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Modern Math through Games: Notes for Discovery Seminar

Tien Chih

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Section 2.3 P(rojective) SET

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Each P card consists of two SET cards “glued together”.
Figure 2.3.1. A PSET card
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Definition 2.3.2.

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A PSET is a collection of 3 cards such that the cards may be flipped over in such a way so that both the top and the bottom form SETs.
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Activity 2.3.2.

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(a)

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What PSETs can you find here?
Figure 2.3.3. 12 SET cards.
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Activity 2.3.4.

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(a)

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What card(s) can you add to form a PSET?
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(b)

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Out of these cards, how many PSETs can you find?
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(c)

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Pick any two cards, can you find what card(s) if any will complete a set? How many PSETs can you find? Repeat.
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Remark 2.3.4.

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We will let a Pline in the PSET context to be a collection of 4 cards so that every 3 card subset forms a PSET.
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Activity 2.3.5.

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(a)

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Pick any three cards who do not form a PSET and arrange them in a corner of the 3×3 grid:
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(b)

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Fill out this grid so that each line forms a Pline.
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(c)

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For each pair of cards on this grid, do they lie on exactly one Pline?
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