asnaseer
  • asnaseer
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Can we use decimal point?
asnaseer
  • asnaseer
yes - looks like you may have found one of the solutions (I know 2 ways of doing this) :-)
anonymous
  • anonymous
Well, don't you know I am the smart one? :P :D

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More answers

asnaseer
  • asnaseer
of course I do :-)
anonymous
  • 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
  • asnaseer
Wow - I guess you really do learn something new everyday - I was not aware of this - thx
anonymous
  • anonymous
You are welcome :)
asnaseer
  • asnaseer
btw - there is a more /pure/ solution which does not involve using a decimal point
anonymous
  • anonymous
I suppose we can't use variable substitution too, isn't ?
asnaseer
  • asnaseer
what do you mean @FoolForMath?
anonymous
  • anonymous
do the powers need to be 2 or anything?
asnaseer
  • asnaseer
remember the rules @Zed - you can ONLY have two constants in the resulting expressions and BOTH must be the digit '2'
anonymous
  • anonymous
ahh i see, read the question wrong
anonymous
  • anonymous
Hm something like this: x=2; x^x + x^(x-x) = 5 :D wait that's with only one 2 :D
asnaseer
  • asnaseer
no sorry @FoolForMath - that is not allowed.
asnaseer
  • asnaseer
CLUE: the /purer/ solution involves right-angled triangles
anonymous
  • 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
  • asnaseer
thats the one! - well done @FoolForMath can the others find the other solution?
anonymous
  • anonymous
Thanks asnaseer :) Should I deleted it ?
asnaseer
  • asnaseer
5=cosec^2(arctan(2))
anonymous
  • anonymous
Well done FoolForMath
asnaseer
  • asnaseer
that is how I wrote it to avoid the "-1"
asnaseer
  • asnaseer
|dw:1325595329168:dw|
asnaseer
  • asnaseer
no need to delete your answer - lets see if anyone can find the other way of doing this
asnaseer
  • asnaseer
CLUE for other way: uses one decimal point, one squareroot and one power
anonymous
  • 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
  • asnaseer
\(cosec^2(arccot(2))\)
asnaseer
  • asnaseer
I wrote arctan above which was wrong.
anonymous
  • anonymous
btw hey your earlier post is not correct 5 \( \neq \)cosec^2(arctan(2))
asnaseer
  • asnaseer
snap!
anonymous
  • anonymous
wait, arccot is defined in latex no ?
anonymous
  • anonymous
See: \[ \arccot \arctan \]
asnaseer
  • asnaseer
hmmm...
anonymous
  • anonymous
okay i think this is right \[\sqrt{0.2^{-2}}=5\]
asnaseer
  • asnaseer
yup - you got it @Zed - well done!
anonymous
  • anonymous
yep! you got that right :)
anonymous
  • anonymous
Yay! That was tricky :)
asnaseer
  • asnaseer
the only thing I don't like about this way is that sqrt(x) is really x^-1/2
anonymous
  • anonymous
yeah i agree
asnaseer
  • asnaseer
so it /feels/ like cheating - but nevertheless - well done @Zed
anonymous
  • 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
  • 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
  • asnaseer
no - I was just waiting for @Hero to return to take up the challenge :-)
anonymous
  • anonymous
lol :D asnaseer, wanna try something from my sleeve ? ;)
asnaseer
  • asnaseer
gulp! - I know your reputation @FoolForMath - but lets for it - you gonna post to the left?
asnaseer
  • asnaseer
*lets GO for it
anonymous
  • anonymous
yeah sure :D
anonymous
  • 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
  • anonymous
no need for big guns this was basic problem solving skills
asnaseer
  • 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
  • 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
  • asnaseer
:-D - enjoy the coffee!
anonymous
  • anonymous
always!

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