Mathematical Problems, Puzzles & Recreations

I have always had a keen interest in mathematics and problem solving. I love puzzles. Due to this interest I spent several years at university - both at University of Melbourne and La Trobe University in Victoria, Australia. During that time I learned and wrestled with a wide range of mathematical problems, puzzles and teasers. I have started this page with the first few of what I hope will be many mathematical problems and challenges over the next few years. Very few of these problems are original and have been doing the rounds for many years. I usually (but not always) like to find a new twist or generalisation to a given puzzle before taking the trouble to put it up. The problem is actually the other way around, there are literally hundreds of marvelous puzzles and problems that I have worked on over the years that are all written on various pieces of paper that I just don't have the the time to convert electronically and upload. Basically, I'm short of time, not material.

I always give credit where I can both for the problem and its solution. This is a pet peeve I have with the information boom and Internet explosion. I don't believe that enough diligence is being expended to credit originators for their work. I will always make an effort to find the origins of everything I put up on my website. If you know anything about the origins of any of my web content, please email me. I will then add your name to a list of contributers to my site.

I hope you enjoy some of my favourite puzzles and projects. I've had hours of fun with all of them.

Prime Numbers And Their Factorisation

  1. Cunningham Numbers (Factorisation of numbers of the form C±(b,n) = bn ± 1 for b=2, 3, 5, 6, 7, 10, 11, 12, up to high powers of n)
  2. The GIMPS Project (Great Internet Mersenne Prime Search)

Puzzles And Competitions Involving Computer Programming

  1. Knights On A 5x5 Chessboard
  2. The Nine Nine's Puzzle
  3. The Attacking Queens Puzzle Pack (My code and results from Al Zimmermann's Programming Contest - no HTML)
  4. The Triangles Puzzle Pack (My code and results from Al Zimmermann's Programming Contest - no HTML)
  5. The GIMPS Project (Great Internet Mersenne Prime Search)

Interesting Mathematical Puzzles

  1. Antipodal Points On The Sphere
  2. [sqrt(n) + sqrt(n+1)] = [sqrt(4n+2)]
  3. A Partitioning Of The Sphere