Author Topic: Most Discarded Tiles  (Read 2418 times)

Offline danisthirty

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Most Discarded Tiles
« on: November 02, 2017, 08:42:29 AM »
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)

Linkback: http://www.carcassonnecentral.com/community/index.php?topic=3613.0
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Offline Halfling

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Re: Most Discarded Tiles
« Reply #1 on: November 02, 2017, 08:53:28 AM »
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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Offline ny1050220

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Re: Most Discarded Tiles
« Reply #2 on: November 02, 2017, 08:53:42 AM »
As we all know, asking a good question is far more important and difficult to answer or try answering it, hence a merit.

Offline danisthirty

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Re: Most Discarded Tiles
« Reply #3 on: November 02, 2017, 08:55:32 AM »
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)
« Last Edit: November 02, 2017, 08:57:08 AM by danisthirty »

Offline Halfling

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Re: Most Discarded Tiles
« Reply #4 on: November 02, 2017, 09:16:34 AM »
Aha. In that case 27 tiles.

Offline danisthirty

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Re: Most Discarded Tiles
« Reply #5 on: November 02, 2017, 09:17:35 AM »
Aha. In that case 27 tiles.

Bingo! That's what I have anyway. Any advances on 27 tiles after 2 played?

Offline glh510

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Re: Most Discarded Tiles
« Reply #6 on: November 02, 2017, 11:03:02 AM »
28 if I could place 3 tiles

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Offline Just a Bill

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Re: Most Discarded Tiles
« Reply #7 on: November 02, 2017, 02:03:27 PM »
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

Yep, I agree with this, too. And those are really the only two viable paths to a large number.
« Last Edit: November 02, 2017, 02:07:45 PM by Just a Bill »
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Offline MrNumbers

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Re: Most Discarded Tiles
« Reply #8 on: November 02, 2017, 02:48:26 PM »
Same here, 27 tiles.
True also for 3/28.
« Last Edit: November 02, 2017, 02:50:51 PM by MrNumbers »
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Offline danisthirty

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Re: Most Discarded Tiles
« Reply #9 on: November 02, 2017, 05:45:19 PM »
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?

Offline MrNumbers

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Re: Most Discarded Tiles
« Reply #10 on: November 03, 2017, 12:20:47 AM »
After first 2/27 discards I was able to find another 27 23 discards after placing 5 more tiles :D
« Last Edit: November 03, 2017, 01:15:47 AM by MrNumbers, Reason: cloisters can\'t be discarded twice :) »

Offline danisthirty

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Re: Most Discarded Tiles
« Reply #11 on: November 03, 2017, 12:24:51 AM »
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)

Offline MrNumbers

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Re: Most Discarded Tiles
« Reply #12 on: November 03, 2017, 12:39:43 AM »
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
« Last Edit: November 03, 2017, 01:13:57 AM by MrNumbers »

Offline danisthirty

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Re: Most Discarded Tiles
« Reply #13 on: November 03, 2017, 02:01:39 AM »
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?!

Offline glh510

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Re: Most Discarded Tiles
« Reply #14 on: November 03, 2017, 02:11:14 AM »
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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