Upper bound on number of diagrams in Chinese chess
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 François 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+...
