rotation puzzle

main.rs

use std::collections::HashMap;
use std::fmt::{Debug, Formatter};
use std::hash::Hash;

// Wrapper around u16. Using the lowest significant 9 bits to store a 3x3 state.
#[derive(Copy, Clone, Eq, PartialEq, Default, Hash)]
struct Bits(u16);

fn main() {
    let mut map = HashMap::new();

    let mut case = 0;
    for i in 0..512 {
        let b = Bits(i);
        if map.contains_key(&b) { continue; }

        println!("{case}: {:?}", b);

        let b = b.rotate();
        map.insert(b, case);
        let b = b.rotate();
        map.insert(b, case);
        let b = b.rotate();
        map.insert(b, case);

        case += 1;
    }

    println!("{case}");
}


impl Debug for Bits {
    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
        let mut formatter = f.debug_list();
        for i in 0..9 {
            formatter.entry(&(if self.bit(i) { 1 } else { 0 }));
        }
        formatter.finish()
    }
}

impl Bits {
    fn bit(self, n: u8) -> bool {
        assert!(n < 9);
        (1u16 << n) & self.0 != 0
    }

    fn from_bits(bits: [bool; 9]) -> Self {
        Bits(
            (bits[0] as u16) | (bits[1] as u16) << 1 | (bits[2] as u16) << 2
            | (bits[3] as u16) << 3 | (bits[4] as u16) << 4 | (bits[5] as u16) << 5
            | (bits[6] as u16) << 6 | (bits[7] as u16) << 7 | (bits[8] as u16) << 8
        )
    }

    fn rotate(self) -> Self {
        Self::from_bits([
            self.bit(6), self.bit(3), self.bit(0),
            self.bit(7), self.bit(4), self.bit(1),
            self.bit(8), self.bit(5), self.bit(2),
        ])
    }
}

output

This is the list of all the distinct bit patterns, excluding duplicates due to rotation

0: [0, 0, 0, 0, 0, 0, 0, 0, 0]
1: [1, 0, 0, 0, 0, 0, 0, 0, 0]
2: [0, 1, 0, 0, 0, 0, 0, 0, 0]
3: [1, 1, 0, 0, 0, 0, 0, 0, 0]
4: [1, 0, 1, 0, 0, 0, 0, 0, 0]
5: [0, 1, 1, 0, 0, 0, 0, 0, 0]
6: [1, 1, 1, 0, 0, 0, 0, 0, 0]
7: [0, 1, 0, 1, 0, 0, 0, 0, 0]
8: [1, 1, 0, 1, 0, 0, 0, 0, 0]
9: [0, 0, 1, 1, 0, 0, 0, 0, 0]
10: [1, 0, 1, 1, 0, 0, 0, 0, 0]
11: [0, 1, 1, 1, 0, 0, 0, 0, 0]
12: [1, 1, 1, 1, 0, 0, 0, 0, 0]
13: [0, 0, 0, 0, 1, 0, 0, 0, 0]
14: [1, 0, 0, 0, 1, 0, 0, 0, 0]
15: [0, 1, 0, 0, 1, 0, 0, 0, 0]
16: [1, 1, 0, 0, 1, 0, 0, 0, 0]
17: [1, 0, 1, 0, 1, 0, 0, 0, 0]
18: [0, 1, 1, 0, 1, 0, 0, 0, 0]
19: [1, 1, 1, 0, 1, 0, 0, 0, 0]
20: [0, 1, 0, 1, 1, 0, 0, 0, 0]
21: [1, 1, 0, 1, 1, 0, 0, 0, 0]
22: [0, 0, 1, 1, 1, 0, 0, 0, 0]
23: [1, 0, 1, 1, 1, 0, 0, 0, 0]
24: [0, 1, 1, 1, 1, 0, 0, 0, 0]
25: [1, 1, 1, 1, 1, 0, 0, 0, 0]
26: [1, 0, 0, 0, 0, 1, 0, 0, 0]
27: [1, 1, 0, 0, 0, 1, 0, 0, 0]
28: [1, 0, 1, 0, 0, 1, 0, 0, 0]
29: [1, 1, 1, 0, 0, 1, 0, 0, 0]
30: [0, 0, 0, 1, 0, 1, 0, 0, 0]
31: [1, 0, 0, 1, 0, 1, 0, 0, 0]
32: [0, 1, 0, 1, 0, 1, 0, 0, 0]
33: [1, 1, 0, 1, 0, 1, 0, 0, 0]
34: [0, 0, 1, 1, 0, 1, 0, 0, 0]
35: [1, 0, 1, 1, 0, 1, 0, 0, 0]
36: [0, 1, 1, 1, 0, 1, 0, 0, 0]
37: [1, 1, 1, 1, 0, 1, 0, 0, 0]
38: [1, 0, 0, 0, 1, 1, 0, 0, 0]
39: [1, 1, 0, 0, 1, 1, 0, 0, 0]
40: [1, 0, 1, 0, 1, 1, 0, 0, 0]
41: [1, 1, 1, 0, 1, 1, 0, 0, 0]
42: [0, 0, 0, 1, 1, 1, 0, 0, 0]
43: [1, 0, 0, 1, 1, 1, 0, 0, 0]
44: [0, 1, 0, 1, 1, 1, 0, 0, 0]
45: [1, 1, 0, 1, 1, 1, 0, 0, 0]
46: [0, 0, 1, 1, 1, 1, 0, 0, 0]
47: [1, 0, 1, 1, 1, 1, 0, 0, 0]
48: [0, 1, 1, 1, 1, 1, 0, 0, 0]
49: [1, 1, 1, 1, 1, 1, 0, 0, 0]
50: [0, 0, 1, 0, 0, 0, 1, 0, 0]
51: [1, 0, 1, 0, 0, 0, 1, 0, 0]
52: [0, 1, 1, 0, 0, 0, 1, 0, 0]
53: [1, 1, 1, 0, 0, 0, 1, 0, 0]
54: [0, 0, 1, 1, 0, 0, 1, 0, 0]
55: [1, 0, 1, 1, 0, 0, 1, 0, 0]
56: [0, 1, 1, 1, 0, 0, 1, 0, 0]
57: [1, 1, 1, 1, 0, 0, 1, 0, 0]
58: [0, 0, 1, 0, 1, 0, 1, 0, 0]
59: [1, 0, 1, 0, 1, 0, 1, 0, 0]
60: [0, 1, 1, 0, 1, 0, 1, 0, 0]
61: [1, 1, 1, 0, 1, 0, 1, 0, 0]
62: [0, 0, 1, 1, 1, 0, 1, 0, 0]
63: [1, 0, 1, 1, 1, 0, 1, 0, 0]
64: [0, 1, 1, 1, 1, 0, 1, 0, 0]
65: [1, 1, 1, 1, 1, 0, 1, 0, 0]
66: [1, 0, 0, 0, 0, 1, 1, 0, 0]
67: [0, 1, 0, 0, 0, 1, 1, 0, 0]
68: [1, 1, 0, 0, 0, 1, 1, 0, 0]
69: [1, 0, 1, 0, 0, 1, 1, 0, 0]
70: [0, 1, 1, 0, 0, 1, 1, 0, 0]
71: [1, 1, 1, 0, 0, 1, 1, 0, 0]
72: [1, 0, 0, 1, 0, 1, 1, 0, 0]
73: [0, 1, 0, 1, 0, 1, 1, 0, 0]
74: [1, 1, 0, 1, 0, 1, 1, 0, 0]
75: [0, 0, 1, 1, 0, 1, 1, 0, 0]
76: [1, 0, 1, 1, 0, 1, 1, 0, 0]
77: [0, 1, 1, 1, 0, 1, 1, 0, 0]
78: [1, 1, 1, 1, 0, 1, 1, 0, 0]
79: [1, 0, 0, 0, 1, 1, 1, 0, 0]
80: [0, 1, 0, 0, 1, 1, 1, 0, 0]
81: [1, 1, 0, 0, 1, 1, 1, 0, 0]
82: [1, 0, 1, 0, 1, 1, 1, 0, 0]
83: [0, 1, 1, 0, 1, 1, 1, 0, 0]
84: [1, 1, 1, 0, 1, 1, 1, 0, 0]
85: [1, 0, 0, 1, 1, 1, 1, 0, 0]
86: [0, 1, 0, 1, 1, 1, 1, 0, 0]
87: [1, 1, 0, 1, 1, 1, 1, 0, 0]
88: [0, 0, 1, 1, 1, 1, 1, 0, 0]
89: [1, 0, 1, 1, 1, 1, 1, 0, 0]
90: [0, 1, 1, 1, 1, 1, 1, 0, 0]
91: [1, 1, 1, 1, 1, 1, 1, 0, 0]
92: [1, 0, 1, 1, 0, 0, 0, 1, 0]
93: [0, 1, 1, 1, 0, 0, 0, 1, 0]
94: [1, 1, 1, 1, 0, 0, 0, 1, 0]
95: [1, 0, 1, 1, 1, 0, 0, 1, 0]
96: [0, 1, 1, 1, 1, 0, 0, 1, 0]
97: [1, 1, 1, 1, 1, 0, 0, 1, 0]
98: [0, 1, 0, 1, 0, 1, 0, 1, 0]
99: [1, 1, 0, 1, 0, 1, 0, 1, 0]
100: [1, 0, 1, 1, 0, 1, 0, 1, 0]
101: [1, 1, 1, 1, 0, 1, 0, 1, 0]
102: [0, 1, 0, 1, 1, 1, 0, 1, 0]
103: [1, 1, 0, 1, 1, 1, 0, 1, 0]
104: [1, 0, 1, 1, 1, 1, 0, 1, 0]
105: [1, 1, 1, 1, 1, 1, 0, 1, 0]
106: [1, 0, 1, 0, 0, 0, 1, 1, 0]
107: [0, 1, 1, 0, 0, 0, 1, 1, 0]
108: [1, 1, 1, 0, 0, 0, 1, 1, 0]
109: [1, 0, 1, 1, 0, 0, 1, 1, 0]
110: [0, 1, 1, 1, 0, 0, 1, 1, 0]
111: [1, 1, 1, 1, 0, 0, 1, 1, 0]
112: [1, 0, 1, 0, 1, 0, 1, 1, 0]
113: [0, 1, 1, 0, 1, 0, 1, 1, 0]
114: [1, 1, 1, 0, 1, 0, 1, 1, 0]
115: [1, 0, 1, 1, 1, 0, 1, 1, 0]
116: [0, 1, 1, 1, 1, 0, 1, 1, 0]
117: [1, 1, 1, 1, 1, 0, 1, 1, 0]
118: [1, 0, 1, 0, 0, 1, 1, 1, 0]
119: [1, 1, 1, 0, 0, 1, 1, 1, 0]
120: [1, 0, 1, 1, 0, 1, 1, 1, 0]
121: [0, 1, 1, 1, 0, 1, 1, 1, 0]
122: [1, 1, 1, 1, 0, 1, 1, 1, 0]
123: [1, 0, 1, 0, 1, 1, 1, 1, 0]
124: [1, 1, 1, 0, 1, 1, 1, 1, 0]
125: [1, 0, 1, 1, 1, 1, 1, 1, 0]
126: [0, 1, 1, 1, 1, 1, 1, 1, 0]
127: [1, 1, 1, 1, 1, 1, 1, 1, 0]
128: [1, 0, 1, 0, 0, 0, 1, 0, 1]
129: [1, 1, 1, 0, 0, 0, 1, 0, 1]
130: [1, 1, 1, 1, 0, 0, 1, 0, 1]
131: [1, 0, 1, 0, 1, 0, 1, 0, 1]
132: [1, 1, 1, 0, 1, 0, 1, 0, 1]
133: [1, 1, 1, 1, 1, 0, 1, 0, 1]
134: [1, 0, 1, 1, 0, 1, 1, 0, 1]
135: [1, 1, 1, 1, 0, 1, 1, 0, 1]
136: [1, 0, 1, 1, 1, 1, 1, 0, 1]
137: [1, 1, 1, 1, 1, 1, 1, 0, 1]
138: [1, 1, 1, 1, 0, 1, 1, 1, 1]
139: [1, 1, 1, 1, 1, 1, 1, 1, 1]
Number of representable states: 140