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
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
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
If that's not enough, then get your friends to play Integermania!
First Four Evens
Largest Four Digits
First Four Composites
First Four Naturals
First Four Nonsquares
First Four Odds
First Four Primes
Mile and a Foot
Theorems & Conjectures