As guessed correctly by 4 people, including 1 new participant, the trio of Scrabble-legal words was READING, WRITING, and ARITHMETIC. According to my calculations, this was the only possible word trio based on the clues available after the final week. Also, one entrant complained that my final hint was way too easy, so I'll make it a spoiler (like this) next time so solvers who wish to try to avoid using it can do so.
The first winner of a $10 gift card for Grandmaster Puzzles plus a surprise gift, selected at random from among those 4 people, is Kevin Orfield! Congratulations!
In addition to Kevin Orfield, 9 other people meaningfully participated in the contest. The second winner of a $10 gift card for Grandmaster Puzzles plus a surprise gift, selected at random from among those 9 people, is Izak Bulten! Congratulations!
Stay tuned next week for Let's Guess Three Words V, but first, I feel like writing a strategy guide!
Part 1: Set Theory 101
On week 0, we learned that of my three mystery words which turned out to be READING, WRITING, and ARITHMETIC, one of them is in "the set of all words in which the second letter is a vowel" and two of them are in "the set of all words containing a string of three or more consecutive consonants (e.g. THREE) and/or a string of two or more consecutive vowels (e.g. THREE)". But what do these even mean? The first one simply means that one of the words has a vowel for the second letter (READING, in this case) and two of them do not. The second one, while a bit wordier, means that two of the words have either three consecutive consonants or two consecutive vowels, and one word has neither three consecutive consonants nor two consecutive vowels. (READING has two consecutive vowels, and ARITHMETIC has three consecutive consonants; WRITING has neither.)
Part 2: ALL and NONE
ALL and NONE results are easy. If ALL of the words are in a specified set, then all words outside of it can be eliminated. For example, if ALL the words are in "The set of all words whose second-to-last letter appears in the words 'RAIN MAN'", then you can eliminate all words whose second-to-last letter is anything else. Similarly, if NONE of the words are in a specified set, then all of those words can be eliminated.
Part 3: Narrowing Down One Word
One relatively easy strategy to make progress without expending a lot of computing power is to solve one word at a time. If you are unable to execute the strategy detailed in the later sections, or unable to read it without your eyes glazing over, this is the best strategy that you can use to help the other players solve the words faster. Remember, the faster the words are solved, the more money I have to give to my food bank to feed the hungry!
As demonstrated above, one of the words has a vowel as its second letter (this word ended up being READING). Thus, you can guess a subset of "the set of all words in which the second letter is a vowel", and you'll get very easy-to-use information about that word alone. For instance, you could guess "the set of all words in which the second letter is A, E, or I", and if you get ONE, then the aforementioned word's second letter has been narrowed down to A, E, or I. If you get NONE, then the aforementioned word's second letter has been narrowed down to O, U, or Y. Optimally, you want to split the set of possible words 50/50 so you're guaranteed to get a good amount of information whether you get NONE or ONE.
Part 4: ONE and TWO
Every time a ONE or TWO result is found, one word is shown to have a property that the other two don't. In this case, one word has a vowel for the second letter (and the other two don't), and one word has no two consecutive vowels and no three consecutive consonants (and the other two have either or both of these). Let's call the set of all words with a vowel for the second letter set 1, and the set of all words with no two consecutive vowels and no three consecutive consonants set 2. We can then categorize the words as follows:
Category 0 (words in neither set 1 nor set 2)
Category 01 (words in set 1 but not set 2)
Category 02 (words in set 2 but not set 1)
Category 012 (words in both set 1 and set 2)
The exact nomenclature isn't terribly important, but this nomenclature has made it easier for me to play along with my readers to see how close they are to solving the words.
One of the three words has to be from set 1, and one of the three words has to be from set 2. Thus, the three words can be categorized in one of the following splits:
012/0/0 (one word from category 012 and two words from category 0)
01/02/0 (one word from category 01, one word from category 02, and one word from category 0)
As it happens, READING is in category 01, WRITING is in category 02, and ARITHMETIC is from category 0.
On week 1, we learned, among other things, that TWO words are in "The set of all words in which a letter appears more than once", and thus that one word has no repeated letters in it. Let's call the set of words with no repeated letters set 3. Now we can make 8 categories (0, 01, 02, 03, 012, 013, 023, and 0123). The number of possible splits across the 8 categories also increases:
0123/0/0
012/03/0
013/02/0
01/023/0
01/02/03
As it happens, READING is in category 013, WRITING is in category 02, and ARITHMETIC is from category 0.
Every ONE or TWO result doubles the number of categories, and approximately triples the number of three-category splits. However, as time passes, some categories will end up being empty, and the splits containing those empty categories can be eliminated. Sometimes, a non-empty category can be eliminated because all of the three-category splits for it are eliminated by other empty categories.
Part 5: Narrowing Down the Word Trio
With this knowledge, what is a good guess to make? A set that splits each category approximately in half is pretty good. Unlike the "narrowing down one word" strategy, which leaves you with 50% of the existing word trios in a worst-case scenario (or in a best-case scenario), this strategy will leave you with 37.5% of the word trios in a worst-case scenario (and 12.5% of them in a best-case scenario). So put this strategy to use if you're really serious about solving the words!
Part 6: Outsmart the Author
I am only human, and humans have biases. Here are all of the word sets I used in the previous contests. See if you can spot any biases:
WILL and GRACE
BLOSSOM, BUBBLES, and BUTTERCUP
LOCK, STOCK, and BARREL
READING, WRITING, and ARITHMETIC
If you do spot some biases, don't tell me. Secretly plot to use my biases against me to solve the words faster!
There may be other strategies to discover, too, but this should be a quick start for future reference.
