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My Great-Uncle Alfred loves sequences and likes to test me with them whenever I visit.
The other day, with a flourish, "Voilà!", he presented me a piece of paper with the following sequence,

UI, AI, EEI, EUI, EEI, AEI, ?

"What comes next?" he asked.

"I'm not sure", I replied, "but I would guess it probably ends with the letter I".

"Wrong!", he exclaimed, with a cackle.

Can you tell what comes next in the sequence?

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Next comes:

IAE

Why? Because these are:

the vowels in the days of the week in French!

LUNDI (Monday), MARDI (Tuesday), MERCREDI (Wednesday), JEUDI (Thursday), VENDREDI (Friday), SAMEDI (Saturday).

Next comes DIMANCHE for Sunday, with no I at the end!

The hint is:

Alfred's use of "Voilà", a French word, suggesting that the French language may be important...

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    $\begingroup$ Amazing @Stiv. So fast. One of these days they will come up with a puzzle that will take you more than a day to solve!!! :) $\endgroup$
    – DrD
    Oct 22, 2020 at 13:08
  • $\begingroup$ @DrD Haha, thanks :) This kind of question (like many of your Grandpa's...) is exactly 'my cup of tea' - something short-and-sweet, which requires you to ransack the corners of your mind for a piece of information that surely must be in there somewhere and apply it in a different way. Here for me the 'aha' moment was noting the number of terms in the sequence and the hint word I mention above... $\endgroup$
    – Stiv
    Oct 22, 2020 at 13:53
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    $\begingroup$ Correct, as always, and very quick! And yes, very much inspired by the grandpa-style puzzles of @DrD $\endgroup$
    – hexomino
    Oct 22, 2020 at 15:15

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