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Answer by Brian M. Scott for Consider a card game-parity

Represent each of the seven cards by a binary vector: the vector for card $i$ is $v_i=\langle b_{i1},\dots,b_{i6}\rangle$, where $b_{ij}=1$ if the $j$-th symbol appears on card $i$, and $b_{ij}=0$...

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Answer by Gerry Myerson for Consider a card game-parity

Suppose you have a subset $T$ of the set of 7 cards. Some symbols may appear an odd number of times in $T$, and some symbols an even number of times. Let $E(T)$ be the set of symbols appearing an even...

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Answer by uncookedfalcon for Consider a card game-parity

Kk I think the following works. Let's call our 7 cards $c_1, \ldots c_7$. View the "symbols on the card $c_j$" as an element $v_j$ of $\mathbb{F}_2^{\oplus 6}$: namely, if our 6 possible symbols are...

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Consider a card game-parity

Consider a card game where the deck consists of 63 distinct cards. The deck is created in the following manner: each card consists of some number of symbols, where no two symbols are the same. There...

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