A Letters Round Quandary

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Johnny Canuck
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A Letters Round Quandary

Post by Johnny Canuck » Fri Jun 03, 2016 1:36 am

Inspired by the apparent spikes in max scores and 9-letter word frequency on TV during the past weeks, I was pondering the following quandary* during a boring class today:

In a standard 15-round game, is there any possible ordering of the letters within the vowel and consonant piles such that all ten letters rounds are guaranteed to yield 9-letter words, irrespective of how many vowels the contestants choose in each round and in what order these vowel counts appear?

If so, is this still possible with the added condition that the letters need to conform to a reasonable Countdown letters distribution, such as the one listed here? And if that too is true, is it possible without any vowel or consonant occurring twice in a row within its pile, emulating the shuffling algorithm from the show?

If ten 9-letter words (thus making for a max of 230) is not possible, what is the ordering that gives the highest worst-case-scenario max score (for example, is there an ordering that will usually yield ten 9s, but in certain cases of bad picking may also yield nine 9s and an 8?)?

*Yes, as soon as I thought of this puzzle, my mind spontaneously dubbed it a "quandary" almost right off the bat. I'm weird that way.
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Charlie Reams
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Re: A Letters Round Quandary

Post by Charlie Reams » Fri Jun 03, 2016 10:42 am

I attempted this many years ago (probably on the mailing list -- I'll see if I can find it). I was able to get guaranteed 9s in the first two or three rounds I think. After that it gets hard. Might be doable with the new dictionary though.

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Re: A Letters Round Quandary

Post by Johnny Canuck » Fri Jun 03, 2016 6:02 pm

By the way, I could write a Python script that would solve this problem for me within an hour, but to do so I'd need a list of all the 9s in the dictionary.
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Re: A Letters Round Quandary

Post by Innis Carson » Fri Jun 03, 2016 6:20 pm

I'd be surprised if it was possible without a very unusual letters distribution. I vaguely remember a short list on the old Countdown Corral of 'perfect games' people had thought up which were specific sets of 11 letters rounds which all yielded nines while conforming to the standard distribution, and from memory they relied on very low-probability nines like QUICKBEAM which would be very sensitive to the order of picking.

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Re: A Letters Round Quandary

Post by David Williams » Fri Jun 03, 2016 7:41 pm

A variant of this question that might be possible. If one of the contestants was able to manipulate the letters piles, would it be possible . . . ?

In this scenario, if Contestant A picks 3, 4 or 5 vowels, then our hero picks 5, 4 or 3 respectively to bring it back on track. He then picks 4 in the next round - always aiming to bring it back to an average of 4 vowels and 5 consonants.

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Re: A Letters Round Quandary

Post by Conor » Fri Jun 03, 2016 9:58 pm

Charlie Reams wrote:I attempted this many years ago (probably on the mailing list -- I'll see if I can find it). I was able to get guaranteed 9s in the first two or three rounds I think. After that it gets hard. Might be doable with the new dictionary though.
3 I think. And I think it may have on The Corral too.

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Re: A Letters Round Quandary

Post by Charlie Reams » Sat Jun 04, 2016 9:16 pm

Johnny Canuck wrote:By the way, I could write a Python script that would solve this problem for me within an hour, but to do so I'd need a list of all the 9s in the dictionary.
Huh, you reckon? I had some thoughts about doing it efficiently but it seemed quite complex and I never got around to it, so maybe I overlooked something. You can try with some easily available wordlist like UKACD and see if it works.

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Re: A Letters Round Quandary

Post by Charlie Reams » Sat Jun 04, 2016 9:24 pm

Conor wrote:
Charlie Reams wrote:I attempted this many years ago (probably on the mailing list -- I'll see if I can find it). I was able to get guaranteed 9s in the first two or three rounds I think. After that it gets hard. Might be doable with the new dictionary though.
3 I think. And I think it may have on The Corral too.
Aha, yes, well remembered -- that was from 2008! My solution, which only went for two rounds, was OAIEEOIAAE and TRSLNLRTCSNT. I had a three-round solution that works assuming people won't pick 5 vowels, which was EAIEIAEOEIOA and RSNTRTLNSRTLSRCNTL. (The actual nines are left as an exercise for the reader, they're all pretty easy by modern standards.)

I agree with Innis that it's highly unlikely that a 10-round solution exists. But perhaps if you dump the worst letters near the beginning you could get close.

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Re: A Letters Round Quandary

Post by Johnny Canuck » Sat Jun 04, 2016 10:00 pm

Charlie Reams wrote:I agree with Innis that it's highly unlikely that a 10-round solution exists. But perhaps if you dump the worst letters near the beginning you could get close.
On the contrary, I would think that putting the worst letters in a cluster at the very end would be more efficient. There are always more consonants in the pile (typically 70-80) than are allowed to be selected in a single show (60), and thus placing them at the end would mean they couldn't be revealed. Similarly, in the vowel pile there will always be a minimum of 10-20 unrevealed vowels, so you could junk most/all of the pesky Us (and, to a lesser extent, some of the Is) by sticking them at the end, interspersing them with others (e.g., UIUOUIUAUI...) if the shuffling constraint is in place.

I don't see how a situation ever arose, in the original puzzle, where one would be confined to 9s such as QUICKBEAM, though I guess since there used to be eleven letters rounds instead of ten you might start needing to delve into the difficult letters at the very end of the game.
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Re: A Letters Round Quandary

Post by Johnny Canuck » Sat Jun 04, 2016 10:10 pm

Charlie Reams wrote:You can try with some easily available wordlist like UKACD and see if it works.
What's John Beresford doing writing a non-Countdown word list :?: :!:
http://www.crosswordman.com/download/UK ... ionary.txt (warning: large file)
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Re: A Letters Round Quandary

Post by Charlie Reams » Sat Jun 04, 2016 10:27 pm

Johnny Canuck wrote:
Charlie Reams wrote:I agree with Innis that it's highly unlikely that a 10-round solution exists. But perhaps if you dump the worst letters near the beginning you could get close.
On the contrary, I would think that putting the worst letters in a cluster at the very end would be more efficient. There are always more consonants in the pile (typically 70-80) than are allowed to be selected in a single show (60), and thus placing them at the end would mean they couldn't be revealed. Similarly, in the vowel pile there will always be a minimum of 10-20 unrevealed vowels, so you could junk most/all of the pesky Us (and, to a lesser extent, some of the Is) by sticking them at the end, interspersing them with others (e.g., UIUOUIUAUI...) if the shuffling constraint is in place.

I don't see how a situation ever arose, in the original puzzle, where one would be confined to 9s such as QUICKBEAM, though I guess since there used to be eleven letters rounds instead of ten you might start needing to delve into the difficult letters at the very end of the game.
Yes, you might be right. Possibly the number of letters in the piles has increased, and cutting a round helps too. (One set I found at the time was UNTRODDEN, OVERVIEWS, CYBERCAFE, UNTHOUGHT, STINGIEST, SUPPLIERS, EXOENZYME, EQUALLING, DIPLOMATS, AMBERJACK, DEFEATISM, which suggests that it wasn't possible to avoid all the bad letters.)

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