EvenMore Games

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). 

Examples of Quads.

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.

Examples of Non-Quads

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. 

Games that use bios

Players:  Exactly 4 players per group and at least 2 groups; game play uses one deck across all groups.

Set-up: Deal 4 cards to each player.

Game play is cooperative. The players come up with yes/no questions that can be asked about the women on the cards. For example, “Is this woman alive?”  “Is this woman Latina?” “Does/did this woman do research in algebra?”

Each Round: First decide together on two questions. Then each player chooses one card to place on the table, so that the four women shown have different answer sets to the two questions (that is, the four cards correspond to yes/no, no/yes, yes/yes, no/no).

Between rounds:  Each player selects one of their cards to swap with one from a player at another table.  Each participant must swap a card with someone outside their group. 

Play resumes in a new round, with each group using the newest collection of cards.  Questions may be reused or new questions may be posed!  Repeat the swapping process as many rounds as you like, being sure to avoid taking back a card you discarded earlier.

Advanced version: First decide together on three questions, and then each player must lay two cards on the table so that the eight women shown have different answer sets to the three questions. Repeat subsequent rounds analogously. 

Creators:  Linda McGuire’s students at Muhlenberg College, PA, USA

Players:  Exactly 4 players 

Set-up: Deal 4 cards to each player.

Game play is cooperative. The players come up with yes/no questions that can be asked about the women on the cards. For example, “Is this woman alive?”  “Is this woman Latina?” “Does/did this woman do research in algebra?”

Step 1: First decide together on two questions. Then each player chooses one card to place on the table, so that the four women shown have different answer sets to the two questions (that is, the four cards correspond to yes/no, no/yes, yes/yes, no/no). 

Step 2: Next, set the four cards aside at (a new) corner of a square, so each player now has three cards.

Repeat Steps 1 and 2, if possible, three times with the remaining cards. If this succeeds, you all win! The game ends with the four sets of four cards forming a quadrangle.

If instead at any point in this process all players agree that no such questions exist and no more cards can be played, then play continues: set aside all previously used cards, deal out four new cards to each player, and start again with Step 1. 

The game ends when either the group wins by each playing all of their four cards or when the deck is depleted.

Creators:  Denise A. Rangel Tracy’s students at Francis Marion University, SC, USA.

Level: Intermediate.

Number of players: An even number, at least 4.

Set-up: Players form pairs (teams of size 2). Each pair should have a device open with access to the internet, and have loaded the EvenQuads pages. (Instructions for a technology-free variant appear at the end of the rules.) Shuffle the deck. You can use Decks 1 and 2 if you have them. Deal 7 cards to each pair, symbol-side up, and place 4 cards bio-side-up in the center of the table.

Definition: Four cards are a Bio Quad if there is a biographical trait that is shared by all four women on the cards. 

Game play: 

  • All players examine the 4 central cards, and decide collectively whether there exists a biographical trait shared by the 4 women. This will be easier if pairs open biographies of the women on the EvenQuads site for ease of reading. Currently, Deck 1 and Deck 2 are available. (On the website, hover over the photo of a mathematician to flip it. Then click “Download One-page Poster” to view a PDF of the card’s bio.)
  • If there is a biographical trait shared by the 4 women, then this is a Bio Quad. Each pair then works to identify and list (in writing) as many biographical traits shared by the 4 women as possible. Internet searches are encouraged to support finding shared traits! 
  • When players agree they are done (or after 15 minutes have passed), lists are compared. Each pair earns one point per biographical trait not on other teams’ lists.
  • If there is no biographical trait shared by the 4 women, then each pair attempts to form a Bio Quad using at least one card from the table and at most 3 cards from their 7-card hand, and to try to find the largest number of shared biographical traits possible.
  • When players agree they are done  (or after 15 minutes have passed), each team presents their proposed Bio Quad and identifies the common biographical traits. The team earns one point per biographical trait.
  • Then a new set of cards (7-card hands, 4 cards in center) is dealt.
  • The game ends when the deck is exhausted. The team with the most points wins. 

Variant—Bio Quads Unplugged: Use only the biographical information on the cards, and limit time to 5 minutes before comparing lists. Be aware that it may be awkward for players to simultaneously read the cards. 

Notes and questions for an educator using the game: 

  • Encourage students to consider biographical traits that are not shown on EvenQuads cards, such as those based on the personal lives and personal identities of the honorees.
  • Note that for Latina women, the freely available Testimonios: Stories of Latinx and Hispanic Mathematicians is an excellent source of traits.
  • Encourage students to reflect on how the information presented on EvenQuads cards shows a different view of a mathematician than does a personal narrative. This can help to validate “the centrality of culture and identity in mathematics alongside professional contributions and accomplishments.”

Creator: Guadalupe Lozano and Cynthia Anhalt, from “Alternate Sources, Alternate Narratives: Creating the Mathematics Ethos That Might Have Been,” in Antiracist Mathematics Education: Stories of Acknowledgment, Action, and Accountability, ed. Strutchens, Krause, White, Bay-Williams, published by TODOS Mathematics for ALL, 2023. Note that this chapter includes other games for EvenQuads decks.

Level: Intermediate.

Number of players: 2 or more. 

Additional Materials: A device with access to the internet, timer, paper, and a pen. 

Set-up: Decide whether to play as individuals or teams of size 2. Each person/team should navigate to the webpage that lists the EvenQuads mathematicians for the deck that is being used. Currently, Deck 1 and Deck 2 are available. (Instructions for a technology-free variant appear at the end of the rules.) Shuffle the deck and place four cards bio-side-up in the center of the table. We’ll call these the central cards. 

Definition: Four cards are a Bio Quad if there is a biographical trait that is shared by all four women on the cards. 

Game play: 

Phase 1: Goal To find as many traits shared by all four women on the central cards.

  • Set a timer for 5 minutes. All players examine the four central cards to determine if it is a Bio Quad. Additionally identify and list (in writing) as many biographical traits shared by the four women as possible. This will be easier if one opens the biographies of the women on the EvenQuads site for ease of reading. (On the website, hover over the photo of a mathematician to flip it. Then click “Download One-page Poster” to view a PDF of the card’s bio.)
  • When the 5 minutes are over, compare lists. Each person/team earns one point per biographical trait not on the others’ lists.
  • If the women did not share any biographical traits, hence was not a Bio Quad, moved to Phase 2. If the four cards were a Bio Quad, then put them in a discard pile, deal out four new cards, and repeat Phase 1. 

Phase 2: Goal To find as many different Bio Quads as possible.

  • Leave the four central cards from Phase 1 that were not a Bio Quad out. Deal out four additional cards to each player/team.
  • Set a timer for 15 minutes. Each player/team works to form as many Bio Quads as possible using at least one of the central cards and at most three cards from their individual hands. Internet searches are encouraged to support finding shared traits!
  • When the 15 minutes are over, each person/team presents their list to the other players. One point is earned for every Bio Quad found. For the purposes of scoring, if four cards form a Bio Quad and there are multiple traits shared by all four women then a point is earned for each shared trait. 
  • Put all cards in the discard pile. Deal out four more cards and repeat Phase 1. 

The game ends when the deck is exhausted. The player/team with the most points wins. 

Variant—Flash Bio Quads Unplugged: Use only the biographical information on the cards, and limit Phase 2 to 10 minutes. Be aware that it may be awkward for players to simultaneously read the cards. 

Creators: Alex Tracy and Denise Rangel Tracy.

Inspiration: Bio Quads, from Guadalupe Lozano and Cynthia Anhalt’s chapter “Alternate Sources, Alternate Narratives: Creating the Mathematics Ethos That Might Have Been,” in Antiracist Mathematics Education: Stories of Acknowledgment, Action, and Accountability, ed. Strutchens, Krause, White, Bay-Williams, published by TODOS Mathematics for ALL, 2023. Note that this chapter includes other games for EvenQuads decks.

Games that use both sides of the cards

Level: Advanced.

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 .  Thanks @AWMmath!" 

Link to YouTube tutorial

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 .  Thanks @AWMmath!"

Number of players: Any.

Additional items needed: 2-minute timer

Game Play:  Play begins the same as the Regular Quad Collector game. That is, 

  1. Shuffle the deck and lay out 8 cards symbol side up.
  2. Everyone looks for a Quad, when found the player says “Quad!”. (If no player finds a Quad, one additional card is dealt out.)
  3. The player who found the Quad collects the four cards from the pool and flips them over to the profile side. 
  4. The player reads each bio out aloud to the group. 
  5. Start the 2-minute timer.
  6. The player who found the Quad has two minutes to find a trait/characteristic/achievement that is common to all four women featured on the profile side of the cards from the Quad. 
    • If the player achieves this, then the Quad is theirs and is put aside out of play. 
    • If the player is unable to do this, then they lose the Quad and those four cards are shuffled back in the deck of cards. 
  7. Four new cards are dealt to replace the missing cards in the pool. 
  8. Repeats steps #1-7 until the deck is depleted and there are no Quads on the table.
  9. The winner is the player who collected the most Quads.

Link to YouTube tutorial

Different Games that use Quads

Number of players: 2 or more.

Set-up: Shuffle the deck. Each player needs a piece of paper and a writing implement. The dealer lays out 16 cards logo-side-up on the table.

Game Play for a Round: 

  • The dealer sets a timer for 4 minutes.
  • All players look for Quads, without touching the cards.
  • Each player makes a list of the Quads ze identifies.
  • When the timer goes off, players put down their writing implements.
  • Each player in turn describes hir listed Quads. Any Quad that another player has listed is removed from all lists. 
  • Each player earns one point for each remaining Quad on hir list.
  • (Optional) A player listing a non-Quad loses one point.

Rounds are played until at least one player earns 16 points.  The winner is then the player with the highest number of points.

Creator: Tom Hull

Implementation: sarah-marie belcastro

Link to YouTube tutorial

Click here for a short video tutorial. 

Use two EvenQuads decks. 

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

Link to YouTube tutorial

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 \(Z_2^6\), can you construct an isomorphism to the game Projective Set?

Creator: Lauren Rose

Link to YouTube tutorial

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.

Level: Advanced.

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.

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.  

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

Game Play: 

  • Proceed as in EvenQuad Collector 32 (or, for an additional challenge, Regular Quad Collector).
  • 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.

Note: When using 32 cards, it is guaranteed that the last four cards will form a Quad. (This result is known but not published as of Fall 2026.) With 64 cards, this property is not guaranteed but there must be even numbers of cards with each attribute remaining in the final layout. This, together with the fact that each attribute value occurs the same number of times in the deck, players can determine the missing card.

Creator: Lauren Rose. 

Number of players: Any. This can be played as a solitaire game, or with 2–4 players, or in teams.

Set-up: Shuffle the deck and deal 16 cards symbol-side-up into a 4 x 4 grid.

Game Play: 

  • The goal is to find a quad in either a row, a column, or along a diagonal.
  • A turn consists of choosing a row, column, or diagonal, and cycling the cards by one position along that row, column, or diagonal.  Examples are shown below.
  • If there are 3 or more players, then there is a 2-minute time limit per move.
  • If at the end of a turn a player or team sees a quad in a row, column, or diagonal, this quad is picked up and cards are replaced from the deck. The player/team may pick up multiple quads as long as the cards are disjoint.
  • If replacement cards form a quad, or if a player/team does not see a quad during their turn, the next player/team may claim that quad.
  • Gameplay ends when the deck is depleted and all possible quads are retrieved. When spaces on the board cannot be filled, condense the board in accordance to the collected quad type (i.e. row/column/diagonal)
  • Whichever player/team has the most quads at the end of the game wins.

Variant: Include affine lines (“broken diagonals,” as in  a diagonal of 3 wrapping around to 1 or a diagonal of 2 wrapping around to 2) as possibilities for both cycling of cards and locations to find quads.

Creator: Monica Mulhern, Muhlenberg College class of 2026, was inspired by the motions of Rubik’s Cubes, magic/semimagic/strong magic squares, and  Tic-Tac-Toe on the Finite Plane by Maureen T. Carroll and Steven T. Dougherty.

Games that use different Quads

Level: Beginner.

Number of players: 2 or more

Set-up: Shuffle the deck and deal all the cards bio-side-up into an 8 x 8 grid.

Game Play: 

  • A turn consists of choosing two cards and flipping them symbol-side up. 
  • If on a turn the symbols match in any attribute (color, number, symbol type), then the player takes these cards. The player then takes another turn.
  • If on a turn the symbols do not match in any attribute, then the player flips the cards back to bio-side up and the player’s turn is over.
  • Whichever player has the most cards at the end of the game wins.

Variant: Shuffle multiple decks together and deal out 64 of the cards into an 8 x 8 grid.  Play proceeds as above, except that a fourth attribute (foreground/background style) is available.

Notes and questions for an educator using the game: 

  • Ask students to consider what strengths are valued in this game. 
  • How do these strengths differ from other games (especially played with this deck)?
  • What roles do each of those strengths play in mathematical thinking?

Creators: Guadalupe Lozano and Cynthia Anhalt, from “Alternate Sources, Alternate Narratives: Creating the Mathematics Ethos That Might Have Been,” in Antiracist Mathematics Education: Stories of Acknowledgment, Action, and Accountability, ed. Strutchens, Krause, White, Bay-Williams, published by TODOS Mathematics for ALL, 2023.

Level: Advanced.

Number of players: 1 or more.

Set-up: Shuffle the deck and place it logo-side-up. The dealer lays out twelve cards on the table.

New Rule: An OddQuad consists of four cards that, simultaneously and for each attribute, must feature three cards with one value of the attribute and one card with a different value of that attribute. (Example: three cards each have two symbols, and one card has four symbols.)

Game Play: 

  • All players look for OddQuads, without touching the cards.
  • Someone who finds an OddQuad yells “Odd!” and indicates the four cards in the OddQuad to the other players.
  • The player who correctly calls “Odd!” takes the four OddQuad 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 OddQuad, one additional card is dealt out.
  • The game ends when the deck is depleted and there are no OddQuads on the table.
  • The winner is the player who collected the most OddQuads.

Notes and questions: 

  • See Section 5 of https://arxiv.org/abs/2010.01882 for the inspiration for this game.
  • For an extra challenge, alternate games of EvenQuads and OddQuads.
  • How many OddQuads are in the deck?
  • How does the probability that four randomly selected cards form an OddQuad compare to the probability that four randomly selected cards form an EvenQuad?
  • Is it possible to partition the deck into OddQuads?
  • What is the minimum number of cards that must be dealt before an OddQuad must be present? (There is a straightforward lower bound of 16; do you see why?)

Creator: Jonathan Schneider

Implementation: sarah-marie belcastro

Level: Advanced.

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

Link to YouTube tutorial