asnaseer
Puzzle time: You are allowed to use any number of mathematical operators or functions (e.g. +, -, *, /, sin, cos, tan, factorial, sqrt, etc) but only two constants both of which must be the number 2.
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asnaseer
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Use these rules to produce the number 5.
karatechopper
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what r sin cos tan and factorial?
asnaseer
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they are trigometry functions
asnaseer
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*trigonometry
karatechopper
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i dont knw em..
karatechopper
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do we need to know then for this?
asnaseer
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I know of two ways of solving this - one requires the use of trig functions but the other one does not...
karatechopper
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3+2
asnaseer
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you are not allowed to use the number 3. the only "number" you can use are 2 and 2 - i.e. two 2's
karatechopper
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o..
moneybird
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Can you use floor and ceiling functions?
asnaseer
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Unfortunately not...
karatechopper
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do u have to use both of the 2s?
asnaseer
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yes - the expression you end up with must have exactly two 2's within it
karatechopper
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ok
karatechopper
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haha thts what ijust typed in my calc
karatechopper
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but its not 5
asnaseer
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@moneybird - that works out to be 2 doesn't it?
moneybird
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i though it needs to be equal to 2 my bad
asnaseer
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:-)
karatechopper
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haha yea
karatechopper
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can there be more 2s?
asnaseer
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trying to use floor and ceiling functions was a clever thought though @moneybird
karatechopper
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what r floor and ceiling functions?
asnaseer
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floor(1.5678)=1
ceiling(1.5678)=2
asnaseer
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floor basically says "drop the decimal part"
asnaseer
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ceiling says "round down to integer"
asnaseer
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*up
karatechopper
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o
karatechopper
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can we more than just two 2s?
asnaseer
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nope
karatechopper
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hmm
asnaseer
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both answers that I have are /fairly/ simple - so no magical complicated functions are needed
karatechopper
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o..
karatechopper
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is one of them with no trignometric functions in it?
asnaseer
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correct
karatechopper
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ok..so it has like somple ones tht a third grader is familiar with?
asnaseer
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yup
karatechopper
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like +,-,/,*
asnaseer
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a bit more than just those...
karatechopper
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factorial and sqrt?
asnaseer
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it has sqrt and powers in it...
karatechopper
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o..
karatechopper
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if i use 2 as a power, does it still count as one of the 2s?
asnaseer
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yes
asnaseer
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but the purer answer uses only trig functions
karatechopper
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argh..
asnaseer
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who said this was going to be easy? ;-)
karatechopper
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not me!
asnaseer
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:-)
karatechopper
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hmmm i need clues...
asnaseer
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I gave you a clue already:
it has sqrt and powers in it...
karatechopper
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but u can have only two 2s! and if i say 2 to the power of 2 then my 2s r used!!!!
asnaseer
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correct - so think of other ways of using sqrt and powers - and remember "power" does not mean it has to be to the power to "2". as long as the only digits that appear in the answer are two 2's - then the solution is valid.
karatechopper
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so u mean they can be to the power of any number?
asnaseer
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if I say anymore I will give the answer away :-)
karatechopper
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hmmmmmmmm