The Wordle Bot says there is a 23% DNF rate. Not surprising, the conventional wisdom being to get the vowels with words like “least” or “adieu.” But when the last 4 letters of a solution have 8 different first letters, the vowels aren’t useful. I generally start with 2 digraphs. After 2 guesses I had eliminated 4 of those 8, had the right first letter in the wrong place, and (according to the bot) had 1 possible word left. #Digraphs
#Wordle 668 3/6*

⬛🟨🟩⬛⬛
⬛⬛🟩⬛🟨
🟩🟩🟩🟩🟩

#RiffsAndRotes • Happy New Year #2023
• https://inquiryintoinquiry.com/2023/01/01/riffs-and-rotes-happy-new-year-2023/

Let \(p_n\) = the \(n^\text{th}~\text{prime}.\)

Then \(2023=7\cdot{17}^2=p_{4}p_{7}^2=p_{{p_1}^{p_1}}p_{{p_4}}^{p_1}=p_{{p_1}^{p_1}} p_{{p_{{p_1}^{p_1}}}}^{p_1}\)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[2023=p_{p^p} p_{{p_{p^p}}}^p\]

Forms like these correspond to a family of #Digraphs called #Riffs and a family of #Graphs called #Rotes.

#GraphTheory #NumberTheory #Primes