# A good book for short problems

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

• Awesome! simply awesome! +1 – Namaste May 2 '13 at 0:16
• @amWhy: Thanks! I have always wondered if the OP got anything out of it. – Amzoti May 2 '13 at 0:20
• It's a list worth bookmarking! (I wish we could favorite answers like we can for questions!) – Namaste May 2 '13 at 0:21
• That would be an excellent feature. I often have a difficult time (maybe I am awful at using the search) even finding old answers of mine because I want to reuse something from them. – Amzoti May 2 '13 at 0:31
• @Amzoti Very late, but yes I did. – MacropusRufus Jun 15 '13 at 10:30