Gareth, Can you provide an example page? My wife asks how that works. Amazon shows a book where you have to find the word by looking at filled out previous lines. But I guess you did it differently...
Posted 14th Mar 2022 at 20:30 Last edited by gareth 14th Mar 2022 at 20:34
gareth Administrator Daily subscriber
Yes, that other book looks like essentially a crossword clue + anagram game. My book works as you would probably hope, with a series of guesses. To see exactly how it works the best way is to watch this video where I explain how to solve.
I'll that video link to the announcement post now too.
Posted 15th Mar 2022 at 16:38
JoergWausW Daily subscriber
Thanks for the video. Interesting mechanism. Same letter in one word would also be possible.
Pros (pesonal opinion after watching the video): - Backwards reconstruction of the solution is possible, but enough of a hassle. - And you don't have to browse to different pages to check your guess. Con (again, limited personal opinion): - The arrows to the next word - I wouldn't use them. I tend to cover as many letters as possible. So I sometimes use completely different letters in the next word, especially dropping the letters that I know the exact position of, and of course shuffling the yellow ones. I would have to deal with different kind of marks (circles around letters and arrows underneith).
Solution: either use diamonds for correct positioned letters, or make a "soultion-row" underneathe the number board where you write down the correct letters. If feel the arrow marks kind of push you to reuse the same letter again in the next guess - limiting for some the possible ways to the solution.
...I was hoping you invented paper that changes colour locally (within outlined squares) dependant of what people write ... ;-)
PS 1: my wife and I go with MEANY, SHIRT and COULD to cover 15 letters, including all vowels. Depending of the number of coloured letters we vary those.
PS 2: Why not have a "super solution page" at the end of the book where people can collect the solution words from various pages to create a sentence (shuffle the words as part of the puzzle, don't tell which of the two words from a page is being used...).
Posted 15th Mar 2022 at 17:46
gareth Administrator Daily subscriber
Glad you had a good look - it's surprisingly fun to solve them, to the point where I actually enjoy it more than doing it online!
You could allow repeated letters, yes, but it can't behave like the Wordle website which only colours as many of a letter (if you repeat it) as appear in the word - so it is simpler to just avoid it, particularly because I don't like that feature of Wordle in any case. It also makes it more satisfying to cross out letters, if you choose to do so.
The notation is entirely up to you - I chose the arrow to go with the 'fall' in the name, but they aren't needed since you already have circles for 'yellow' and crossing-out for 'grey', so anything else by default is 'green'.
You can backward solve if you want, but you won't do it accidentally which is all I cared about. I made sure of that! :) Similarly you could look the solution up in any puzzle book, if you want.
I like your idea for the back of the book - book 2 is already printed but maybe if there's a book 3! :)
Posted 15th Mar 2022 at 17:47
gareth Administrator Daily subscriber
We've also added an example to the Amazon product page now too.
Posted 16th Mar 2022 at 01:10
JoergWausW Daily subscriber
I guess I didn't think it to the end. Multiple letters are a problem with your current system... I think two rows of numbers per letter might solve it to allow a letter up to twice, but then the checking process becomes too complicated. I guess the current way seems to be the easiest one for the player.
Posted 22nd Mar 2022 at 10:30
winterer Daily subscriber
(Coming a bit late for the discussion...)
I like the game mechanics for a paper based wordle! But why would multiple letters be a problem with it? Take "LEVEE" as an extreme example. The letter "E" could have the numbers 17/23/37/43/59, and the clues would list all 5, with 23/43/59 underscored... What am I missing? (apart from players noticing the numbers' appearances in both lists and deducing that this letter must be repeated... well, yes, it'd need more obfuscation...)
Anyway, after I read the first article about Wordle in the Grauniad, I thought that my solution method for "Mastermind" should work with Wordle as well. I had doubts about the starting words proposed in this and other articles (LATER based on letter frequency, ADIEU to cover most vowels), though. So I did some experiments, using all the words in Wordle's solution list, scoring the average number of tries with my strategy and the number of fails (not solved after 6 tries), and settled on CLASP. (the exact best word varied with randomization, and whether I included Wordle's blacklisted words as well, but CLASP always scored highly)
The reason is that consonants are much more important that vowels in guessing the right word. If LATER was the correct solution, _A_E_ wouldn't tell you much while L_T__ would.
The strategy is then: start with a word with few vowels (but common consonants); always make the next guess consistent with all the clues you got so far; don't repeat letters unless forced to do (or the word with repeated letters is much more common than a possible word without repetition).
With this strategy, I'm currently at a 4.03 average in English and 3.81 in German, both with 100% solved.
Posted 22nd Mar 2022 at 13:12
gareth Administrator Daily subscriber
You're right of course that you could have repeated letters if you wanted, but it then needs slightly more clarification in the instructions and I wanted to keep it as simple as possible. Also I personally dislike repeated letters, so decided to outlaw them. :) If you did have repeated letters, however, I don't think it would significantly increase your chance of spotting the numbers by accident because I have taken steps to ensure everything as unmemorable as possible - there is quite a lot of subtlety in how it distributes and chooses numbers, based on my own psychological assumptions about what is and isn't memorable or easily noticeable. I find you have to very actively concentrate on 'cheating' to use the numbers by accident, and so far as I know no one has had this problem.
And I agree on starting words - I tend to use one with T, R and S in, like STARE or TEARS, but I don't claim this is entirely optimal. Or when solving in my book, I quite enjoy starting with the previous solution word for a slight extra challenge!
Posted 23rd Mar 2022 at 02:57 Last edited by JoergWausW 23rd Mar 2022 at 03:05
JoergWausW Daily subscriber
@winterer about letters used twice:
Let's say "VIDEO" was the solution. You try "VIVID".
That would give you underlined numbers for the first v and i, and additionally not underlined numbers for the d and also for the second v and i. Looks like you found all 5 letters. But there is only one v and one i in the solution. And VIDVI or VIIDV are the only possible logic implications.
To allow letters to maybe appear twice, you then need two rows of numbers for each letter - one for the possible first occurence, one for the possible second... and then the user has to go through a flow shart to figure out what to do with these 2 rows (depending on how many times the user used the same letter)... maybe there is an easier way to make it working, but this is the version that I came up with.
Added: in the current version you'd get the same answer as in my example. But you should know that the not underlined numbers for v and i refer to the same solution letter as the underlined ones. That explains my idea for a second row per letter with a different set of numbers that deals with the second occurrence.
Posted 23rd Mar 2022 at 08:39
winterer Daily subscriber
@JoergWausW:
Sorry, I was a bit slow here and didn't see your point immediately. I was thinking only in one direction: Multiple letters in the solution wouldn't be a problem. The problem is in the other direction: Multiple letters in the guess, where the letter appears in the solution less often than in the guess.
Not sure that there is a paper-based version possible that doesn't leak too much information while not being misleading regarding surplus letters in the guess.
Posted 24th Mar 2022 at 10:05
JoergWausW Daily subscriber
I made the same mistake at first (see my first statement here).
You'd have to double the amount of numbers to check (and double player's time to perform the check) to allow a letter twice (even more efford for three times). But that's how the paper version would very probably become way less pleasant to play.
Posted 24th Mar 2022 at 11:19
gareth Administrator Daily subscriber
Yes - or you would have to simply acknowledge that you didn't have that information available as to how many times a letter appeared. It doesn't have to mirror any online format precisely so that wouldn't itself be an issue. But I decided I preferred it without worrying about that, so I excluded repeated letters.
Posted 24th Mar 2022 at 19:42
JoergWausW Daily subscriber
another thought: if you know that the letter might be there a second time: you may be tried to check the other four numbers for that letter which of them might be underlined...
So considering the options, I agree that excluding repeated letters is the best way to go.
Posted 26th Mar 2022 at 08:26
winterer Daily subscriber
I think I found a way how one could handle multiple letters without too much overhead.
Suppose you print on each page a random number between 1 and 3 (could also go higher or use a special character for "larger"). You could then use these as upper bounds for the number of repeated letters in the word.
So for each letter, you'd have two additional numbers (in addition the the 5 positional numbers as in the current game mechanics), each pointing to a page somewhere in the book. The first can be used if the guess contains this letter twice (and the solution at least once), the second if the letter appears three times in the guess (there are no words with more than 3 same letters, and for single letters it's not needed).
If the letter appears at least as often as in the guess, then the number on the page would have to be at least as high, but it could also be higher. E.g., "LEVER" as guess and "TEENS" as solution, the additonal clue for 2 "E"s could point to a page with number 2 or 3 (or higher if available). The upper bound must not be guaranteed to be tight, so as to avoid leaking information.
If the letter appears less often, then the number on the page will reveal the exact number. E.g., "LEVER" as guess and "TEARS" as solution, the additonal clue for 2 "E"s points to a page with number 1, revealing that there's only one "E" in the solution.
This way, one would know how many of the clues can be used. In the former case, the first "E" would have an underscored number, the second "E" will have a regular number. But both clues can be used, as the additional clue states that the upper bound is at least 2. In the latter case, the number of "E"s is revealed as being 1. One then knows that the underscored number for the first "E" takes precedence over the regular number for the second "E".
In the case of, e.g., "LEVER" vs "STERN" as solution, the additional clue reveals that only one "E" is in the solution, and you can use either "E" to continue, as both have non-underscored numbers.
If the letter appears only once in the guess, you'd just use the number of that letter's position. If the letter appears thrice (as in "LEVEE" or "SASSY"), you'd use the additional clue for three appearances to work out whether three letters is good or too many. Again, underscored reveals take precedence over non-underscored reveals.
This would mimic the information given by the green/yellow colouration in the online version, where green takes precedence over yellow, and the total number of coloured letters is at most the number of that letter in the solution.
Whether having the words with double/triple letters available is worth the additional complexity...?
It'd allow about 50% more words: Of the 2315 words in Wordle's whitelist (= possible solutions), 1566 do not have repeated letters, 749 do. If we include the blacklist with rare/obscure/local/slang words and plural/conjugated forms (= allowed guesses, but not solution words), 8322 do not have repeated letters, 4650 do.
Posted 26th Mar 2022 at 17:54
JoergWausW Daily subscriber
Interesting concept.
Probable Problems: I don't think that a number on the same page should give a clue how often a letter might be in the word. If it's a 1 you would know that no letter appears twice or more, so you can exclude those words from your guesses to start with. Since you need at least one puzzle with a 1 in the book, that puzzle is of less quality than the others. You could use numbers on different pages, but those shouldn't rely to the puzzle on that page (maybe I got you wrong with that and you didn't mean it that way).
As I mentioned before: already too much flow chart - If you want to sell that book to the general public, it would be too much. Too few people wouldn't mind.
The other advantage that goes away: the current version could also work in existing printed newspapers. Editors probably won't like to put some puzzle related information on some unrelated sports page...
I think the current solution is a compromise that covers most of the needs. Variations/adaptations are possible for different audiences.
Can you provide an example page?
My wife asks how that works.
Amazon shows a book where you have to find the word by looking at filled out previous lines. But I guess you did it differently...
Last edited by gareth 14th Mar 2022 at 20:34
I'll that video link to the announcement post now too.
Same letter in one word would also be possible.
Pros (pesonal opinion after watching the video):
- Backwards reconstruction of the solution is possible, but enough of a hassle.
- And you don't have to browse to different pages to check your guess.
Con (again, limited personal opinion):
- The arrows to the next word - I wouldn't use them. I tend to cover as many letters as possible. So I sometimes use completely different letters in the next word, especially dropping the letters that I know the exact position of, and of course shuffling the yellow ones. I would have to deal with different kind of marks (circles around letters and arrows underneith).
Solution: either use diamonds for correct positioned letters, or make a "soultion-row" underneathe the number board where you write down the correct letters.
If feel the arrow marks kind of push you to reuse the same letter again in the next guess - limiting for some the possible ways to the solution.
...I was hoping you invented paper that changes colour locally (within outlined squares) dependant of what people write ... ;-)
PS 1: my wife and I go with MEANY, SHIRT and COULD to cover 15 letters, including all vowels. Depending of the number of coloured letters we vary those.
PS 2: Why not have a "super solution page" at the end of the book where people can collect the solution words from various pages to create a sentence (shuffle the words as part of the puzzle, don't tell which of the two words from a page is being used...).
You could allow repeated letters, yes, but it can't behave like the Wordle website which only colours as many of a letter (if you repeat it) as appear in the word - so it is simpler to just avoid it, particularly because I don't like that feature of Wordle in any case. It also makes it more satisfying to cross out letters, if you choose to do so.
The notation is entirely up to you - I chose the arrow to go with the 'fall' in the name, but they aren't needed since you already have circles for 'yellow' and crossing-out for 'grey', so anything else by default is 'green'.
You can backward solve if you want, but you won't do it accidentally which is all I cared about. I made sure of that! :) Similarly you could look the solution up in any puzzle book, if you want.
I like your idea for the back of the book - book 2 is already printed but maybe if there's a book 3! :)
I guess the current way seems to be the easiest one for the player.
I like the game mechanics for a paper based wordle!
But why would multiple letters be a problem with it?
Take "LEVEE" as an extreme example.
The letter "E" could have the numbers 17/23/37/43/59, and the clues would list all 5, with 23/43/59 underscored...
What am I missing? (apart from players noticing the numbers' appearances in both lists and deducing that this letter must be repeated... well, yes, it'd need more obfuscation...)
Anyway, after I read the first article about Wordle in the Grauniad, I thought that my solution method for "Mastermind" should work with Wordle as well. I had doubts about the starting words proposed in this and other articles (LATER based on letter frequency, ADIEU to cover most vowels), though. So I did some experiments, using all the words in Wordle's solution list, scoring the average number of tries with my strategy and the number of fails (not solved after 6 tries), and settled on CLASP. (the exact best word varied with randomization, and whether I included Wordle's blacklisted words as well, but CLASP always scored highly)
The reason is that consonants are much more important that vowels in guessing the right word. If LATER was the correct solution, _A_E_ wouldn't tell you much while L_T__ would.
The strategy is then: start with a word with few vowels (but common consonants); always make the next guess consistent with all the clues you got so far; don't repeat letters unless forced to do (or the word with repeated letters is much more common than a possible word without repetition).
With this strategy, I'm currently at a 4.03 average in English and 3.81 in German, both with 100% solved.
And I agree on starting words - I tend to use one with T, R and S in, like STARE or TEARS, but I don't claim this is entirely optimal. Or when solving in my book, I quite enjoy starting with the previous solution word for a slight extra challenge!
Last edited by JoergWausW 23rd Mar 2022 at 03:05
Let's say "VIDEO" was the solution.
You try "VIVID".
That would give you underlined numbers for the first v and i, and additionally not underlined numbers for the d and also for the second v and i. Looks like you found all 5 letters. But there is only one v and one i in the solution. And VIDVI or VIIDV are the only possible logic implications.
To allow letters to maybe appear twice, you then need two rows of numbers for each letter - one for the possible first occurence, one for the possible second... and then the user has to go through a flow shart to figure out what to do with these 2 rows (depending on how many times the user used the same letter)... maybe there is an easier way to make it working, but this is the version that I came up with.
Added:
in the current version you'd get the same answer as in my example. But you should know that the not underlined numbers for v and i refer to the same solution letter as the underlined ones.
That explains my idea for a second row per letter with a different set of numbers that deals with the second occurrence.
Sorry, I was a bit slow here and didn't see your point immediately.
I was thinking only in one direction: Multiple letters in the solution wouldn't be a problem.
The problem is in the other direction: Multiple letters in the guess, where the letter appears in the solution less often than in the guess.
Not sure that there is a paper-based version possible that doesn't leak too much information while not being misleading regarding surplus letters in the guess.
You'd have to double the amount of numbers to check (and double player's time to perform the check) to allow a letter twice (even more efford for three times). But that's how the paper version would very probably become way less pleasant to play.
So considering the options, I agree that excluding repeated letters is the best way to go.
Suppose you print on each page a random number between 1 and 3 (could also go higher or use a special character for "larger").
You could then use these as upper bounds for the number of repeated letters in the word.
So for each letter, you'd have two additional numbers (in addition the the 5 positional numbers as in the current game mechanics), each pointing to a page somewhere in the book. The first can be used if the guess contains this letter twice (and the solution at least once), the second if the letter appears three times in the guess (there are no words with more than 3 same letters, and for single letters it's not needed).
If the letter appears at least as often as in the guess, then the number on the page would have to be at least as high, but it could also be higher. E.g., "LEVER" as guess and "TEENS" as solution, the additonal clue for 2 "E"s could point to a page with number 2 or 3 (or higher if available). The upper bound must not be guaranteed to be tight, so as to avoid leaking information.
If the letter appears less often, then the number on the page will reveal the exact number. E.g., "LEVER" as guess and "TEARS" as solution, the additonal clue for 2 "E"s points to a page with number 1, revealing that there's only one "E" in the solution.
This way, one would know how many of the clues can be used. In the former case, the first "E" would have an underscored number, the second "E" will have a regular number. But both clues can be used, as the additional clue states that the upper bound is at least 2. In the latter case, the number of "E"s is revealed as being 1. One then knows that the underscored number for the first "E" takes precedence over the regular number for the second "E".
In the case of, e.g., "LEVER" vs "STERN" as solution, the additional clue reveals that only one "E" is in the solution, and you can use either "E" to continue, as both have non-underscored numbers.
If the letter appears only once in the guess, you'd just use the number of that letter's position. If the letter appears thrice (as in "LEVEE" or "SASSY"), you'd use the additional clue for three appearances to work out whether three letters is good or too many. Again, underscored reveals take precedence over non-underscored reveals.
This would mimic the information given by the green/yellow colouration in the online version, where green takes precedence over yellow, and the total number of coloured letters is at most the number of that letter in the solution.
Whether having the words with double/triple letters available is worth the additional complexity...?
It'd allow about 50% more words:
Of the 2315 words in Wordle's whitelist (= possible solutions), 1566 do not have repeated letters, 749 do.
If we include the blacklist with rare/obscure/local/slang words and plural/conjugated forms (= allowed guesses, but not solution words), 8322 do not have repeated letters, 4650 do.
Probable Problems:
I don't think that a number on the same page should give a clue how often a letter might be in the word. If it's a 1 you would know that no letter appears twice or more, so you can exclude those words from your guesses to start with. Since you need at least one puzzle with a 1 in the book, that puzzle is of less quality than the others. You could use numbers on different pages, but those shouldn't rely to the puzzle on that page (maybe I got you wrong with that and you didn't mean it that way).
As I mentioned before: already too much flow chart - If you want to sell that book to the general public, it would be too much. Too few people wouldn't mind.
The other advantage that goes away: the current version could also work in existing printed newspapers. Editors probably won't like to put some puzzle related information on some unrelated sports page...
I think the current solution is a compromise that covers most of the needs. Variations/adaptations are possible for different audiences.
You can however view other players' statistics and comments in the tables above.