Open source game will be at https://sourceforge.net/projects/visualintfactor after I build a basic version, and hopefully if the discussions here lead to new ideas for how to interact with the available transforms on the hexagon grid (to factor or unfactor or move the 1 bits around randomly without solving), it will soon be in the next version... I know the math, but the game part of it is harder.
I'm looking for ideas how to make it more Human friendly, instead of looking like a bunch of hard work dragging around digits. I'd like it to become a massively multiplayer game where different places long possibly solving it fit together and players work together to combine and explore from these.
VisualIntFactor will be an interactive educational and scientific tool demonstrating multiply, factor, conversion between unary counting and binary integers, all in the same grid of hexagons. This grid is based on pascals triangle, which is a 1d cellular automata that calculates (X choose Y) factorials by each cell being the sum of the 2 cells upleft and upright. Draw a binary integer from a cell going upright, then explore the allowed transforms which may lead you to a factored state in 2 dimensions, from the lowest digit of the 2 odd integers both upright and upleft, its factors, and in the 2d space they are rectangle edges of, those pixels/digitbits must be on when there is an on bit somewhere downleft and downright after crossing empty cells, but if it finds either whole diagonal row empty then it must also be empty/zerodigit. The 2 main rules are: Any 2 cells below may both turn off and turn on the one above, or the reverse, and any on cell may move horizontally to an empty cell.
New discovery about integer factoring - play with it on screen
http://VisualInteger.com (version 0.2.0) is a puzzle view of binary integer factoring. Its opensource software (GNU GPL 2+), for those who want to experiment farther.
Its multiplied when all in 1 row or column.
Its factored when the same number or zero is in each row, and the same other number or zero is in each column.
A single operator acts on each cell on screen, swapping 2 below if they are opposites, else swapping 2 below with 1 heavier digit above.
This is an example of a "one way function" http://en.wikipedia.org/wiki/One-way_function something thats easy to do forward but hard to do backward. You can use the 2 buttons above "swap up (first found)" and "swap left (first found)" to change anything to multiplied form, but theres at least an exponential number of ways to get from there to factored, especially if it has many factors.
The default game board is 8x8 but has a variable to expand, to be used in later versions. The rectangle sizes are bigger to show which digits are bigger and smaller, and this will change when you move the mouse, in later versions.
This doesnt answer how hard it is to factor integers, but you can try out new algorithms visually or just play with it.
Unary counting is on the diagonals (swap left, swap right). Translation between unary and binary is done with swap up vs swap down. All those can be done by clicking, since its only possible do do 1 of those at a time, it automatically figures out which to do when you click.