Most of these riddles seem to be about writing computer programs than about finding a solution with nothing but your brain (like #7). Others riddles seem to involve an impossible amount of work with pen and paper, but are actually not that much of it (like #2... fibonacci numbers become huge rather quickly). There are also a few which have a very easy solution which might not be that apparent (like #1).
I'm already proud of having found the way to solve #1 in 10 seconds (and performed it in a few minutes)
3*sum(1...(1000/3)) is the sum of all multiples of 3, 5*sum(1...(1000/5))is the sum of all multiples of 5. When adding them, we have the sum of all multiples of 3 or 5, but whose which are in both sums have been added up twice. These numbers are the multiples of 15 from 1 to 1000, so we have to deduct 15*sum(1...(1000/15)). This speeds up a lot by applying sum(1..n)= n*(n+1)/2. The result is 117835 if I'm not mistaken.