This single-player game was proposed by Soviet matematician Grigory Tseytin, perhaps, in 1950s - as a "model for behavior of a scientist trying to solve some problem". Verily so - unlike solving tasks with supposedly known result, people of science deal with situations when result is not necessarily known beforehand and may happen to be different than expected. Classical example is Hertz study to prove non-existence of electromagnetic waves (which resulted in opposite).
While author studied behavior of real people with this game and even had written a program for DOS at some point, I'm not aware of attempts on mathematical analysis, proposed algorithm or anything alike. In this sense it is supposedly "an open problem" - whoever tries to solve it, becomes a scientist too, to some degree.
We have a hexagonal map in a shape of rhombus (same as used in game Hex). All cells are painted black or
white (or marked with Xs and Os in our case) - but this painting is not known to the player. So initial
state looks like this:
0 a
X-side 1 - b O-side
2 - - c
3 - - - d
4 - - - - e
5 - - - - - f
6 - - - - - - g
- - - - - - -
- - - - - -
- - - - -
- - - -
O-side - - - X-side
- -
-
note that we introduce coordinate system - lines going from bottom-left to upper-right are marked with letters and lines going from upper-left to bottom-right are marked with numbers.
Player on each turn opens one of the cells, to see what mark it has. The goal is to discover one of two paths:
XsOsEdges are inscribed with X-side and O-side to clarify this. Due to hexagonal geometry only one of these
paths exists. Below is example of the game won in 16 moves
(path of Xs found):
X
- X
X O -
- O X O
- O O O -
- - - X - -
- - - - O - -
- - - X - -
- - - O -
- - X -
- - X
- -
-
Send the token to server using GAME-NAME hexplore and the url found in
the instruction on interactive puzzles.
Game is initialized, you got response containing moves counter and field state (in rectangular mapping,
rows glued together with semicolon mark - feel free to ignore it or parse and visualize for your convenience.
Field size is always 13.
With next requests include move with value consisting of letter and number, e.g. e5. Response will
have additional value cell to tell you whether you found X or O at the given coordinate.
Feel free to play manually. However you'll get the winning token only if you spend no more than 120 seconds
and 40 moves.
The value end in response means game is over - you either get winning token with it (submit it as answer
below) or message explaining what is wrong.
If you use field value from response for visualisation, keep in mind, cells are connected (besides
horizontal and vertical lines) by one of diagonals - from upper-left to bottom-right (but not the other!)