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asnaseer
 4 years ago
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
 4 years ago
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.

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FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4Can we use decimal point?

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0yes  looks like you may have found one of the solutions (I know 2 ways of doing this) :)

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4Well, don't you know I am the smart one? :P :D

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4Anyways, I won't spoil the problem for others, but here is something related http://en.wikipedia.org/wiki/2_%2B_2_%3D_5

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0Wow  I guess you really do learn something new everyday  I was not aware of this  thx

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0btw  there is a more /pure/ solution which does not involve using a decimal point

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4I suppose we can't use variable substitution too, isn't ?

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0what do you mean @FoolForMath?

Zed
 4 years ago
Best ResponseYou've already chosen the best response.1do the powers need to be 2 or anything?

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0remember the rules @Zed  you can ONLY have two constants in the resulting expressions and BOTH must be the digit '2'

Zed
 4 years ago
Best ResponseYou've already chosen the best response.1ahh i see, read the question wrong

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4Hm something like this: x=2; x^x + x^(xx) = 5 :D wait that's with only one 2 :D

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0no sorry @FoolForMath  that is not allowed.

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0CLUE: the /purer/ solution involves rightangled triangles

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4Hm then how about this one \( \csc^2(\cot^{1}(2)) \) , Checking: http://www.wolframalpha.com/input/?i=Csc%5BArcCot%5B2%5D%5D%5E2

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0thats the one!  well done @FoolForMath can the others find the other solution?

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4Thanks asnaseer :) Should I deleted it ?

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0that is how I wrote it to avoid the "1"

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0no need to delete your answer  lets see if anyone can find the other way of doing this

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0CLUE for other way: uses one decimal point, one squareroot and one power

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4The 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
 4 years ago
Best ResponseYou've already chosen the best response.0\(cosec^2(arccot(2))\)

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0I wrote arctan above which was wrong.

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4btw hey your earlier post is not correct 5 \( \neq \)cosec^2(arctan(2))

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4wait, arccot is defined in latex no ?

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4See: \[ \arccot \arctan \]

Zed
 4 years ago
Best ResponseYou've already chosen the best response.1okay i think this is right \[\sqrt{0.2^{2}}=5\]

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0yup  you got it @Zed  well done!

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4yep! you got that right :)

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0the only thing I don't like about this way is that sqrt(x) is really x^1/2

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0so it /feels/ like cheating  but nevertheless  well done @Zed

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4Hero wants hard, lets give him a bit harder :D I just found two other ways of getting the same result, could anybody wanna try ?

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4Guys 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
 4 years ago
Best ResponseYou've already chosen the best response.0no  I was just waiting for @Hero to return to take up the challenge :)

FoolForMath
 4 years ago
Best ResponseYou've already chosen the best response.4lol :D asnaseer, wanna try something from my sleeve ? ;)

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0gulp!  I know your reputation @FoolForMath  but lets for it  you gonna post to the left?

ixforrest
 4 years ago
Best ResponseYou've already chosen the best response.0ummm 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

ixforrest
 4 years ago
Best ResponseYou've already chosen the best response.0no need for big guns this was basic problem solving skills

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0you 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.

ixforrest
 4 years ago
Best ResponseYou've already chosen the best response.0eh 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
 4 years ago
Best ResponseYou've already chosen the best response.0:D  enjoy the coffee!
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