Beginning with a small set A of required symbols (usually numbers), and a set of mathematical operations, can you create the entire set of positive integers?  Or how many different integers can you create?  Can you create all of the integers from 1 to 100?  Can you create exquisite solutions?

The basic rules for playing Integermania are as follows:

  • Every symbol in the original set must be used exactly once.
  • Numbers having more than one digit cannot be "split".
  • No other constants (real or imaginary) or variables can be used.
  • No user-defined functions can be used.  Only standard mathematical functions are allowed (although some are considered more exquisite than others).

Get your creations posted on this web site and become a certified integermaniac!  Use the online form accessible from each Integermania problem page.  Each solution will be assigned an exquisiteness level, so you may want to try for the best (lowest) level possible!

Integermania can be addictive, but we won't let you become obsessive.  This is a group project, and we desire lots of participation.  Therefore, the number of entries you may submit each month for each problem is limited.

  • For featured problems, you can submit five new or improved solutions each month.  A "new" solution is a solution for an integer not yet listed, at any exquisiteness level.  An "improved" solution is a solution for an integer already listed, but at a lower exquisiteness level than previously submitted (except that you cannot improve a solution in the same month it was originally submitted).
  • For semi-retired problems, you can submit any number of new or improved solutions. However, there are no guarantees on the speed at which they will be posted, or how long they might remain before being bumped by an improvement.
  • A featured problem will become semi-retired when four years have elapsed, or when the first unsolved integer is at least 100 beyond the fifth level 4.0+ (green or yellow) solution, where such solutions do not appear likely (at least in the opinion of the webmaster) to be further improved.

If that's not enough, then get your friends to play Integermania!

Featured Problems
Digits of Pi
Jonny's Birthday

Semi-Retired Problems
Dave's Birthday
First Four Composites
First Four Evens
First Four Naturals
First Four Nonsquares
First Four Odds
First Four Primes
Four Fours
Four Nines
Jan Hus
JCCC Letters
Largest Four Digits
Mile and a Foot
Quattro Ones
Ralph's Birthyear
Zip 66210

Related information
Certified Integermaniacs
Expert Tips
Theorems & Conjectures