Author Topic: Selection of words  (Read 4337 times)

pat

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Selection of words
« on: February 11, 2011, 10:36:46 PM »
As a matter of interest, Alan, how are the nine-letter words for the two puzzles actually selected? The reason I ask is that it's not at all unusual for both puzzles to have several of the same letters in them; today, for example, there are five common letters. I'm no mathematician but it's more than I'd expect to occur by chance (although no doubt someone out there will be able to correct me on that point!)


TRex

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Re: Selection of words
« Reply #1 on: February 12, 2011, 11:27:14 AM »
As a matter of interest, Alan, how are the nine-letter words for the two puzzles actually selected? The reason I ask is that it's not at all unusual for both puzzles to have several of the same letters in them; today, for example, there are five common letters. I'm no mathematician but it's more than I'd expect to occur by chance (although no doubt someone out there will be able to correct me on that point!)

I would also be interested in learning this, as well as how the required letter is determined. The latter, I suspect, is randomly determined, but the former might not be random lest the same word be used too quickly.

When there are a fair number of common letters, such as the situation Pat describes, I sometimes find myself missing a word in one of the puzzles because I've already used it in the other puzzle! If I had more time, I'd do like some and play the two separately, hours apart.

Alan W

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Re: Selection of words
« Reply #2 on: February 12, 2011, 03:27:37 PM »
In fact, the process is biased against the two daily puzzles having words in common, and consequently there are probably fewer common letters between the puzzles than would otherwise occur.

The issue was raised in the forum in 2007. (Incidentally, the forum last week passed, without fanfare, its 4th anniversary: the first posts were on 4 February 2007.)

I reported here that I had changed the puzzle to reduce, but not eliminate, the incidence of daily puzzles with common words. The change I actually made was along these lines: after the selection of the letters for the second daily puzzle, there is a check to see if the proposed letters of the two puzzles would allow any words in common at all. If so, the letters for one of the puzzles are re-selected. However the test for a possible word overlap is only performed once, so it can happen that the re-selected letters may also permit some words in common with the other puzzle.

So the check is not directly on letters in common, but on the possibility of words in common, taking into account the letter that must be used in every word. In theory, two puzzles could have 7 letters in common and still not be able to make any words in common - if the mandatory letter of each puzzle is not part of the other puzzle.

I said in the original post that there were common words about one day in five. The change I made then should mean, I think, that common words occur now only about one day in 25. I haven't actually checked the past puzzles to see if that is true.

However, to get back to your question, Pat, there still might be more common letters between the puzzles than would happen if the choice of letters were completely random. But it isn't. Firstly, the nine letters have to make a reasonably common nine-letter word. Secondly, the set of letters, including the designated mandatory letter, must be able to make a fairly large number of common words. Both of these requirements tend to favour the selection of the letters that are most commonly used in English words: ETAOINSHRDLU, or thereabouts. So, since any set of candidate letters is likely to favour the high-usage letters, the chances of any two puzzles having a number of letters in common are quite high.

TRex, regarding the issue of the same nine letters re-appearing too quickly, the rule currently being applied is that they must not have been used in any daily puzzle in the past 12 months. But the exact same puzzle, with the same letters and the same mandatory letter, must not have been a daily puzzle in the past three years.
Alan Walker
Creator of Lexigame websites

pat

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Re: Selection of words
« Reply #3 on: February 13, 2011, 12:11:05 AM »
Thanks for that very detailed explanation, Alan. For some reason I imagined that the initial selection would be a word rather than individual letters, with the process then going on to determine the number of possible words that could be made from those letters.

Fancy letting the anniversary of the forum pass without fanfare. Here's to the next four years! :-)

Alan W

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Re: Selection of words
« Reply #4 on: February 14, 2011, 02:38:29 PM »
You are right, Pat. The selection does start out from a nine-letter word. There are about 5000 nine-letter words that I consider common enough to use. These can make about 38,000 different puzzles, once you take account of the possible choices for the mandatory letter. For each of these puzzles, I have pre-calculated how many common words can be made from that set of letters. For each type of puzzle, there is a range of acceptable values for the number of common words.

So when I spoke about the initial selection of letters for a puzzle, I meant a selection from those possible puzzles, derived originally from nine-letter words.

Incidentally, there are 7 selections of letters that can make only one common word - that is, the nine-letter word. For some reason, chihuahua is not one of them - I didn't include it among my seed words, even though I used it to name the puzzle because it can make no shorter common words.

So, here are 7 puzzles you will never see, because the niner is the only common word possible:


O G S
O X N
T B R

T T I
I C I
M W S

A H A
P B I
I M N

This one, among its three rare words, has a second niner!
G U I
G X N
P E N

Z B K
I M I
U T B

R E N
E C V
E E R

N G R
I Y N
G S I


The first example is the champion, because it can make no rare words at all.

At the other end of the scale is this puzzle, that can make 211 common words, plus 267 rare ones. You might see this one in Your puzzles, when the "very large" option has been chosen:


A D E
P E L
R S T

Alan Walker
Creator of Lexigame websites

TRex

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Re: Selection of words
« Reply #5 on: February 14, 2011, 03:11:25 PM »
Okay, I'm confused (as usual).

Alan, you say 'here are 7 puzzles ...' but I only see three -- or maybe six ???

And you didn't tell us what words the letters make!!!!!!!!!!!  (You  >:D )


pat

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Re: Selection of words
« Reply #6 on: February 14, 2011, 08:11:03 PM »
I see 7!

Perhaps Alan could post the answers to the puzzles in the thread for that purpose? I'm sure we won't all be able to get all of the words!
« Last Edit: February 14, 2011, 08:20:09 PM by pat »

Alan W

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Re: Selection of words
« Reply #7 on: February 14, 2011, 11:24:25 PM »
I've put the answers in the Conundrums - Answers thread, in Whatever.
Alan Walker
Creator of Lexigame websites