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I'm hoping this is a valid entry for the Monthly Topic Challenge #12 (mobile-friendly puzzles).

I went to the house of a retired math teacher, and he showed me the following setup. On a brown wooden table were five objects: two slightly used yellow birthday cake candles (one shaped like a 7, another shaped like a 5), several connected sheets of thick white toilet paper neatly folded, a dark brown tobacco pipe, and a hard, dry, round, brown thing that came from a plant (wrinkled like a walnut).

The pipe and the plant-thing were on the toilet paper; the candles were not. The pipe was the heaviest of the five objects; the toilet paper was the lightest. The house was small but was surrounded by a large area of land containing many plants. The windows were open. The teacher used to smoke but gave it up due to health reasons.

The teacher stated that the setup represented an arithmetic operation (addition, subtraction, multiplication, or division) on the two numbers (7 and 5). What was the arithmetic operation being represented?

Hint 1:

The numbers (7 and 5) are irrelevant; using other numbers won't change the answer to the puzzle.

Hint 2:

The colors (brown, yellow, white) are irrelevant; using other colors won't change the answer to the puzzle.

Hint 3:

The objects being used as weights so that the toilet paper won't get blown away (pipe, plant-thing) are irrelevant; using other objects won't change the answer to the puzzle.

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  • $\begingroup$ Could you add another hint? rot13(V fnj n jvxvcrqvn ragel bs cvcr flzobyf va znguf, cncre sbyqvat zvtug unir gb qb jvgu senpgvbaf) $\endgroup$
    – WOWOW
    Commented Jul 25, 2023 at 19:26
  • $\begingroup$ (I added a hint.) $\endgroup$
    – JRN
    Commented Jul 26, 2023 at 13:11
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    $\begingroup$ @JRN I see, that is an interesting take. A bit daring : ) but I appreciate you trying something unexpected and different. All the best, happy to see puzzles! $\endgroup$
    – Amoz
    Commented Jul 26, 2023 at 14:36
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    $\begingroup$ Thanks for sharing your philosophy on the setup in this puzzle, @JRN. Like Amoz, I got the eventual answer early, but thought there would be more to it. I think, at least in this case, it's rot13(n ovg hasnve: Vg'f abg n erny-jbeyq fvghngvba. Gur grnpure unf neenatrf gur frg-hc gb ercerfrag fbzrguvat yvxr n zngurzngvpny sbezhyn, naq lbh qba'g jevgr fdeg(|n·o|) jura lbh jnag gb pnyphyngr n·o naq fnl, bu, gur fhned ebbg naq nobyhgr inyhr vf whfg veeryrinag qrgnvy). On the other hand, iIf this were a crime scene ... $\endgroup$
    – M Oehm
    Commented Jul 26, 2023 at 16:09
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    $\begingroup$ Oh, I don't feel cheated, just surprised that there wasn't more to it, given all the décor. (So "unfair" was probably not the right choice of word.) $\endgroup$
    – M Oehm
    Commented Jul 26, 2023 at 16:32

2 Answers 2

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The operation is ...

... multiplication. The important item is the thick toilet paper, which probably has several layers. In other words, it is multi-ply toilet paper.

The factors are the two candles that are shaped like numbers, of course, but what are the other two objects, the pipe and the "plant thing" for? The pipe is heavy and could be used as paperweight for the toilet paper, because the windows are open.

I don't know what the "plant thing" is for or even what it is in the first place. My first thought was it could be a homophone of a preposition such as "by" or "with" so that the formula might read "7 multi-plied by/with 5". The various bay plants – yes, yes, I'm not buying it as homophone for "by", either – have fruits, but they are not hard and wrinkly like a walnut. So it's just a red herring, I guess. (OP has more or less confirmed this in comments.)

That exlpains ...

... why explicit multiplication signs are habitually left out of formulas. it's just to cumbersome to fold a piece of multi-ply tissue and put something heavy on it for each multiplication. :)

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  • $\begingroup$ Yes, the "other two objects" are red herrings. $\endgroup$
    – JRN
    Commented Jul 26, 2023 at 15:10
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Is the answer

division?

You can take some toilet paper,

7 sheets long, and fold it neatly in fifths, so it become five layers thick.
The new length of this thick stack is 1.4 sheets long, and you can see the perforation that marks the point that splits it into the integer part, 1, and the fractional part 0.4=2/5.
Are the pipe and plant-thing not only used to weigh the paper down, but also to mark the quotient and the remainder/fractional part? If so, is there some pun or homonym at work here that I'm not seeing? The description of the plant-thing makes me think of the stone of a peach, but I don't see the connection there.

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    $\begingroup$ Your answer is incorrect. Note that the numbers are arbitrary. For example, one number could be a multiple of the other. The tag is 'wordplay' so there is "some pun or homonym at work here." You are quite close to the correct answer in the sense that you have identified the important element (gur gbvyrg cncre). $\endgroup$
    – JRN
    Commented Jul 26, 2023 at 8:49
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    $\begingroup$ Nyfb, gur ahzore bs furrgf bs gbvyrg cncre cerfrag vf abg eryngrq gb gur bcrenaq ahzoref. $\endgroup$
    – JRN
    Commented Jul 26, 2023 at 8:52
  • $\begingroup$ V fnj n jvxvcrqvn ragel bs cvcr flzobyf va znguf, cncre sbyqvat zvtug unir gb qb jvgu senpgvbaf, is that useful? $\endgroup$
    – WOWOW
    Commented Jul 26, 2023 at 8:59
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    $\begingroup$ Well, the wordplay I can see is a certain property of the thick toilet paper. Ho, ho. The heavy pipe is just a paperweight. $\endgroup$
    – M Oehm
    Commented Jul 26, 2023 at 12:32
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    $\begingroup$ @JRN: Sorry, was busy getting soaked on my bike, so didn't read your,er, order. Will do it now. Apparently, I've missed a good deal of activity on this question in the meantime ... $\endgroup$
    – M Oehm
    Commented Jul 26, 2023 at 14:49

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