3
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You start with a mystery number from 1 to 100000.

Add the number of United States,
Divide by a quarter incense by sounding it out,
Subtract the month of Hallowe'en,
Take the square root of your number,
Subtract this number from the beads on a mala (or the number of feelings a person can have),
Subtract the alive fruit punch,
Take the square root again,
Divide by the least lucky number in Asia,
Multiply this number by the height of Mount Everest in metres,
Figure what Zaccheaus would have paid back if he'd taken that much from you,
And finally, subtract by the square of the second perfect number.

Every step along the way is a positive integer. What is the mystery number, and what is the final result of this calculation?

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  • 1
    $\begingroup$ There seem to be multiple answers. What is the role of the last two steps? Multiplying by the height of Mt.Evt in m and the subtraction afterwards don't affect the positive integrity of any number. $\endgroup$ – Aravind Apr 11 '15 at 9:00
  • $\begingroup$ If I start with 21 and add 50, then divide by anything that isn't 1, I don't get a positive integer because 71 is prime. $\endgroup$ – Ian MacDonald Apr 11 '15 at 13:48
  • $\begingroup$ @IanMacDonald: That just means the starting number isn't 21, doesn't it? $\endgroup$ – Joe Z. Apr 11 '15 at 16:24
  • $\begingroup$ Oh, you meant that the number is chosen for us, not that we choose a number. That wasn't clear to me. $\endgroup$ – Ian MacDonald Apr 12 '15 at 1:52
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The final answer that I got is:

70016

The number obtained after step 4 is one of:

$\{3,22,39,54\}$. Let $y$ be the number obtained after step 4. Then $y \leq 67$ because if $x$ is the mystery number, then $y=\sqrt{\frac{x-200}{25}}$. Since the number of beads is 108 and Five Alive is a fruit punch, we have $z=\sqrt{103-y}$, the number obtained as the second square root. For this to be a positive integer, $y$ must be in $\{3,22,39,54\}$ - this corresponds to $z \in \{10,9,8,7\}$. Also note that given such $y$, we can obtain $x$ without any restriction.

After the additional information, we get:

$z$ is divisible by 4, so $z$ is 8; after doing the extra steps, we get $8850 \times 8-784=70016$.

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  • $\begingroup$ I've edited the question to include two new statements that should narrow the number of solutions down to one. $\endgroup$ – Joe Z. Apr 11 '15 at 16:24
  • $\begingroup$ I've edited the answer considering the new information. $\endgroup$ – Aravind Apr 11 '15 at 17:33
  • $\begingroup$ I meant for the answer to be 70,000 exactly because the height of Mount Everest was supposed to be 8848 metres, but I guess it changed... $\endgroup$ – Joe Z. Apr 11 '15 at 17:54

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