Question

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.

Answer 1

Can we use decimal point?

Answer 2

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

Answer 3

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

Answer 4

of course I do :-)

Answer 5

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

Answer 6

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

Answer 7

You are welcome :)

Answer 8

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

Answer 9

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

Answer 10

what do you mean @FoolForMath?

Answer 11

do the powers need to be 2 or anything?

Answer 12

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

Answer 13

ahh i see, read the question wrong

Answer 14

Hm something like this:

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

Answer 15

no sorry @FoolForMath - that is not allowed.

Answer 16

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

Answer 17

Hm then how about this one \( \csc^2(\cot^{-1}(2)) \) ,

Checking: http://www.wolframalpha.com/input/?i=Csc%5BArcCot%5B2%5D%5D%5E2

Answer 18

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

Answer 19

Thanks asnaseer :) Should I deleted it ?

Answer 20

5=cosec^2(arctan(2))

Answer 21

Well done FoolForMath

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

I wrote arctan above which was wrong.

Answer 28

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

Answer 29

snap!

Answer 30

wait, arccot is defined in latex no ?