The Reconstruction Theorem is an open problem in Mathematics from the field of Graph Theory. First a few basic definitions.
Graph: A set of points and lines connecting them.
Isomorphic: Two graphs are isomorphic is you can rearrange the points and lines so that they match up exactly, but you cannot disconnect any lines or add any lines.
These are all Isomorphic
The Reconstruction Theorem states that every graph up to isomorphism (with three or more verticies) has a unique deck of sub-graphs, each one being the same as the original graph except one vertex and all lines connected to it is deleted.
Now, that is a pretty abstract concept, and the theorem has never been proven, but no one has come up with a counter-example yet, which means you can use it to play a fun game (at least, I think it is fun). First you take a simple picture, which you turn into a graph. Then you break down that graph into its set of subgraphs, and really mix the subgraphs up, and then you give the subgraphs to a friend and see if they can reconstruct the original picture. Below is an example of such a process.
Original Graph
Deck of Subgraphs
Scrambled Subgraphs
As you can see, that last step adds a significant degree of difficulty to the process, I haven't even rearranged the order of the subgraphs, they correspond one to one with the unscrambled deck. Note that when trying to solve for the original graph, you do not just do these steps in reverse, first find some graph that could make all the subgraphs, and then you can poke and prod that thing into a coherent picture.
So anyways, the game is pretty simple, one person makes a deck, everyone else tries to figure out what the original graph is, it could be they can just say what it is (It is a stick guy), or maybe they could draw it themselves. I don't feel like there should be any restriction on when new decks can be posted, multiple problems could be open without previous ones needing to be solved, mostly due to the effort involved in making a deck. For similar reasons, the answer should probably sblocked. To get things started, here is a simple deck without a solution.
Deck 1
Good luck! I hope other people enjoying do this and I'm not just a crazed, lonely mathematician.
