12

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.

Parcly Taxel
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ThomasL
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  • Is the modulo function allowed? (It's used in an answer below) – Matthieu M. Mar 07 '23 at 10:45
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    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. – Andrew Savinykh Mar 07 '23 at 19:49
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    @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. – ManfP Mar 08 '23 at 11:34

4 Answers4

25

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

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

Parcly Taxel
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10

Below equation should give desired result:

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

ACB
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Aman
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1

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

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

loopy walt
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-1

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):

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