Carcassonne Central
Carc Central Community => Quizzes, Puzzles and Challenges => Topic started by: danisthirty on November 02, 2017, 08:42:29 AM
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As we all know, when a tile is drawn that can’t legally be placed, the tile is discarded from the game and the game continues without it. In my experience this is usually the cccc tile but I’ve played many games where other tiles have had to be discarded, sometimes 2 or 3 consecutively (although this is rare)!
This got me thinking about what the maximum number of tiles that could be discarded from a regular base game of Carcassonne actually is, and which tiles would have to be placed beforehand in order to create such a situation. I think I’ve arrived at the correct answer now, but I’m keen to hear from other perspectives so am posing the following head-scratcher...
In a regular game of Carcassonne with no expansions, which two tiles might be drawn and placed according to the usual rules (including the use of the start tile) in order to maximise the number of tiles that would then have to be discarded? How many tiles would be discarded as a result?
This requires a little bit of lateral thinking as well as good knowledge of the tile distribution in the basic game, so I’m offering +1 merit to anyone who can come up with a better answer than my own (which I will share if anybody matches it). Good luck! :(y)
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If a second start tile is drawn and placed so the field sides are joined, there are 4 cloister tiles that will be discarded if drawn.
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As we all know, asking a good question is far more important and difficult to answer or try answering it, hence a merit.
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If a second start tile is drawn and placed so the field sides are joined, there are 4 cloister tiles that will be discarded if drawn.
Very true. I think you're thinking along the right lines. But I think more is possible... ;) (also, please bear in mind that I'm thinking about the next two tiles rather than just one)
As we all know, asking a good question is far more important and difficult to answer or try answering it, hence a merit.
Thank you ny! Glad you're enjoying the question! :) :(y)
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Aha. In that case 27 tiles.
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Aha. In that case 27 tiles.
Bingo! That's what I have anyway. Any advances on 27 tiles after 2 played?
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28 if I could place 3 tiles emoji code41]
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Aha. In that case 27 tiles.
Bingo! That's what I have anyway. Any advances on 27 tiles after 2 played?
Agreed, 27 is the highest achievable answer.
28 if I could place 3 tiles emoji code41]
Yep, I agree with this, too. And those are really the only two viable paths to a large number.
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Same here, 27 tiles.
True also for 3/28.
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Thanks for the feedback everyone.
So with this thinking in mind, what's the maximum number of tiles that could be discarded in a basic game?
I'm thinking crrr, frrr, 27 discarded, then an frrr on each side, ffrr on each corner, fffr at the top and bottom, and 11 more discards. Make sense? Is 38 total discards the maximum or is there another way of getting more?
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After first 2/27 discards I was able to find another
27 23 discards after placing 5 more tiles :D
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After first 2/27 discards I was able to find another 27 discards after placing 5 more tiles :D
Seriously?! 54 discards after 7 placements?! Great work! I must be missing something... (like a brain)
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Seriously?! 54 discards after 7 placements?! Great work! I must be missing something... (like a brain)
Answer is below, 1pt big :)
Add cccr on top, bottom and to the right of crfr. Then add 2 ccrr on the left. That way all rfrf,
rrff, rrrr, 6 2 cloisters and remaining frrr will go away :)
P.S. Just realized that 4 cloisters were gone in first discard, so only 23 left
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Seriously?! 54 discards after 7 placements?! Great work! I must be missing something... (like a brain)
Answer is below, 1pt big :)
Add cccr on top, bottom and to the right of crfr. Then add 2 ccrr on the left. That way all rfrf,
rrff, rrrr, 6 2 cloisters and remaining frrr will go away :)
P.S. Just realized that 4 cloisters were gone in first discard, so only 23 left
You've spoilt it now as I know your solution involves there being a smiley at the end! ;)
In all seriousness though, I haven't read your answer yet as I'm enjoying trying to solve it for myself. It looks like there could be some pretty short games of Carcassonne coming up though. Perhaps even a new world record for smallest game of Carcassonne?!
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Similar number possible with 3/28 and then 8/22. But more tiles to be placed, MrNumbers solution is more elegant then
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Mr Numbers, does your double counting mean that you only discarded 50?
I think I have a game which discards 53, but I’ll have to play it through once more…
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Mr Numbers, does your double counting mean that you only discarded 50?
I think I have a game which discards 53, but I’ll have to play it through once more…
Yes, I discarded only 50. But I reconstructed this only theoretically, on paper, so after I will try it with actual tiles, maybe I could find some other, better solution.
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Here is my 53 discard game: https://imgur.com/a/ceVYP
I think it's very possible that this can be improved upon, so a bit of tinkering is still in order!
Great puzzle, Dan! Thanks. :D
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Your method is a little bit different, and I am not sure it corresponds to the rules of the quiz: when it is time for discard - you keep some tiles, which could be discarded on current step. On the other hand, the main question is "how many tiles could be discarded in a game", without specifying the details of discarding :)
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Your method is a little bit different, and I am not sure it corresponds to the rules of the quiz: when it is time for discard - you keep some tiles, which could be discarded on current step.
Dan's question was just:
So with this thinking in mind, what's the maximum number of tiles that could be discarded in a basic game?
So I think my method is valid, since the tiles could be drawn in that order. :)
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Here is me summarizing previous posts (aka literature review ::) ):
MrNumbers selects a certain tile from the entire pool at each step, places it strategically, and discards all the tiles that would be discarded if they were randomly drawn at next step.
JT Atomico arranges the tiles into a certain order (aka gives a permutation of the tiles), draws tiles sequentially, places the tiles where he wants to, and continues as per normal game play (discards a tile when it can't be placed).
It seems that we have two problems to solve now.