i guess the article is currently being edited, but at the moment it isn't so clear what is common and what different between the two groups. i think it would b

i guess the article is currently being edited, but at the moment it isn't so clear what is common and what different between the two groups. i think it would be better if the motivation came earlier: solving a problem is sometimes harder than checking you have the right answer. for example, it is easy to check that you have the secret key to a code. you can decode a message and see the original text. but it is hard to find the key if you do not know it. so the problem of finding the key to a code is much harder than checking whether a key is correct. other problems can be easy to solve and to check. for example, adding 2 and 2 is both easy to solve and to check. this difference can be used to divide problems into two groups. these groups are called P and NP. it is easy to check the answers for problems in both groups, but only problems in group P are easy to solve. the problem of adding two numbers is in P, because it is easy to solve and to check. the problem finding a secret key to a code is in NP because is is easy to check but hard to solve. i know my writing isn't simple enough here, but an approach like the above makes it easier to understand the relationship between them. in particular, the commonality between the two groups is emphasised.