I read quite a bit of books of that kind when I was young. I didn't read in English, but "One hundred thousand whys" - maths in Chinese was a great one, and this [1] in Vietnamese is a great one. They are all old books and some have solutions we can figure out by using a computer, but in general, they are really cool.

My personal favorite that has an English translation available, although it's not on Maths is "Physics for entertainment" by Perelman -- you can get it on Amazon right now. It was published 100+ years ago and problems are still relevant now. It discussed questions such as "When you jump out of a train, should you jump forward or backward?" "Who is wetter, a person standing in the rain or a person running in the rain?"

I guess basic maths and science hasn't changed that much, or maybe I was reading them when I was young, so I might not have known any better.

1: http://khoia0.com/PDF-Files/80-BAI-TOAN-THONG-MINH_handuc_v2...

I was linked to this blog from a post here the other day. It has a lot of these kinds of questions and the solutions. Here is the prisoners problem:

http://datagenetics.com/blog/december12014/index.html

And here is the dots problem:

http://datagenetics.com/blog/october22012/index.html