Post me your hardest maths question you know

tntcoder said:
Does P=NP?

Sadly the answer isn't if N is 1 :p
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Surely, if by verifying a solution you know the solution is correct, You have already solved the problem and therefore verification doesnt do anything but prove that the solution was succesfull, Its like saying im making a cup of tea. After 2 minutes my tea is made so all ive done is verified that making a cup of tea takes 2 minutes and solved the problem. "How long does it take me to make a cup of tea under xy variables"

You cant verify anything that doesnt work. Like i cannot verify that the above answer is correct unless it is indeed correct

Therefore verification can infact take the same time as computing a solution!
 
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Angelos_n said:
Surely, if by verifying a solution you know the solution is correct, You have already solved the problem and therefore verification doesnt do anything but prove that the solution was succesfull, Its like saying im making a cup of tea. After 2 minutes my tea is made so all ive done is verified that making a cup of tea takes 2 minutes and solved the problem. "How long does it take me to make a cup of tea under xy variables"

You cant verify anything that doesnt work. Like i cannot verify that the above answer is correct unless it is indeed correct

Therefore verification can infact take the same time as computing a solution!
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Time to claim the £1 million up for grabs!

Consider this example as opposed to the cup of tea:

The most important sample problem set in P is "Is X the correct decryption key for this encrypted file?" Obviously, checking to see whether a key is correct for an encrypted file is a very straightforward process, otherwise we would be sitting around all day waiting for things to fully decrypt.

However, this has a corresponding problem in NP which is "Which of all the possible decryption keys for this encrypted file is the correct one?" In the same amount of time that a deterministic Turing machine takes to check one key, a nondeterministic Turing machine running the exact same algorithm could check every single key simultaneously and tell you the correct one.
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Proving that at a generic level for the whole P/NP sets is where it gets mind boggling.
 
How about this one -

You travel to america at 100km/h. You then travel back at a constant speed. The average speed for the entire journey is 50km/h. What was your speed in returning from america?

heh heh heh
arent i funny
 
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