This is one of the most awesome questions ever, because it offers us an amazing book even while asking for another. Like so:
My daughter is seven and a fairly strong reader for her age. Last week she found this book at the library and loved it. Today she asked me if we could find "more books like this."
By "like this," she she meant the form of the book rather than the subject matter. Check out the "see inside" pages on Amazon — each section gives you a set of unusual medical cures and wants you to guess which ones work.
Books she has liked reading on her own in the past few months are Babymouse (many times over), Magic Treehouse books (though not so much lately), and Nate the Great (which she just found at her summer day camp and picked up on her own). Books she's enjoyed hearing aloud lately: Tumtum and Nutmeg, Abel's Island, Charlie and the Chocolate Factory.
So … suggestions for books that contain quizzes or guessing games, ask questions, or otherwise ask the reader to solve a problem? The subject matter could be just about anything.
So if you do go check out the book, you will see that it is awesome. One, it is interesting. Two, it is gross. What could be better?
In my experience kids love books that ask them to participate in some way. There's You Be the Jury, which I think she would love. It asks kids to predict the verdicts (power!). But the best books of all in this line, to my way of thinking, are those tried-and-true old school classics. Yes, ladies and gentlemen, it's time to pay homage to one of the great ones:
Image courtesy libn.com
I am sure you are all aware that the author of this series, the great Donald Sobol, died recently, and it called attention to these rightly venerated books. Because they are AWESOME. The girl is the muscle! Encyclopedia always gets the bad guy! You can reread them over and over with no ill effect!
I know that this parent has probably already thought of these, but I still had to throw it out there. And now it's time for the rest of you to weigh in: books with questions? What do you got?
marcialerner.com 
The Mysterious Benedict Society books? We loved those.
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We just got out of the library Still More Stories to Solve:
http://www.amazon.com/Still-Stories-Solve-George-Shannon/dp/0688147437/ref=sr_1_4?ie=UTF8&qid=1343960129&sr=8-4&keywords=stories+to+solve
I haven’t seen the others in the series, but assume that they are equally as much fun. It’s a similar format to Encyclopedia Brown, but with classic logic puzzles embedded in folk tales, and my 7-year-old is enjoying it quite a bit!
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My elementary students seem obsessed with the Who Would Win? books. You can see them at this link:
http://www.amazon.com/Collection-Hammerhead-Grizzly-Tyrannosaurus-Velociraptor/dp/B005LICIO2/ref=sr_1_4?ie=UTF8&qid=1343962693&sr=8-4&keywords=who+would+win
There’s a whole series, and each does head to head match-ups of similar animals in different situations. So, who would win, a grizzly bear or a polar bear? On the ice? In a forest? etc. It has that mix of asking questions and then delivering the facts.
And a similar picture fiction book, very silly: Shark vs. Train.
http://www.amazon.com/Shark-vs-Train-Chris-Barton/dp/0316007625/ref=sr_1_1?s=books&ie=UTF8&qid=1343962892&sr=1-1&keywords=shark+vs+train
Same idea, but between a shark and a train. Pretty funny!
Another series my students love is Scholastic True or False (the link is to Pets, but there are a bunch of topics):
http://www.amazon.com/Scholastic-True-False-Melvin-Berger/dp/0545003962/ref=sr_1_7?s=books&ie=UTF8&qid=1343963267&sr=1-7&keywords=scholastic+true+or+false
This series proposes a fact (eg, True or false: all dogs have wet noses) and then you turn the page to see if it’s true or false and get more information.
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Who Will Win? That seems SO AMAZING. It’s like a book form of the superhero vs. superhero competition. I want to read it right now.
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re Shark vs. Train, mentioned above–my daughter is seven, and she and her classmates love that book.
Next–I want to mention a book that was a favorite of my sister and myself when we were in elementary school. I think we checked it out of the public library dozens of times.
It is Cross Your Fingers, Spit in Your Hat: Superstitions and Other Beliefs, collected by Alvin Schwartz. (listed as for ages 8 and up). Mr. Schwartz is the author of Scary Stories to Tell in the Dark and its sequels.
Cross Your Fingers doesn’t have questions and answers, but tells about all kinds of wonderful things including the evil eye, how to predict the weather, cures for common ailments, how to determine your lucky number, sure ways to pass a test in school (wearing your socks and underwear inside out is one way), and much more.
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I’m going to go way out there and suggest this book by Graeme Base: The 11th Hour. It is a mystery book. With clues on each page. Hard, hard clues. Very, very fun. Unfortunately I’ve only found one of its kind, but it is superfabulous. Also, the book the recomendee seems to be seeking reminds me of the Moongobble series, but I’m not quite sure why?
Finally we just took out two books by Lucinda Landon–the Meg MacIntosh mystery series. I can’t say whether they are super or not. We’ll read them this weekend.
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Cam Jansen mysteries are entertaining for a certain period of time. I don’t quite remember whether they specifically have a ‘you solve it’ aspect, but you can definitely read them that way — the solution to the mystery isn’t given until the very end and the clues are laid out clearly enough for young readers to test their mystery-solving prowess.
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When I went for overnights at my aunt’s house as a small person, she always left something like this on the bedside table:
http://www.amazon.com/Two-Minute-Mysteries-Apple-Paperbacks-Donald/dp/0590447874/ref=pd_sim_b_1
Again, similar to Encyclopedia Brown in that you, as the reader, have the clues to solve the puzzle.
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There are also “five minute mysteries” by various authors if she is not a Donald Sobol kind of gal.
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I don’t have a book recommendation this time around (although the recommendations look fabulous) but I did want to chime in for the “Who Would Win” folks that we are loving http://what-if.xkcd.com/ “What-if” your hypothetical questions answered by physics! Answering questions such as “How much Force power can Yoda output?” and “What would happen if you tried to hit a baseball pitched at 90% the speed of light?”
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