What is a good book for problems which can be done without much mathematical background? I don't mean IMO-level, since those questions generally require a fairly big amount of mathematical knowledge, but more like questions along the line of the toughest questions on a kangaroo test, some examples:
We call a natural number a funny number if it is the smallest of all numbers that have the same sum of their digits. For example: 29 is funny, because it is the smallest number of which the sum of its digits is 11. We add up all funny three-digit numbers. What is the outcome?
Mister Small, Mister Medium and Mister Large are going for a walk. Mister Large says: “Funny, how our names are all about lengths, but each of us has a wrong name.” The smallest of the three answers: “Yes, that is true”. What are the names of the gentlemen from smallest to largest?
If you multiply 1, 2, 3, …..up to n (inclusive), the result is $2^{15} \times 3^6 \times 5^3 \times 7^2 \times 11 \times 13$. Which number is n?
So fun questions like these which aren't too long and can be purely done with a decent mathematical intuition.
You might want to peruse this list and see if anything catches your eye a,d it hopefully gives you some ideas on other things to look for.
Entertaining Math Puzzles, Martin Gardner
Mathematics, Magic and Mystery, Martin Gardner
The Colossal Book of Mathematics, Martin Gardner
The Last Recreations, Martin Gardner
More Perplexing Puzzles and Tantalizing Teasers, MARTIN AUTOR GARDNER
Classic Brainteasers, MARTIN AUTOR GARDNER
The Moscow Puzzles, Boris A. Kordemsky
Logic Puzs to Bend Yr Brain, Kurt Smith
More Mathematical Puzzles of Sam Loyd
Challenging Logic Puzzles, Barry R. Clarke
Second Scientific American Book of Mathematical Puzzles and Diversions
Hard-To-Solve Math Puzzles, Derrick Niederman
A Passion for Mathematics, Clifford A. Pickover
Problem Solving Through Recreational Mathematics, Bonnie Averbach and Orin Chein
The Ultimate Book of Puzzles, Mathematical Diversions, and Brainteasers, Erwin Brecher
25 Real Life Math Investigations That Will Astound Teachers and Students by Edward Zaccaro
50 Mathematical Puzzles and Problems Green Collection by Gilles Cohen (Editor)
50 Mathematical Puzzles and Problems Orange Collection by Gilles Cohen (Editor)
50 Mathematical Puzzles and Problems Red Collection by Gilles Cohen (Editor)
A Moscow Math Circle: Week-by-week Problem Sets by Sergey Dorichenko
Chinese Brain Twisters by Baifang
Challenging Critical Thinking Puzzles by Michael A. DiSpezio
Great Critical Thinking Puzzles, by Michael A. DiSpezio
Problem Solving Through Recreational Mathematics by Bonnie Averbach, Orin Chei
You might also like to explore Enjoying Math - Learning Problem Solving with Fun Math Puzzles
Regards