Notakto is a variant of the well-known pen-and-pencil game Tic Tac Toe, but with a few key differences.
The game is played on an arbitrary number of 3x3 boards and the two players take turns marking a cell of their choosing with an X. When there are three Xs in a row on a board, either vertically,
horizontally, or diagonally, that board is considered "dead" and can no longer be played on. The goal of the game is to force your opponent to mark the third X in a row on the last "live" board,
in a sort of reversal of the original game's rules. In other words, the person who marks three in a row on the last "live" board loses.
The "special game", as it is called here, is another variant of Tic Tac Toe. It is played on a single 4x4 board and, as with the regular Notakto, is played with only Xs and the player who marks
three in a row loses.
Each board in the normal 3x3 Notakto game is assigned a value based on the combination of Xs. For example, the empty board is assigned the value 'c' and a dead board is assigned the identity 1.
You can figure out a winning strategy by taking the value of each board and multiplying them together. If the result is in a set of certain configurations you are in a winning position.
Here are all the possible configurations: 1, a, ab, bb, abb, c, ac, bc, abc, cc, acc, bcc, abcc, d, ad, bd, abd
When multiplying together the values and figuring out the configuration, there are certain rules that apply:
aa = 1
bbb = b
bbc = c
ccc = acc
bbd = d
cd = ad
dd = cc
The winning configurations are: a, bb, bc, cc
Remember, you want the game to be in a winning configuration after your turn.
All rotations and reflections of the above configurations have the same value as the original.
All dead boards have the value 1.