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General Tabletop Discussion
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The math behind Carcassonne tiles
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<blockquote data-quote="Nareau" data-source="post: 4003657" data-attributes="member: 969"><p>If you haven't played Carcassonne, it's a little like dominoes in that you lay down tiles that have to match up edge-to-edge.</p><p></p><p>Each tile has 4 sides, and each side can have 3 different "features": A road, city, or meadow (R, C, or M).</p><p></p><p>I think this is a pretty simple permutation problem, but there's a twist in it. If you read the sides of the tile in a clockwise fashion, you might get: Road, Road, Road, City.</p><p></p><p>RRRC is the same as RRCR, RCRR, CRRR because the sides wrap around.</p><p></p><p>But a tile that is CCRR is not the same as CRCR.</p><p></p><p>Am I overthinking (or underthinking) this? Can someone help me figure out how many possible different tiles there could be?</p><p></p><p>Nareau</p></blockquote><p></p>
[QUOTE="Nareau, post: 4003657, member: 969"] If you haven't played Carcassonne, it's a little like dominoes in that you lay down tiles that have to match up edge-to-edge. Each tile has 4 sides, and each side can have 3 different "features": A road, city, or meadow (R, C, or M). I think this is a pretty simple permutation problem, but there's a twist in it. If you read the sides of the tile in a clockwise fashion, you might get: Road, Road, Road, City. RRRC is the same as RRCR, RCRR, CRRR because the sides wrap around. But a tile that is CCRR is not the same as CRCR. Am I overthinking (or underthinking) this? Can someone help me figure out how many possible different tiles there could be? Nareau [/QUOTE]
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