Navigation-Compass-Solver

Brute-force solver for Navigation Compass puzzles web version

_{Initial upload (May 9, 2023)}

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Requirements

• python 3.8+
• numpy 1.23+

Problem

The Navigation Compass problem is a game involving 3 rings, $A, B,$ and $C$, which each have their own initial angle and rotation per step, rings may rotate in multiples of $\frac{\pi}{3}$ either clockwise or counter-clockwise. Additionally, the rings only rotate in 3 groups, e.g. ring $A$ may move simultaneously as a group with ring $B$ and/or with ring $C$ or as a group by itself. These patterns are not known prior to starting the problem. The goal of the player is to rotate the rings such that they are all oriented $\pi$ radians or $180\degree$. This can be formulated as solving the following system of equations.

$$ \cos(a_1 x_1 + a_2 x_2 + a_3 x_3 + a_0) = -1 $$

$$ \cos(b_1 x_1 + b_2 x_2 + b_3 x_3 + b_0) = -1 $$

$$ \cos(c_1 x_1 + c_2 x_2 + c_3 x_3 + c_0) = -1 $$

The solution to this, $x_1, x_2,$ and $x3$, are the number of times to rotate each group of rings. The python script navigation_compass.py attempts to brute-force a solution.

Usage

navigation_compass.py has several arguments to specify the configuration of a navigation compass puzzle.

Flag	Required	Valid Argument	Description
--inner	Yes	Number that is a multiple of 60	Degree of the inner axis
--middle	Yes	Number that is a multiple of 60	Degree of the middle axis
--outer	Yes	Number that is a multiple of 60	Degree of the outer axis
--marks-inner	Yes	Natural number	Number of marks on inner ring, indicating rotation per step
--marks-middle	Yes	Natural number	Number of marks on middle ring, indicating rotation per step
--marks-outer	Yes	Natural number	Number of marks on outer ring, indicating rotation per step
--inner-cw	No	None	Specify flag only if inner ring rotates clockwise
--middle-cw	No	None	Specify flag only if middle ring rotates clockwise
--outer-cw	No	None	Specify flag only if outer ring rotates clockwise
-a, --group-a	Yes	At least one of inner, middle, and outer	First group of rings that rotate together
-b, --group-b	Yes	At least one of inner, middle, and outer	Second group of rings that rotate together
-c, --group-c	Yes	At least one of inner, middle, and outer	Third group of rings that rotate together
-N, --maxit	No	Natural number	Maximum number of brute-force attempts (default 100)

Example

python navigation_compass.py --inner 60 --middle 0 --outer 180 --marks-inner 4 --marks-middle 3 --marks-outer 1 --inner-cw --middle-cw --outer-cw -a inner -b middle outer -c inner outer
>>>
         answer = [20.  1. 11.] % 6 = [2 1 5]
         rotate group A ['inner'] 2 times
         rotate group B ['middle', 'outer'] 1 times
         rotate group C ['inner', 'outer'] 5 times
Solved in 11 brute-force iterations

If no solution is found, check if the arguments are correct.