This was inspired by many puzzles that use three/four numbers to create other numbers. I chose these numbers in particular because of this post.
Can you find a way to make all the natural numbers from $1$ to $15$ with all four of just following numbers?
$3,9,9,9$
You are allowed to use any operation only the following operations, but can jumble up the order and even turn $9$s upside-down to make a $6$ (though that will be replacing a $9$). You can also use an operation more than once if you like.
$+\;\;\times\;\;\div\;\;-\;\;\sqrt{\cdot}\;\;0.\;\;\lfloor\rceil\;\;!\;\;\$\;\;\%\;\;(\,)\;\;\hat\,$
Be as creative as you want. Why limit the mind? And $\$$ does not necessarily mean dollars...
You can include zeroes for decimals if you want, because really, $1=01$ and $2=0002$ so I see no difference.
Challenge Solution:
I am interested to see all the solutions, especially those containing only the mainstream operations and/or one radical and/or floor/ceiling functions. In that particular case, I myself have discovered a few solutions from $1$ to $5$ which means... well... I genuinely don't know if there exist these particular types of solutions for greater numbers.
Accepting an Answer:
The answer will be accepted to the person who finds challenge solutions from $1$ to $15$, and no, the first one won't be accepted... unless it is the most creative answer, because I will accept an answer if it has found all these challenge solutions and is the most creative (partly based on upvotes so the decision of accepting a certain answer is not too subjective).
As for solely creativity, a $50$ rep bounty will be awarded to the answer that has the most creative solutions (that might be the accepted, as well).
No answer must have just one solution, especially partial answers. There must be more than one solution in the posted answer before any further progress is made. This rule just gives others time to come up with solutions themselves without being tempted to look at an answer!
Enjoy!
$$$$
P.S. If you like mathematical challenges, go here!
Answer
1
$\frac{3}{\sqrt{9}!+\sqrt{9}!-9}$
2
$\frac{3!*9}{\sqrt{9}^{\sqrt{9}}}$
3
$\frac{3}{\frac{9!}{9!}^{9!}}$
4
$\frac{3*9-\sqrt{9}}{\sqrt{9}!}$
5
$\frac{3*9+\sqrt{9}}{\sqrt{9}!}$
6
$\frac{3!}{\frac{9!}{9!}^{9!}}$
7
$\frac{3*9-\sqrt{9}!}{\sqrt{9}}$
8
$\frac{3!*9-\sqrt{9}!}{\sqrt{9}!}$
9
$3*9-\sqrt{9}*\sqrt{9}!$
10
$\frac{3!}{\sqrt{9}+\sqrt{9}}+9$
11
$\frac{3*9+\sqrt{9}!}{\sqrt{9}}$
12
$\frac{3!*9}{\sqrt{9}}-\sqrt{9}!$
13
$\frac{3!}{\sqrt{9}!}+\sqrt{9}+9$
14
$\frac{3!}{\sqrt{9}}+\sqrt{9}+9$
15
$\frac{3!*9}{\sqrt{9}}-\sqrt{9}$
Bonus:
16
$\frac{3!*9-\sqrt{9}!}{\sqrt{9}}$
17
$\frac{3!*9-\sqrt{9}}{\sqrt{9}}$
18
$3!*9^{\sqrt{9}/\sqrt{9}!}$
19
$\frac{3!*9+\sqrt{9}}{\sqrt{9}}$
20
$\frac{3!*9+\sqrt{9}!}{\sqrt{9}}$
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