[jonathan@c2q-q9400 ~]$ perl math02.pl 12
It should move [168] steps!
0: [111111111111-000000000000]
1: [11111111111-1000000000000]
2: [1111111111101-00000000000]
3: [11111111111010-0000000000]
4: [111111111110-010000000000]
5: [1111111111-01010000000000]
6: [111111111-101010000000000]
7: [11111111101-1010000000000]
8: [1111111110101-10000000000]
9: [111111111010101-000000000]
10: [1111111110101010-00000000]
11: [11111111101010-0100000000]
12: [111111111010-010100000000]
13: [1111111110-01010100000000]
14: [11111111-0101010100000000]
15: [1111111-10101010100000000]
16: [111111101-101010100000000]
17: [11111110101-1010100000000]
18: [1111111010101-10100000000]
19: [111111101010101-100000000]
20: [11111110101010101-0000000]
21: [111111101010101010-000000]
22: [1111111010101010-01000000]
23: [11111110101010-0101000000]
24: [111111101010-010101000000]
25: [1111111010-01010101000000]
26: [11111110-0101010101000000]
27: [111111-010101010101000000]
28: [11111-1010101010101000000]
29: [1111101-10101010101000000]
30: [111110101-101010101000000]
31: [11111010101-1010101000000]
32: [1111101010101-10101000000]
33: [111110101010101-101000000]
34: [11111010101010101-1000000]
35: [1111101010101010101-00000]
36: [11111010101010101010-0000]
37: [111110101010101010-010000]
38: [1111101010101010-01010000]
39: [11111010101010-0101010000]
40: [111110101010-010101010000]
41: [1111101010-01010101010000]
42: [11111010-0101010101010000]
43: [111110-010101010101010000]
44: [1111-01010101010101010000]
45: [111-101010101010101010000]
46: [11101-1010101010101010000]
47: [1110101-10101010101010000]
48: [111010101-101010101010000]
49: [11101010101-1010101010000]
50: [1110101010101-10101010000]
51: [111010101010101-101010000]
52: [11101010101010101-1010000]
53: [1110101010101010101-10000]
54: [111010101010101010101-000]
55: [1110101010101010101010-00]
56: [11101010101010101010-0100]
57: [111010101010101010-010100]
58: [1110101010101010-01010100]
59: [11101010101010-0101010100]
60: [111010101010-010101010100]
61: [1110101010-01010101010100]
62: [11101010-0101010101010100]
63: [111010-010101010101010100]
64: [1110-01010101010101010100]
65: [11-0101010101010101010100]
66: [1-10101010101010101010100]
67: [101-101010101010101010100]
68: [10101-1010101010101010100]
69: [1010101-10101010101010100]
70: [101010101-101010101010100]
71: [10101010101-1010101010100]
72: [1010101010101-10101010100]
73: [101010101010101-101010100]
74: [10101010101010101-1010100]
75: [1010101010101010101-10100]
76: [101010101010101010101-100]
77: [10101010101010101010101-0]
78: [101010101010101010101010-]
79: [1010101010101010101010-01]
80: [10101010101010101010-0101]
81: [101010101010101010-010101]
82: [1010101010101010-01010101]
83: [10101010101010-0101010101]
84: [101010101010-010101010101]
85: [1010101010-01010101010101]
86: [10101010-0101010101010101]
87: [101010-010101010101010101]
88: [1010-01010101010101010101]
89: [10-0101010101010101010101]
90: [-010101010101010101010101]
91: [0-10101010101010101010101]
92: [001-101010101010101010101]
93: [00101-1010101010101010101]
94: [0010101-10101010101010101]
95: [001010101-101010101010101]
96: [00101010101-1010101010101]
97: [0010101010101-10101010101]
98: [001010101010101-101010101]
99: [00101010101010101-1010101]
100: [0010101010101010101-10101]
101: [001010101010101010101-101]
102: [00101010101010101010101-1]
103: [0010101010101010101010-11]
104: [00101010101010101010-0111]
105: [001010101010101010-010111]
106: [0010101010101010-01010111]
107: [00101010101010-0101010111]
108: [001010101010-010101010111]
109: [0010101010-01010101010111]
110: [00101010-0101010101010111]
111: [001010-010101010101010111]
112: [0010-01010101010101010111]
113: [00-0101010101010101010111]
114: [000-101010101010101010111]
115: [00001-1010101010101010111]
116: [0000101-10101010101010111]
117: [000010101-101010101010111]
118: [00001010101-1010101010111]
119: [0000101010101-10101010111]
120: [000010101010101-101010111]
121: [00001010101010101-1010111]
122: [0000101010101010101-10111]
123: [000010101010101010101-111]
124: [00001010101010101010-1111]
125: [000010101010101010-011111]
126: [0000101010101010-01011111]
127: [00001010101010-0101011111]
128: [000010101010-010101011111]
129: [0000101010-01010101011111]
130: [00001010-0101010101011111]
131: [000010-010101010101011111]
132: [0000-01010101010101011111]
133: [00000-1010101010101011111]
134: [0000001-10101010101011111]
135: [000000101-101010101011111]
136: [00000010101-1010101011111]
137: [0000001010101-10101011111]
138: [000000101010101-101011111]
139: [00000010101010101-1011111]
140: [0000001010101010101-11111]
141: [000000101010101010-111111]
142: [0000001010101010-01111111]
143: [00000010101010-0101111111]
144: [000000101010-010101111111]
145: [0000001010-01010101111111]
146: [00000010-0101010101111111]
147: [000000-010101010101111111]
148: [0000000-10101010101111111]
149: [000000001-101010101111111]
150: [00000000101-1010101111111]
151: [0000000010101-10101111111]
152: [000000001010101-101111111]
153: [00000000101010101-1111111]
154: [0000000010101010-11111111]
155: [00000000101010-0111111111]
156: [000000001010-010111111111]
157: [0000000010-01010111111111]
158: [00000000-0101010111111111]
159: [000000000-101010111111111]
160: [00000000001-1010111111111]
161: [0000000000101-10111111111]
162: [000000000010101-111111111]
163: [00000000001010-1111111111]
164: [000000000010-011111111111]
165: [0000000000-01011111111111]
166: [00000000000-1011111111111]
167: [0000000000001-11111111111]
168: [000000000000-111111111111]