Reposting puzzle since no one has solved it yet:
You are allowed to use any number of mathematical operators or functions (e.g. +, -, *, /, sin, cos, tan, factorial, sqrt, powers, etc) EXCEPT floor and ceiling functions. The only constants that can appear in the solution are two digits - both of which must be '2'.
Use these rules to make the number 5.

- asnaseer

- chestercat

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- anonymous

Can we use decimal point?

- asnaseer

yes - looks like you may have found one of the solutions (I know 2 ways of doing this) :-)

- anonymous

Well, don't you know I am the smart one? :P :D

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## More answers

- asnaseer

of course I do :-)

- anonymous

Anyways, I won't spoil the problem for others, but here is something related http://en.wikipedia.org/wiki/2_%2B_2_%3D_5

- asnaseer

Wow - I guess you really do learn something new everyday - I was not aware of this - thx

- anonymous

You are welcome :)

- asnaseer

btw - there is a more /pure/ solution which does not involve using a decimal point

- anonymous

I suppose we can't use variable substitution too, isn't ?

- asnaseer

what do you mean @FoolForMath?

- anonymous

do the powers need to be 2 or anything?

- asnaseer

remember the rules @Zed - you can ONLY have two constants in the resulting expressions and BOTH must be the digit '2'

- anonymous

ahh i see, read the question wrong

- anonymous

Hm something like this:
x=2;
x^x + x^(x-x) = 5 :D wait that's with only one 2 :D

- asnaseer

no sorry @FoolForMath - that is not allowed.

- asnaseer

CLUE: the /purer/ solution involves right-angled triangles

- anonymous

Hm then how about this one \( \csc^2(\cot^{-1}(2)) \) ,
Checking: http://www.wolframalpha.com/input/?i=Csc%5BArcCot%5B2%5D%5D%5E2

- asnaseer

thats the one! - well done @FoolForMath
can the others find the other solution?

- anonymous

Thanks asnaseer :) Should I deleted it ?

- asnaseer

5=cosec^2(arctan(2))

- anonymous

Well done FoolForMath

- asnaseer

that is how I wrote it to avoid the "-1"

- asnaseer

|dw:1325595329168:dw|

- asnaseer

no need to delete your answer - lets see if anyone can find the other way of doing this

- asnaseer

CLUE for other way: uses one decimal point, one squareroot and one power

- anonymous

The other one is a bit hard in my opinion, I have seen this problem before sooo ;) anyways, the latex version of my solution \( \csc^2(\arccot(2)) \)

- asnaseer

\(cosec^2(arccot(2))\)

- asnaseer

I wrote arctan above which was wrong.

- anonymous

btw hey your earlier post is not correct 5 \( \neq \)cosec^2(arctan(2))

- asnaseer

snap!

- anonymous

wait, arccot is defined in latex no ?

- anonymous

See: \[ \arccot \arctan \]

- asnaseer

hmmm...

- anonymous

okay i think this is right
\[\sqrt{0.2^{-2}}=5\]

- asnaseer

yup - you got it @Zed - well done!

- anonymous

yep! you got that right :)

- anonymous

Yay! That was tricky :)

- asnaseer

the only thing I don't like about this way is that sqrt(x) is really x^-1/2

- anonymous

yeah i agree

- asnaseer

so it /feels/ like cheating - but nevertheless - well done @Zed

- anonymous

Hero wants hard, lets give him a bit harder :D I just found two other ways of getting the same result, could anybody wanna try ?

- anonymous

Guys if you are trying, then please note it is not a good one and the second is ugly lol, and there is not much of useful maths we can learn from those two.

- asnaseer

no - I was just waiting for @Hero to return to take up the challenge :-)

- anonymous

lol :D asnaseer, wanna try something from my sleeve ? ;)

- asnaseer

gulp! - I know your reputation @FoolForMath - but lets for it - you gonna post to the left?

- asnaseer

*lets GO for it

- anonymous

yeah sure :D

- anonymous

ummm this is kind o really easy.. at first I thought it was hard but i realized i was thinking too much....
2^2 +2^3 = (12)^2 = 144 /2 = 72 /2 =36 /2 =18/2 =9 √9 = 3+2 = 5

- anonymous

no need for big guns this was basic problem solving skills

- asnaseer

you didn't read the rules properly - the ONLY constants allowed are two digits - both of which must be the digit 2.
e.g. 2^2+2^3 uses three 2's and a 3 - breaking the rules.

- anonymous

eh it was one of three or four answers ive got more. threre is also something interesting that happens between radians, but let me guess the implied conversion of a radian as 180 counts as a number other than 2 ? I still dont believe this requires higher level math I will stab at this later for now I have a date w/ Mathematica 8 and a vat of coffee. Thanks for clarifying !

- asnaseer

:-D - enjoy the coffee!

- anonymous

always!

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