I am asking for a book/any other online which has the following quality:
The book, before introducing a particular topic (eg. Calculus/Topology) poses some questions which are answered by the topic (eg. Calculus allows you to study motions (eg. of celestial bodies) and blah blah) and encourages the reader to answer the questions by themselves, in their own unique way. The book thus, must be read in a very active way. The main attraction of the book is not the topic itself, but the deep and super exciting questions, which can spawn up new pathways, and often reaches to very deep stuff's exploration, by the reader, without any crutches.
0. Instead of book you can also mention any other source, be online or offline.
1. The closest book which almost fits to my criteria is Paul Lockhart's Measurement, and some questions are very deep (There was a question about proving which functions' integration is expression-able in closed form, just after introducing calculus!), and that book is excellent. I'm just asking for more book/online sources .
2. While there's nothing wrong with questions that require a bit of preknowledge, I prefer more deep questions that sounds elementary like: "Can you go through the seven bridges of Koingsberg and return to the starting place ?" (and then discover Graph Theory by your own !) or "Can you compute the area of the shape traced by two pencil and a string, exactly? Can you generalize it ?" (and then discover something similar to Diff Galois Theory or something new and unique by your own !) or "Can you find out how you can solve your Rubik's cube toy in minimal number of moves ? Can you generalize to other Erno Rubik products ?". Anyway feel free to mention books having both/any type of questions. But, The least the preknowledge required, the better.
3. I am not asking for a regular definition-problem textbook and/or a motivation book. See my and Thorsten S's second comment in the question for clarification
4. It's preferable that in the book the questions should be separate and/or presented in a non-spoilery manner, so that the reader can work on the questions without spoiling him with the answer. Also, it's preferable (as mentioned in #2) the question is simple to state, but is very deep. Though I am asking for books with question as the main feature, theory building questions (examples in 2) are more preferred than general puzzles (you can generalize any good puzzle to the point of a good theory, but you should understand which type questions I want) but feel free to add books of both/any type.
As per comments spawning from answers, This may be very very very slightly related. If you have a puzzle book in mind, which is vaguely fitting these criterion's, you can add it there.