# Use numbers 1-9 to yield 300000

Inspired by @Saiid's earlier question.

Using $+,-,×,÷,$ exponents and factorials, use all the numbers $1-9$ (once and only once each) to generate $300 000$.
Don't compose numbers from their digits, just operate on them.

Bonus points for keeping digits in order.
Bonus points for using all operators.

Will accept answer that I find most interesting after 24 hours.

• All numbers only once?
– Sid
Oct 4, 2016 at 17:02

I'm just a guest for now but felt like showing my answer with all bonuses.

$(1+2)((3!+4)^{\frac{5}{(6-7)(8-9)}})$
$3×10^{5/1}$
$3$e$5$
$300000$

• Gorgeous simplicity; well done! Oct 7, 2016 at 5:30

Time to get 300,000, now that the body matches the title. I tried to get something fancy like my original 30,000 answer but gave up after a while:

$(3×(4+6)^5 + 7 + 9 - (8×2))/1!$

It ticks all the boxes, but in a pretty soulless way I'll admit.

BONUS: My previous answer to get 30,000

Here goes:

$(((9^5) + (3^6) + (8×7×4)) / 2) - 1 = 30000$

(I can't kill spoilers on more than the first line for some reason so I edited to omit the breakdown)

EDIT: Thanks to Jonathan for teaching me how to spoiler better so I could put in the breakdown

$((59049 + 729 + 224)/2) - 1$
$(60002/2) -1$
$30001 -1$

• I just noticed you can make this use all operators very easily using the fact that $1!=1$ (or even $2!=2$). Oct 4, 2016 at 17:37
• Oh, and for multiline spoilers end your lines with two spaces. Oct 4, 2016 at 17:49
• @Jonathan Allan, the degenerate cases of ÷1, ×1, 1! and 2! I deem less interesting ;)
– Ax.
Oct 4, 2016 at 18:31

$300,000$ is such a

nice round number in decimal that this is particularly easy to do with $1-9$ in order:
$(1+2+3+4)^5\times(6(7-8)+9)$

$300,000$ can be reached using

two powers, and with digits in order, by $\dfrac{1(2^3)4(5^6)}{7+8}\times 9$

• Second runner up for being so darn cute.
– Ax.
Oct 6, 2016 at 20:14

Transforming my 30,000 answer for 300,000 that also uses all operators:

$(6!+(7+8)\times(\frac93-1))\times (4\times 5)^2$

$=((6\times 5\times 4\times 3\times 2)+15\times 2)\times 20^2$
$=(720+30)\times 400$
$=750\times 400$
$=300000$

Here is an answer (to the original 30,000) using all operators:

$(6!+\frac{8\times 4 + 7 - 9}{1})\times 2^3\times 5$

$=((6\times 5\times 4\times 3\times 2)+\frac{32 + 7 - 9}{1})\times 8\times 5$
$=(720+30)\times 40$
$=750\times 40$
$=30000$

• First runner up for having the largest n!
– Ax.
Oct 6, 2016 at 20:12

Here goes:

This is the answer to number 30000

$((8+2)^4)\times3+(9+5)-(1+6+7)$

After op has changed their number to 300000

$((9+1)^5)\times3+(4-\frac{6}{2})-(8-7)!$

Motive:

$(100000\times3)+1-1$

In case anyone's still interested in the earlier target of $30,000$, I found an expression that seems more interesting than mine for $300,000$.

$30000=3\times 10^4=3\times (2\times 5)^4=5^4\times (2^4\times 3)=625\times 48$ so

$30000=1(2+3)^4(5(6+7)-8-9)$

My original solution when forming the question:

$9!+((1+6^2)-3×7×8)×4×5!$

Which I thought a bit cute.

$(1^2)+(3*4^5)-6-7-8-9-1-2-3-4-5-6-7-8-9+(1*2)$