48 lines
974 B
Typst
48 lines
974 B
Typst
#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.3.1"
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#show: handout.with(
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title: [Warm-Up: Wild Tic-Tac-Toe],
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by: "Mark",
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)
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#let ttt = align(
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center,
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cetz.canvas({
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import cetz.draw: *
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let s = 0.7 // scale
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set-style(stroke: (thickness: 0.5mm * s))
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line((-1 * s, 3 * s), (-1 * s, -3 * s))
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line((1 * s, 3 * s), (1 * s, -3 * s))
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line((3 * s, -1 * s), (-3 * s, -1 * s))
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line((3 * s, 1 * s), (-3 * s, 1 * s))
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}),
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)
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#problem()
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In wild tic-tac-toe, players may place either an X or O on each move. The player that first completes a
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row of any three symbols wins. Show that the first player always has a winning strategy.
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#v(4mm)
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#table(
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stroke: none,
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align: center,
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columns: (1fr, 1fr, 1fr),
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ttt, ttt, ttt,
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);
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#v(1fr)
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#problem()
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Now, say the first player to complete a row loses. Who has a winning strategy now?
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#v(4mm)
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#table(
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stroke: none,
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align: center,
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columns: (1fr, 1fr, 1fr),
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ttt, ttt, ttt,
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);
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#v(1fr)
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