diff --git a/docs/index.html b/docs/index.html index f74afe8..8c163af 100644 --- a/docs/index.html +++ b/docs/index.html @@ -196,15 +196,15 @@

Ternary numbers

Number of possible boards

Part of a reason why we did all the ☝️ algebra was to came up with number of possible tic-tac-toe - boards. We know that the theoretical upper bound of possible games is 39! = 19 683. Factorial + boards. We know that the theoretical upper bound of possible games is 9! = 362 880. Factorial takes in count also boards where the game already ended but we added another steps. Henry Bottomley's came up with nice calculations where they - estimated 2 466 possible games. + estimated 255 168 possible games.

We know that we can do even better by removing all the symmetrical boards, we can count the numbers using some more advance algebra e.g. Burnside's lemma - [without any further calculations] can give us better estimate of 19 683 + [without any further calculations] can give us better estimate of 2 475 2) or write a fairly short code.

@@ -441,7 +441,7 @@

References:

get: $$\frac{1}{|D_4|}\sum_{g\in G}\big |X^g \big| = \frac{1}{8}\bigg( 1\times 3^9 + 3 \times 3^1 + 4 \times 3^3 \bigg) - = 2\ 475 + = 2\ 475$$ (There is one element which leaves all elements unchanged [identity], there are 3 [rotations] which leave one element unchanged and 4 [axes] which leave 3 elements unchanged.)