Math & Physics Problems Wikia
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Problem created by Tao Steven Zheng (郑涛).

Problem

The game of weiqi (Go in Japanese, Baduk in Korean) consists of a board with a 19 by 19 grid in which black and white stones are placed on the intersections. The number of legal weiqi moves amounts to roughly 1.2% of all possible configurations. How many legal moves are there? Express the answer in scientific notation.

Go.png

Solution

There are three possible configurations for each intersection: black stone, white stone, or no stone. So for the entire board we have

To express this astronomically large number as a power of ten, take the base 10 logarithm:

.

Thus

.

However, only 1.2% of the configurations are legal moves, so the number of legal moves is

.


Note: For more details about the mathematics of weiqi (Go), check out Configurations of Go 围棋变局.

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