, what is a winning strategy?
• Necessary and sufficient conditions for winning are not known.
• If the parity of the number of cards per value is not the same for a given attribute, it is not possible to win the game. (Challenge to the reader: do you see why?)
• What is the maximum number of Quads that can be removed during Phase 1 and still have a winning strategy for Phase 2?
• Is this related to “cap sets” for the EvenQuads deck, and if so, how?

Creator: Denise A. Rangel Tracy.

#### EvenBetter Trivia

Number of players: Any.

Game Play: Can you find four cards that form a Quad and where all the women…

…are Latinx?

…do research in algebra?

…are Black?

…have worked in industry or government?

…are Asian?

…do research in mathematics education?

…are LGBT+?

Choose your own characteristic of women in the deck—can you find a Quad where all the women share that characteristic?

Inspired by a tweet of Japheth Wood (4:57 pm 3/30/2021):

“In EvenQuads, there is exactly one more card that completes a Quad.  I found out today that Julia Robinson is the Even Quad completion of {Emmy Noether, Ingrid Daubechies, Carolina Araujo}.  Thanks @AWMmath!”

Use only the green and pink cards from an EvenQuads deck.  (Or choose your own favorite two colors.)

Set-up: The dealer lays out eight cards on the table.

New Rule: An EvenQuad consists of four cards that, simultaneously and for each attribute, must feature an even number of cards of each value. That is, for each attribute (shape, number, color, and background style) no cards must have the same value, all four cards must have the same value, or two cards must have one value and the other two cards must have a different value.  (This differs from regular Quad Collector only in that the color of the four cards must all be the same, or two must be one color and two the other color.)

Game Play: Proceeds as does regular Quad Collector.

Inspired by Lauren Rose’s EvenQuad Collector 128.

#### The End Game

Set-up: Shuffle the deck.  Set aside the top card, face down.

Game Play:

• When the deck is exhausted, each player guesses which card has been set aside.  (Optional: players may have a discussion in advance of the guessing round.)
• The player who correctly identifies the missing card wins the last group of cards as a “bonus Quad.”
• The winner is the player who collected the most Quads.

Creator: Lauren Rose.

Number of players: 1 or more.

Set-up:

• Shuffle the deck and place it logo-side-up.
• The dealer lays out four cards to one side of the main play area.
• Analyze the attribute value distribution of these cards. That is, for each attribute determine how many values are the same and how many are different. (Example: Two cards are green, one card is yellow, and one card is blue. This is a 2–1–1 split.)
• Make a note of the three attribute value distributions. (Example: Two attributes have 2–1–1 splits and one attribute has a 3–1 split.) This is the goal WackQuad for the game.  That is, A WackQuad is a set of cards matching the attribute value distribution of the goal WackQuad.
• The dealer lays out eight cards on the table.

Game Play:

• All players look for WackQuads, without touching the cards.
• Someone who finds a WackQuad yells “Wack!” and indicates the four cards in the WackQuad to the other players.
• The player who correctly calls “Wack!” takes the four WackQuad cards and the dealer deals four more cards.
• If the player is incorrect, the cards are put back on the table.
• If no player finds an WackQuad, one additional card is dealt out.
• The game ends when the deck is depleted and there are no WackQuads on the table.
• The winner is the player who collected the most WackQuads.

Notes and questions:

• It’s best to do collaborative exploration the first time players encounter WackQuads.
• See Section 5 of https://arxiv.org/abs/2010.01882 for the inspiration for this game.
• For a given attribute distribution, how many WackQuads can there be in eight cards?

Creator: Jonathan Schneider

Implementation: sarah-marie belcastro

Number of players: 1 or more.

Set-up: Shuffle the deck.

Game Play for a Round:

• Deal out three cards.
• Look at the logo side of the cards. Determine which card is needed to complete a Quad.
• Find that card in the deck. If the card has been used in a previous Double Quad, the game ends.
• Determine how many attributes are all-the-same, how many are all-different, and how many are two-and-two. (Example: the colors and symbols are all different, but there are two cards with one symbol and two cards with four symbols.)
• Look at the biographical side of the cards. Can you find three characteristics of the four women that match the attributes of the Quad on their reverse? (Example: there are two characteristics for which the women are all different, and one characteristic where two of the women are the same, and the other two women are the same but for a different value of that characteristic.)
• If so, set the cards aside. If not, shuffle the cards back into the deck.

The Goal: Players collaborate to find as many Double Quads as possible before the game ends.

Inspired by a tweet of Japheth Wood (4:57 pm 3/30/2021):

“In EvenQuads, there is exactly one more card that completes a Quad.  I found out today that Julia Robinson is the Even Quad completion of {Emmy Noether, Ingrid Daubechies, Carolina Araujo}.  Thanks @AWMmath!”