Visualizing a popular game

I was over a friend’s house and they had a game called “Spot It!” - a set of cards where each card had 6 different characters on it. We were talking about the constraint that every card has to have exactly one match with the other. I realized that it couldn’t be random because there were 20 cards and 31 distinct characters, so simply selecting randomly would not ensure this. So I became curious about what the structure WAS behind the character selection on each card. I wrote a python script to visualize co-occurrence of symbols on the cards.

    import numpy as np
    import webweb
    import matplotlib.pyplot as plt

    card1 = ["car","frog","giraffe","monkey","turtle","zebra"]
    card2 = ["chameleon","frog","owl","paw print","snail","tiger"]
    card3 = ["fish","flamingo","lion","sun","tiger","turtle"]
    card4 = ["banana","butterfly","giraffe","lion","owl","palm tree"]
    card5 = ["compass","palm tree","rhino","snail","toucan","turtle"]
    card6 = ["boot","compass","hat","lion","paw print","zebra"]
    card7 = ["banana","compass","elephant","ladybug","monkey","tiger"]
    card8 = ["alligator","boot","butterfly","chameleon","ladybug","turtle"]
    card9 = ["butterfly","fish","flower","monkey","paw print","rhino"]
    card10 = ["alligator","flower","kangaroo","palm tree","tiger","zebra"]
    card11 = ["fish","giraffe","hat","kangaroo","ladybug","snail"]
    card12 = ["boot","camera","elephant","fish","frog","palm tree"]
    card13 = ["alligator","camera","fox","lion","monkey","snail"]
    card14 = ["binoculars","chameleon","hat","monkey","palm tree","sun"]
    card15 = ["binoculars","flower","frog","ladybug","lion","toucan"]
    card16 = ["alligator","binoculars","car","compass","fish","owl"]
    card17 = ["alligator","elephant","giraffe","paw print","sun","toucan"]
    card18 = ["binoculars","butterfly","elephant","flamingo","snail","zebra"]
    card19 = ["binoculars","boot","fox","giraffe","rhino","tiger"]
    card20 = ["butterfly","camera","car","hat","tiger","toucan"]

    listOfCards = [card1,card2,card3,card4,card5,card6,card7,card8,card9,card10,
                   card11,card12,card13,card14,card15,card16,card17,card18,card19,
                   card20]

    listOfNames = sorted(set([item for sublist in listOfCards for item in sublist]))
    print(listOfNames)

    n = len(listOfNames)
    A = np.zeros([n,n])

    displayNames = dict()
    names = dict()
    for i in range(n):
        names[i] = {"name":listOfNames[i]}
    displayNames["nodes"] = names

    for name in listOfNames:
        i = listOfNames.index(name)
        for card in listOfCards:
            if name in set(card):

                for character in set(card).difference({name}):
                    j = listOfNames.index(character)
                    A[i,j] = A[i,j] + 1
    print(A)
    plt.figure()
    plt.pcolor(A)
    plt.colorbar()
    plt.show()

    web = webweb.Web(A, display=displayNames)
    web.display.charge = 1000
    web.display.linkLength = 200
    web.display.colorBy = 'degree'
    web.display.sizeBy = 'degree'
    web.display.showNodeNames = True
    web.display.attachWebwebToElementWithId = 'spotit'
    web.show()

From this, I visualized the following table of co-occurrences:

From this, we see that two characters can co-occur on a card at most once, and some characters never co-occur. Visualizing this as a network,

And as it turns out, other people have thought about this too! Very interesting problem and a nice little diversion.