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


  • $\begingroup$ Awesome! simply awesome! +1 $\endgroup$ – Namaste May 2 '13 at 0:16
  • $\begingroup$ @amWhy: Thanks! I have always wondered if the OP got anything out of it. $\endgroup$ – Amzoti May 2 '13 at 0:20
  • $\begingroup$ It's a list worth bookmarking! (I wish we could favorite answers like we can for questions!) $\endgroup$ – Namaste May 2 '13 at 0:21
  • $\begingroup$ 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. $\endgroup$ – Amzoti May 2 '13 at 0:31
  • $\begingroup$ @Amzoti Very late, but yes I did. $\endgroup$ – MacropusRufus Jun 15 '13 at 10:30

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