# How to use the numbers 3, 5, 6, and 7 to get 100? [closed]

Any mathematics symbols and processes to use the numbers 3, 5, 6, and 7 once each to get 100.

$\sqrt{7^6}-3^5$ ...need more characters

• Pretty! ...need more characters
– Bass
Feb 14 '18 at 19:18

$100=(57+3)/.6$ if decimal point is allowed.

With the numbers in order:

$\frac{(3!)! - 5!}{6 \mod 7}$

$76 - 3 + 5 = 100$ (octal numerals)
$S(3*5*7-6)$ (successor function)
$$-\frac{\log\left[\left(\log\underbrace{\sqrt{\sqrt{\cdots\sqrt6}}}_{100}\right) / \log(3!)\right]}{\log{(7-5)}}$$ (generic method for obtaining any positive integer with 3,5,6 and 7, layout borrowed from ffao)

$(3 + 7) ^ {\left\lceil \frac{6}{5} \right\rceil}$

• no way, thought about getting 2 out of 6 and 5 forever, never thought of that Feb 14 '18 at 20:30

If the "floor" function is acceptable:

$\left\lfloor 3\times5\times6.7 \right\rfloor$

$7!!-5×6/3!$ using double factorial

35+67-2 $%The question doesn't say we can't use other digits$

• Where did the 2 come from?
– Catija
Feb 14 '18 at 21:57
• @Catija It's a "loophole" answer: the question doesn't say only those numbers. Feb 14 '18 at 22:07

${{6}\choose{3}} * 5 + \dot{7}$

• Could you explain a bit more what each step here means? I get that C(6,3) is combinations, but what's the apostrophe supposed to be? Is it a derivative? Feb 14 '18 at 22:03
• Yeah, that's it... Derivation of constant trick Feb 14 '18 at 22:11
• I've updated it to use MathJax, if that's alright with you. Feb 14 '18 at 22:23

$$\left \lceil 357 * \sin(-6) \right \rceil = 100$$