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> Sadly there's a rule not letting you use a known letter more than once in a word (once A is known, you can't write ALPHA)

This is not entirely correct (or at least it's worded a bit weirdly).

If you know that A goes in a certain place you can still try a word using A more than once. It's only once you know that A does not appear twice (because you tried a word containing A twice, and the second A way gray!) then you can no longer use A twice.

In your case you tried MAMMA which contained 2 As and the second one gave you the information that there's no second A.

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Are there no words with the same letter three or more times?
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If there was a second of the same letter, but in the wrong place, it would be yellow. If it's gray, that means there is no repetition of that letter. So once you've seen that the second one is gray, you have the information you need to know that letter is not repeated.
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Mamma has 3 M's.
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Grepping /usr/share/dict/words shows 110 words that have five letters and the same letter 3 or more times, e.g. sassy, added, daddy, nanny, melee, levee, mummy
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It also accepted GEESE
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The best I could do with today's word, and the wordlist, but no scoring function to minmax the rules:

- FUFFY (8159) (shipping of Faith and Buffy from Buffy the Vampire Slayer)

- IMMIX (4544) (to mix or blend)

- ZOCCO (2142) (low plinth, from the Italian word for sock)

- QAJAQ (530) (alternative form of kayak)

- TRATT (155) (clipping of trattoria)

- KHAPH (7) (alternative form of khaf, the 11th letter of the Hebrew alphabet)

I get the feeling that if this game had 7 steps instead of 6, it would almost always be impossible.

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Theoretically, you could still win today's if there were 8 steps. The ninth is the word you have to avoid.

I haven't found a way to win today with 9 steps.

https://gist.github.com/erikcorry/b21723a0ba49c044b03a6030dc...

Edit: Using some of your words you can get to 9 steps (10 including the word you have to avoid): https://gist.github.com/erikcorry/d55d263b129eb7a56c8c212296...

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I had two word possibilities left at the end, so it's possible.
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> Sadly there's a rule not letting you use a known letter more than once in a word (once A is known, you can't write ALPHA),

That rule doesn't make sense.

What if the answer is AORTA, and you want to guess ALBUM and then ALPHA?

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The sibling comment pointed it out; MAMMA is revealed with one yellow A and one grey A, meaning it has told you there's only one A. If the answer was AORTA, then both As in MAMMA would be yellow.
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> If the answer was AORTA, then both As in MAMMA would be yellow

Why would the last A be yellow and not green? It's the correct letter in the correct location. MAMMA should be gray, yellow, gray, gray, green.

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Oops, yes. In that case, if the answer was AGAIN, both As in MAMMA would be yellow (as opposed to one yellow one grey)
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