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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:

Someone who is not telling the truth about a form of mass transit
Prospect for gold in American state
Condemn one not a part of religion

Accessible version:

         ????
     --------
????|????????
     PELPR
     -----
      RARIA
      RNARA
      -----
        SOIMA
        SEAPL
        -----
         PMAL
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  • $\begingroup$ Currently, I have that rot13(V rdhnyf mreb), rot13(gur ynfg sbhe qvtvgf bs gur qvivqraq ner ENZN), and rot13(N rdhnyf A cyhf bar). $\endgroup$
    – Someone
    Commented Jan 24 at 19:55

1 Answer 1

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Cryptic clues:

A good place to start is deducing from the unsolved alphametic that the letters used has to be the letters I,M,P,E,R,S,O,N,A,L…

Someone who is not telling the truth about a form of mass transit

LIAR(Someone who is not telling the truth) reversed(about)= RAIL (A form of mass transit)

Prospect for gold in American state

Or (Gold) in Panama (American ‘State’)= PANORAMA (Prospect) (We can deduce from the alphametic the last four letters of the word has to be ‘RAMA’)

Condemn one not a part of religion

Take (not part of) I (Roman numerals of one) from Islam = SLAM (Condemn)

A solution path for the alphametic:

We first need to decide whether PANORAMA is being divided by RAIL or SLAM. We can deduce PANORAMA is not being divided by RAIL because if it was divided by RAIL then A=0 because according to the alphametic now AxRAIL=0 but since I=0 too since PANOR-PELPR=RARI, A cannot equal 0.

SO PANORAMA IS BEING DIVIDED BY SLAM by reductio ad absurdum.

enter image description here

Right of the bat then know that RxSLAM=PELPR, AxSLAM=RNARA, LxSLAM=SEAPL and PANOR-PELPR=RARI, RARIA-RNARA=SOI, SOMIA-SEAPL=PMAL.

To reiterate because PANOR-PELPR=RARI, I=0.

Since LxSLAM=SEAPL therefore M=1.

Because of SOIMA-SEAPL=PMAL it means 2L=?A so we know A has to be even. Also because AxSLAM=RNARA, A^2=?R, A is now either 2, 4 or 8 and thus R is either 4, 6. But because we know that RARIA-RNARA=SOI therefore A=N+1 and so A>R meaning A=8, R=4, N=7.

Knowing that AxSLAM=RNARA and the values we have ascertained we get 8xSL81=47848 and so S=5, L=9.

Since LxSLAM=SEAPL, if we therefore input the values we have deduced we get 9x5981=53829 and we see P=2, E=3.

Since SOIMA-SEAPL=PMAL or 5?018-53829=2189, O=6.

The Completed Grid

enter image description here

enter image description here

The answer is:

IMPERSONAL!!

The Title:

Is a reference to GODFATHER I where Michael Corleone said “ITS NOT PERSONAL ITS STRICTLY BUSINESS”.

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  • 1
    $\begingroup$ hi PDT, not sure where you think I've made a mistake. I just double-checked my work and didn't find any errors, and you've also come to the correct answer. could you give me more specifics as to where and how you found a mistake? $\endgroup$
    – juicifer
    Commented Jan 24 at 20:26
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    $\begingroup$ in any case, I can't accept this answer as is, as you haven't actually solved the alphametic; rather, you've backdoored into the solution from the given letters and then provided a justification as to why the answer you've found matches it. I would need to see the logic used to work through the puzzle in order for this answer to be complete $\endgroup$
    – juicifer
    Commented Jan 24 at 20:27
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    $\begingroup$ neither of the things you've pointed out in your most recent edit are actually errors with the puzzle. for the first one, note that there is a remainder (PMAL) at the end of the division, so a decimal portion of the answer is expected when dividing the dividend by the divisor. as for the second, the subtraction of 0 from SOIM is implicit and is not usually written explicitly in long division (either standard or puzzle-y). as you note, the math does check out when multiplying the divisor by the fourth digit of the quotient $\endgroup$
    – juicifer
    Commented Jan 24 at 21:12

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