Go Combinatorics!

Probability Level 5

In the 11th century, Shen Kuo calculated the number of possible weiqi ( go in Japanese; baduk in Korean) positions and recorded it in the Meng Xi Bi Tan . The game consists of a board with $19 \times 19$ intersections in which black and white stones are placed on the intersections. However, Shen Kuo did not calculate the number of legal weiqi positions, which amounts to roughly 1.2% of all possible moves.

If $N$ represents the number of legal moves, calculate $\left[\ln{N}\right]$ .

The answer is 392.

1 solution

Mikael Marcondes
Jan 24, 2015

Any intersection may be empty, with a white stone or with a black stone. Hence, there are $3^{19.19}$ positions. Since just $1.2\%$ are legal positions, $ln\ N=ln\ 0.012+361.ln\ 3=392.18$ , whose nearer integer is $\boxed{392}$ .

The problem was fairly simple. I don't understand how it was level 5.

Kunal Verma - 5 years, 8 months ago

Go Combinatorics!

The answer is 392.

1 solution

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