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This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link.

In order to solve the alphametic, you'll first need to fill in the dividend, divisor, and quotient by solving the cryptic clues. I've left the enumerations off to provide a bit of extra challenge. Once you fill those in, the puzzle should be solvable with only arithmetic and logic. The solution is a 10-letter word or phrase found by ordering the letters from 0 through 9. A complete answer should provide this solution along with explanations of the cryptic clues and your path through the alphametic.

As always, I've created an interactive version that will autofill from the grid to the clues and vice versa. Have fun!

Clues:

  • Energetic measure of choral arrangement – "Total Eclipse of the Heart," that is
  • Whole note held by baritone section lasts for quite a while
  • Like one who obsesses over Ms. Del Rey
an image of the puzzle. see below for an accessible version

Accessible version:

       ????
    -------
???|???????
    CSNR
    ----
     NSER
     ILCR
     ----
      AOMI
      CSNR
      ----
       AAAE
       ARSC
       ----
        ONO
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  • $\begingroup$ What do you mean by "your path through the alphametic"? $\endgroup$ Commented 11 hours ago
  • $\begingroup$ @RyanM the logical steps you took to get to the solution $\endgroup$ Commented 10 hours ago

1 Answer 1

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The cryptic clues solve (with bolded definitions) as

Energetic measure of choral arrangement – "Total Eclipse of the Heart," that is = CALORIE = (C(-h)ORAL)* + IE [h deleted (eclipsed) as it is the centre (heart) of 'the']

Whole note held by baritone section lasts for quite a while = EON = (bariton)E + O + (sectio)N [the symbol for a whole note is a circle without a stem (thanks bobble!), hence the o]

Like one who obsesses over Ms. Del Rey = ANAL = (LANA)<-

Which word corresponds to which among the dividend, divisor, and quotient is obvious.

For the alphametic,

We see from the unit's place in the second step that R - R = M, so M = 0.

From the same place, we know that N*N = R, but also (from the unit's place of the first and third steps) N*A = R. This means that N can only be 2, 4, 5, 6, or 8. [This is also why the third cryptic clue could not have solved to LANA = (ANAL)<-, as then the unit's place of the second and fourth steps would both be N*A but result in different digits R and C respectively.]

N cannot be 5 or 6, because then R will be the same digit.

If N is 8, R is 4, and A is 3. But then the last step reads 333E - 34SC = ONO (a positive number), which is impossible, so N can't be 8.

If N is 4, R is 6, and A is 9. We now have in the last step EO4*L = 96SC. But in the third step, EO4*9 = CS46, where C must be less than 9; no L can satisfy its equation. So, N can't be 4.

Therefore, N = 2, R = 4, and A = 7.

From here, basic arithmetic gets the job done.

In the hundred's place of the last step, 7 - 4 = O, so O must be 2 or 3. With 2 taken, O = 3. In the unit's place of the first step, 3 - 4 = E, so E = 9. With our divisor fully known, we can just multiply it by the known digits of the quotient to get the remaining letters, C = 6, S = 5, I = 1, and L = 8.

The equation thus is (932 * 7278) + 323 = 6783419.

Finally, putting together all the letters in the order of their corresponding numbers,

we get MINOR SCALE, alluded to by the title for its use in music for evoking sadness or melancholy.

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  • $\begingroup$ For "whole note", reveal spoiler a whole note is shaped like an O -- just a circle/oval without a stem $\endgroup$ Commented 9 hours ago
  • $\begingroup$ @bobble Thank you, it didn't occur to me to parse the phrase as one thing. $\endgroup$ Commented 9 hours ago

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