All Answers 358146 Answers

It wasn't that stupid - I can understand your annoyance.

You have presented some really clever answers there :)

You're right Melody, when I posted it I realized how stupid my remark was

I found a fourth way :

[(0! + 0!)^{(0! + 0!)} + 0!]!=(2²+1)!=(4+1)!=5!=120

But it seems to be impossible to do with only one symbol.

$${\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{4}}$$

omg, Dawn is here?

dang, now she's gonna cast some spells and have fun torturing people (that's how witches are at my school)

also, she's gonna be using her larry terms, not as annoying as number thingys, but still really annoying

"any one mathematical operator"     -      any one means ONLY one 

That is a quote from the question.  

It doesn't matter though - I liked your answer  :)

I like you second answer too.

I would like to see anon do it with ony one operator as well    LOL

He didn't say only one mathematical operator, so it means I can use two ones.

And, if you're so smart Anonymous, find a way you can do it using one mathematical operator.

Good luck !

I found two other ways (the second is a little bit tricky, since a 8 is formed by a 0 put atop another 0)

[(0!+0!)(0!+0!)+0!]!=[(1+1)(1+1)+1]!=(4+1)!=5!=120

$$({\sqrt{({\sqrt{{\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}}}){!}{\mathtt{\,\small\textbf+\,}}{\mathtt{0}}{!}}}){!}$$=$$({\sqrt{({\sqrt{{\mathtt{16}}}}){!}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}}}){!}$$=$$({\sqrt{{\mathtt{4}}{!}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}}}){!}$$=$$({\sqrt{{\mathtt{25}}}}){!}$$=5!=120

@@ End of Day Wrap   Wed 20/5/15   Sydney, Australia Time   12:30am  (Thurs really) ♪ ♫

Hi all, 

Great answers today from:  Alan, CPhill, Andrew1714, TheJamesMachine, Dbg4thebest, MathsGod1, DarkBlaze347, ShadowBolt04, Zacismyname, Heureka, GoldenLeaf, MathWitch and Badinage.  Thank you. 

Thurs 21/5/15

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

Interest Posts:

FTJ means 'For the juniors' 

It will calculate  10^308 but not 10^309.....strangely, though.....it will (seemingly) calculate.....

(10^308) (10^308) (10^308) (10^308) (10^308)......  

all day long......however it balks at (10^308)^2   (???)

Maybe one of our mods - Alan - can explain why this happens......he knows a lot about calculator operations

But, anyway.....it will probably handle most "normal" calculations just fine

Hi Nauseated,

Zac's hemisphere and my hemisphere had a bottom on it.

A hemisphere is a half of a sphere - if the sphere is solid then the hemisphere definitely has a base.

Our brains have ceribral hemispheres.  

Mine is full of grey matter.   Does yours is contains nothing?

$${\sqrt{{\frac{{\mathtt{25}}}{{\mathtt{100}}}}}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\mathtt{0.5}}$$

  The anser is 50.2 

It wasn't too much of a struggle.....but.......it does make me nervous when I get answers like 4.405....It defeats my "Nice Round Numbers"  theory........LOL!!!

We can find the answer just by getting the least common denominator between 12 and 20

12 = 2^2 x 3

20 = 2^2 x 5

And the LCD =  2^2 x 3 x 5 = 13 x 5 = 60 inches

So  60/12  = 5    and 60/20 = 3

When the length is 60 inches......3 of the 20 inch bocks will have been laid and 5 of the 12 inch blocks will have been laid.

the square root of 9 is 3, because 3x3 is 9. :)

Did you struggle with that one for as long as I did Chris?

I have done heaps of these but they turn into a saga EVERY time.    LOL

Oh well I got there in the end, CPhill and I did it a bit differently but we both got the same answer.

That is always a good sign   

2 taps A and B can fill a swimming pool in 3 hours. If turned on alone, it takes tap A 5 hours less than tap B to fill the same pool. How many hours does it take tap A to fill the pool?

A is the fast one:   let tap A take X hours to fill the pool

A fills 1 pool in X hours

that is 3 pools in 3X hours   OR      3/X pools in 3 hours

B fills 1 pool in X+5 hours

that is 3 pools in 3(X+5) hours    OR        3/(X+5) pools in 3 hours

So together in 3 hours they will fill

$$\frac{3}{X}+\frac{3}{X+5} \;\;pools\\\\
=\frac{3(X+5)+3X}{X(X+5)}\;\;pools\; in\; 3 \;hours\\\\
$But in 3 hours they fill 1 pool so $\\\\
\frac{3(X+5)+3X}{X(X+5)}=1\\\\
3(X+5)+3X=X(X+5)\\\\
3X+15+3X=X^2+5X\\\\
6X+15=X^2+5X\\\\
X^2+5X-6X-15=0\\\\
X^2-X-15=0\\\$$

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{15}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{{\mathtt{2}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{3.405\: \!124\: \!837\: \!953\: \!327\: \!2}}\\
{\mathtt{x}} = {\mathtt{4.405\: \!124\: \!837\: \!953\: \!327\: \!2}}\\
\end{array} \right\}$$

Obviously the negative answer is invalid  so X = 4.4051 hours to fill the pool

$${\mathtt{60}}{\mathtt{\,\times\,}}{\mathtt{0.405\: \!1}} = {\mathtt{24.306}}$$

So that is near enough to 4 hours and 24 minutes

A will take 4 hours and 24 minutes to fill the pool

and

B will take 9 hours and 24 minutes to fill the pool.

I dont wanna likes for increase score, just for look who likes music and for know if this report must continue.

1 PERSON ALLRIGHT FOR JOKES. ANYONE ELSE???

Congrats taylor!!!!!!!!!!

SPAG HEDDY sounds really well...

I WANT JOKES!! Who not?

im suscribed!!!!!!

Let x be the time (in hours) that B takes to fill the pool.....then( x - 5)  is the time it takes for A to fill the pool.

And every hour, B fills 1/x of the pool and A fills 1/(x -5) of the pool 

And we know that :

Rate per hour x time  = amount of job done....so.......

[(1/x) * 3]  + [1/(x -5) * 3]  = 1

3/x + 3/(x -5)  = 1

[ 3(x - 5) + 3(x)] = x(x - 5)

[6x - 15 ] = x^2 - 5x     simplify

x^2  - 11x + 15  = 0       and using the onsite solver, we have

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{11}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{15}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,-\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{1.594\: \!875\: \!162\: \!046\: \!672\: \!8}}\\
{\mathtt{x}} = {\mathtt{9.405\: \!124\: \!837\: \!953\: \!327\: \!2}}\\
\end{array} \right\}$$

Reject 1.59......so A takes about (x - 5)= (9.405 - 5) = 4.405 hours to fill the pool working alone

Check....  (3/9.405) + (3/4.405) ≈ 1

$${\sqrt{{\mathtt{9}}}} = {\mathtt{3}}$$

CONGRATS TAYLOR!!!!!!!!!!!

little triangles can mean a small change in something  

Or a little triangle is used for the discriminant in the quadratic formula

Or it may actually mean triangle   lol

5is the biggest number