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Upper bound on number of diagrams in Chinese chess

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After some work on the number of reachable positions for chess, I turned some attention to Chinese chess. Here is proof of an upper bound for the number of reachable diagrams, I am using the Fran├žois Labelle definition of diagrams from Statistics on chess positions.

A very simple upper bound is:

71415518081535297586850424458320988966669113375477110 which is under 10^53 and 176 bits
Here is the proof, compile with gcc cc-simple.c -l gmp
// A very simple upper bound for Chinese chess diagrams #include <stdlib.h> #include <stdio.h> #include <gmp.h> int main() {   /* Precompute factorials */   long f[6] = {1, 1, 2, 6, 24, 120};   mpz_t fac[91];   mpz_t total;   mpz_t current;   mpz_init(total);   mpz_init(current);   for (int i=0; i<91; i++) {     mpz_init(fac[i]);     mpz_fac_ui(fac[i], i);   }   for (int G=1; G<=1; G++)   for (int A=0; A<=2; A++)   for (int C=0; C<=2; C++)   for (int R=0; R<=2; R++)   for (int H=0; H<=2; H++)   for (int E=0; E<=2; E++)   for (int S=0; S<…

Update to 19 Questions

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Just made an update to our online guessing game.

>> http://phor.net/apps/19q/


This is an experimental program that uses entropy and Bayesian probability to run and learn from player input rather than the "neural network" that other games use. This technique is applicable to large data sets some original research on the entropy function.