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Use $1, 3, 5, 7, 9$ in any order to make number $985$:

  1. You must use all $5$ digits $1, 3, 5, 7, 9$ exactly once. You can make multi-digit numbers out of the numbers, e.g. $13$ or $975$.

  2. $+, -, *, /, (), \text{^}, \text{and }!$ (factorial) are the only allowed functions. Example: factorial may be used more than once, e.g. $(3!)!=720$ is acceptable.

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  • $\begingroup$ Is the modulo function allowed? (It's used in an answer below) $\endgroup$ Mar 7, 2023 at 10:45
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    $\begingroup$ Since it never says it's disallowed we must assume it is allowed. I would not advise changing the puzzle after some one came up with a good answer just because it was not the intended one. $\endgroup$ Mar 7, 2023 at 19:49
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    $\begingroup$ @AndrewSavinykh "Since it never says it's disallowed we must assume it is allowed" I don't think that's valid reasoning - then clearly, the constant-985 function should also be allowed! To me, rule 5 seems like an explicit list of allowed functions. $\endgroup$
    – ManfP
    Mar 8, 2023 at 11:34

4 Answers 4

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A small modification to the program from this answer of mine yielded this:

$$985=(3!)!+\frac{7!-5}{19}$$

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  • $\begingroup$ Excellent, great finding! $\endgroup$
    – ThomasL
    Mar 7, 2023 at 19:54
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Below equation should give desired result:

$$\mod(5, 3!) * 197 = 5 * 197 = 985$$

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  • $\begingroup$ +1 for this solution as well! $\endgroup$
    – ThomasL
    Mar 7, 2023 at 20:39
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Slightly cheeky:

$-5-\dfrac{(-9)!}{(1-3!-7)!}$

"Justification"

$\displaystyle\lim_{x\to-n} \frac{\Gamma(x+1)}{\Gamma(x)} = -n$

The same method allows for a variation of @Aman's answer

$-197 \times (-5)! / (-(3!))!$

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A cheeky, but ingenious way:

We do $7+1$ to make $8$ and then use $9$, $8$ (The number from the previous equation) and $5$ to make $985$.
Here's the cheeky part: We use the last digit ($3$) by doing $x = 3$. Then we can do $985 + (x - x)$ to get $985$.
$x = 3$ isn't a function!

Full equation ($answer$ means answer):

$$answer = (985) + (x - x), x = 3, 1 + 7 = 8$$

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  • $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Mar 10, 2023 at 17:27
  • $\begingroup$ @Community It's so clear lol $\endgroup$ Mar 10, 2023 at 17:28

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