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Many students pass their A-Levels (UK), High School Degree or their countries' equivalent. Most of them passionately have to study mathematics and in one of their courses, they might have heard:

indivisibility

Some of them might have noticed: "what a curious word with so many i in it!".

This puzzle is to discover a secret word behind the as best as possible iEnglish word.

What is an iEnglish word?

  • It's an English word, with the rule that it must exists in a 2019 or earlier English dictionnary.
  • an iEnglish word, noted $w$ is associated with a score $s(w)$, which is computed as follows:
    • $n_i(w) = \text{number of letters i in } w$
    • $n_d(w) = \text{number of letters different than i in }w$
    • $s(w) = n_i(w)(n_i(w)+\text{is_prime(}n_d(w)\text{)})$
    • $\text{is_prime(}n_d(w)\text{)}$ helps untie by being equal to one if $n_d(w)$ is prime and 0 otherwise.
    • An example is $s(\text{indivisibility}) = 6(6 + 0) = 36$
  • Of course, the best iEnglish word is the one with the highest score!

What is a secret word?

Let $w$ be an iEnglish word, a secret word of $w$ has $n_i(w)$ letters but contains no letters of $w$. A secret word of indivisibility can be August.

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  • 2
    $\begingroup$ I've downvoted this both because the metric being used is arbitrary, and the rule about Wiktionary means the answer is subject to change over time as new words are recognized and added. $\endgroup$ – Deusovi Jun 19 at 21:04
  • $\begingroup$ You are right @Deusovi, I tried changing the metric and changing the wikitionnary rule ^^' $\endgroup$ – JKHA Jun 19 at 21:21
  • $\begingroup$ Do you intend for it to be $n_i(w) +$ is_prime(w) or do you really intend for it to be $n_i(w) \times$ is_prime(w)? $\endgroup$ – Adam Jun 19 at 21:28
  • $\begingroup$ @Adam, I don't know which would be best. Second would surely make the puzzle a search of primary numbers, and indivisibility won't be a good score anymore! I hesitate $\endgroup$ – JKHA Jun 19 at 21:37
  • $\begingroup$ I've finaly choosen a compromise between the two options $\endgroup$ – JKHA Jun 19 at 21:43
5
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What about

Floccinaucinihilipilification is a word $9(9+0)$ = $81$ https://en.wiktionary.org/wiki/floccinaucinihilipilification

For the secret word:

A secret word for indivisibilities is camphor.

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  • $\begingroup$ I had to change the formula ;p $\endgroup$ – JKHA Jun 19 at 21:05
  • $\begingroup$ @RShields, you both had the same idea at nearly the same instant, but who will find the second part first? :D $\endgroup$ – JKHA Jun 19 at 22:41
  • $\begingroup$ puzzling.stackexchange.com/questions/79198/… what a coincidence +1! $\endgroup$ – Omega Krypton Jun 20 at 16:52
  • $\begingroup$ Yeah, I've seen this word in many, many riddles. $\endgroup$ – Duck Jun 20 at 16:53
3
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A note:

indivisibilities is a valid word with score $7(7 + 0) = 49$.

Another note, since the formula was changed:

pneumonoultramicroscopicsilicovolcanoconiosis is a valid word with score $7(7 + 1) = 56$.
floccinaucinihilipilification is a valid word with score $9(9 + 0) = 81$. I stand corrected.

Another note: the formula got changed again.

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  • $\begingroup$ Welcome to Puzzling! that's a really nice answer providing a great score ;p Can you find better? I +1 you ;) $\endgroup$ – JKHA Jun 19 at 20:29
  • $\begingroup$ I got that before you @RShields. +1 $\endgroup$ – Duck Jun 19 at 21:03
  • $\begingroup$ I'm sorry, I had to change the formula again so the puzzle makes more sense $\endgroup$ – JKHA Jun 19 at 21:05
  • $\begingroup$ Timestamps say the posts were made within the same second @Duck $\endgroup$ – RShields Jun 19 at 21:05
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    $\begingroup$ Except for the fact that I put floccinaucinihilipilification in a comment even before the new formula came. @RShields $\endgroup$ – Duck Jun 19 at 21:06

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