Preamble

It is routine to end up in a position where 3 or more possible answers exist. This can happen after the 1^st guess, though the probability is small.  It usually happens after the 2^nd or 3^rd guess.  There are at least 2 ways of playing at this juncture – 1) enumerate and 2) eliminate.

Enumerate: try one possible solution at a time. If there are N possible solutions, then the probabilities of guessing the correct word are 1÷N, 2÷N……N÷N in 1st , 2nd, …. Nth try.  Due to the constraint of the game, N can’t be higher than 6.

Eliminate: enter a guess that eliminates all but 1 possible solution.  This way the puzzle can be solved in 2 guesses.  There is a special case of the eliminate strategy.  Sometimes one of the possible solutions itself works as an elimination word.  Under this scenario, it is possible to solve the puzzle in one guess. If the possible solutions are “too many”, then it may not be possible to find one word to eliminate all but one possible solution.  In such a case the goal has to be to narrow down the possibilities to a “few”.

Eliminate-not-Enumerate example #3: Elimination possibility after the second Guess using one of the two possible answers as the elimination word

The advantage of this sub-strategy is that there is a likelihood of solving the puzzle with the elimination word itself, saving at least one guess.

 

Wordle # 425 (August 18, 2022): Seed word ALERT

After the second guess there are four possibilities – NATTY, TAWNY, THANK and TWANG.  Both THANK and TWANG are suitable elimination words, as explained below.

 

THANK as the elimination word.

THANK could be the answer, but if it is not, then elimination happens as explained below.

• TWANG as the answer: as shown in the grid, A and N became green in positions 3 and 4 respectively. The only word among the remaining three with A and N in positions 3 and 4 is TWANG. The other 2 get eliminated
• NATTY as the answer: if this were to be the case, the colors for the elimination word THANK will be Yellow, Black, Yellow, Yellow, and Black. T as Yellow in position 1 eliminates TWANG as well as TAWNY.

 

• TAWNY as the answer: if this were to be the case, the colors for the elimination word THANK will be Green, Black, Yellow, Green, and Black. T as green in position 1 eliminates NATTY; A as Yellow in position 3 eliminates TWANG, leaving TAWNY as the answer.

TWANG as the elimination word.

TWANG could be the answer, but if it is not, then elimination happens as explained below.

• THANK as the answer: A and N become green in positions 3 and 4 respectively. The only word among the remaining three with A and N in positions 3 and 4 is THANK. The other 2 get eliminated.

• NATTY as the answer: if this were to be the case, the colors for the elimination word TWANG will be Yellow, Black, Yellow, Yellow, and Black. T as Yellow in position 1 eliminates both THANK as well as TAWNY, leaving NATTY as the answer.

 

• TAWNY as the answer: if this were to be the case, the colors for the elimination word TWANG will be Green, Yellow, Yellow, Green, and Black. T as green in position 1 eliminates NATTY; A as Yellow in position 3 eliminates THANK, leaving TAWNY as the answer.

In this example, we have two elimination words (TWANG and THANK) that are among the 4 possible answers. So the question arises – how to select from the two?  There is no magic answer.   We can approach it from the point of view of what is the most probable answer based on the frequencies and characteristics of Wordle we know.  Some of the “learnings” through the analysis of Wordle words from #1 to #426 that are relevant to this question are as follows:

• # Of vowels: In about 60% of the cases, there are two vowels (including Y as the 6^th vowel)
• Frequency of “compound” constants (two or three consonants side by side, such as TRace , TWaNG, CHaRT, piNCH, , etc.): In about 65% of the cases, there are two or three compound consonants
• Frequency of the last letter: Four letters dominate the last position: E, T, Y and R with frequencies of 18.5%, 13.1%, 12.9% and 9.8 % respectively (through Wordle #426). These add up to about 56%.
• Frequencies of the five letters: this is more complicated since you have to multiply the frequencies by position for each of the two words to get to overall frequencies for the two words. We could ignore this since this requires a lot of work.
• “Cuteness/elegance” of the words: this is subjective. As an example, for Wordle #424, I ended up with two possibilities after the second guess: TWICE and EDICT.  I consider TWICE to be more “elegant” and it turned out to be the answer – just a matter of luck.

Let’s now evaluate the two words (THANK and TWANG) along these lines.

• # Of vowels: both have only one vowel
• Frequency of “compound” constants: both have 2 sets of compound consonants
• Frequency of the last letter: There is a small difference: K – 4.7%, G – 2.3%
• Frequencies of the five letters: I won’t elaborate. THANK came out ahead of TWANG.
• “Cuteness/elegance”: Perhaps TWANG over THANK

There is no overriding factor for the selection. I picked THANK due to the last letter (K) being more frequent than the last letter in TWANG (G). The word THANK didn’t turn out to be the answer.  Still the eliminate-not-enumerate strategy worked.

In this case, since there are only 4 possible answers, I could have applied the evaluation criteria to all four possibilities to get at the rankings and then picked according to the rankings.   It would have taken more time and effort.  Since the evaluation is probability based, there is always a chance that the top ranking among the four words may not be the answer. The worst-case scenario for enumeration is 6 guesses vs 4 guesses in the case elimination strategy.

© 2022 Ashok Gupta All rights reserved.

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