The Hexadecimal Puzzle is the very first puzzle made by Binary Arts (now called Think Fun). Unlike all their later puzzles, this one is made of wood. It is closely related to their second puzzle, which was Spinout.
It has a stationary base inside of which is a sliding carriage. On this sliding carriage are 8 switching bars. Each bar has two states, tilted up (0) or down (1). At the start they are all tilted up (00000000), and the aim is to tilt them all down (11111111) so that the carriage can be slid out of the base. The switching bars can only be tilted at one place in the middle of the base, where there is a gate that is opened by pushing in a block piece at the front. However, the block piece has a series of four keys sticking out, so the gate can only be opened if the state of the switching bars to the left of the gate match the pattern of the four blocking keys (and any bars further to the left must be in the down state).
The pattern of the four blocking keys may be changed (by temporarily removing the blocking pin that keeps them fixed), and each of the 16 patterns gives rise to a different puzzle. The easiest key pattern is 1111, because this allows you to switch all bars in order from left to right. This pattern comes in handy when you want to reset the puzzle. The hardest pattern is 1110, which needs 170 moves. This pattern gives a puzzle that is equivalent to Spinout (but with 8 switches).
Like the Spinout puzzle, the Hexadecimal Puzzle was invented by William Keister, patent US 3,637,216 (patent 3,637,215 was for Spinout). Apparently he tried to implement an electronic version of the Chinese Rings, made a mistake in the wiring, producing these variants. He then invented a mechanism to play those variants in physical form. For more details, see the short article on William Keister at puzzles.com.
Here's a table showing the patterns in order of difficulty, together with their solution lengths.
Pattern | Length |
1111 | 8 |
0111 | 16 |
0000 | 20 |
1011 | 26 |
1000 | 28 |
0101 | 36 |
0100 | 38 |
0011 | 42 |
1101 | 52 |
1100 | 54 |
1010 | 56 |
0010 | 72 |
0110 | 102 |
1001 | 118 |
0001 | 150 |
1110 | 170 |
Solution:
Let me reproduce the hints leaflet that Binary Arts included with their puzzle.
Helpful Hints for your Hexadecimal Puzzle(Please Read Only When Frustrated)
This is a helpful hint we can share with those who might welcome a little assistance in overcoming the puzzle's challenges. As you start, try to think of each blocking key combinationi as eight separate puzzles, one puzzle for each switching bar, starting with the eighth bar (furthest from the exit block). Focus first on how to switch that eighth bar. To get to it and move it, you must first set the other seven slide bars in exactly the right combination in relation to the blocking key pattern and the exit block to allow the gate to open for the eighth bar. If even one of the first seven bars is switched in the wrong direction, the last bar cannot reach the gate, or the gate cannot be opened to switch this bar.
How should you set up the first seven bars? Focus next on the seventh bar. In its current position, would it be blocked by the blocking key which it would oppose when the eighth bar is in the gate to be switched? If so, it must be switched before the eights bar can be switched.
If switching the seventh bar is necessary to switch the eighth bar, focus next on the sixth bar. Would the sixth bar be blocked by its opposite blocking key when the seventh bar is in the gate? If so, it must be switched to switch the seventh bar to switch the eighth bar. Is the fifth bar in proper position when the sixth would be at the gate? The fourth? and on and on.
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The essential concept of the puzzle is to concentrate on solving the switching bars furthest from the main block, even though the puzzle constrains most of your actions to the bars nearest the block. Progress made on the near bars must give way to progress made on the farther bars, because the relationship between switching bars and their opposing blocking keys changes with each puzzle, you have to lose some to win some.
After the eighth bar is switched, of course, you are left with a new switching sequence to solve, which now has seven bars which may or may not have to be switched, instead of eight. The process explained above must be repeated, switching the seventh bar to the open position, and then the sixth, etc., until each of the eight bars have been solved in order.
Fortunately, each succeeding bar is easier than the last, because fewer remaining bars get in the way. When only the second and first bars are left, you are almost out of the woods. Out of the woods that is, until you realize that the process must be reversed to get the carriage back in the base for the next would be puzzlesolver to take his or her turn!
One final suggestion. Although resetting the puzzle can be as challenging as solving it, once the puzzle has been solved it is sometimes handy to readjust all the keys to the "1" position. The bars can then be moved back into starting position in order, and the keys repositioned in any arrangement for the next puzzle sequence.
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That hints leaflet pretty much explains how to solve the puzzle. It is simply the following steps:
- Initially, the combination to aim for is 11111111
- Find the rightmost bar that does not match the combination you are aiming for.
- If you cannot immediately flip that incorrect bar, work out what the combination should be in order to flip it. This is the new combination to aim for. Then go back to step b with this new aim in mind.
- If on the other hand you can just flip that incorrect bar, do so.
- Repeat steps a-d, until the puzzle is solved.
Here's a table showing not just the solution lengths for each key pattern, but also the worst combination, and the number of moves that combination takes to solve.
Pattern | Length | Antipode | Diameter |
0000 | 20 | 11111110 | 33 |
0001 | 150 | 00000000 | 150 |
0010 | 72 | 11111110 | 115 |
0011 | 42 | 00000000 | 42 |
0100 | 38 | 11111110 | 63 |
0101 | 36 | 00000000 | 36 |
0110 | 102 | 11111110 | 161 |
0111 | 16 | 00000000 | 16 |
1000 | 28 | 11111110 | 47 |
1001 | 118 | 00000000 | 118 |
1010 | 56 | 11111110 | 89 |
1011 | 26 | 00000000 | 26 |
1100 | 54 | 11111110 | 85 |
1101 | 52 | 00000000 | 52 |
1110 | 170 | 11111110 | 255 |
1111 | 8 | 00000000 | 8 |
The table shows an interesting repeating pattern. Whenever the key pattern ends in a 1 the worst combination is the starting position, which has all bars set to 0. Otherwise, the worst combination has all but the last bar set to 1.
For completeness, I include full solutions for all 16 key patterns.
Pattern 0000 |
| 12345678 | Move |
0: | 00000000 | 3 |
1: | 00100000 | 2 |
2: | 01100000 | 1 |
3: | 11100000 | 8 |
4: | 11100001 | 1 |
5: | 01100001 | 2 |
6: | 00100001 | 3 |
7: | 00000001 | 2 |
8: | 01000001 | 1 |
9: | 11000001 | 7 |
10: | 11000011 | 1 |
11: | 01000011 | 2 |
12: | 00000011 | 1 |
13: | 10000011 | 6 |
14: | 10000111 | 1 |
15: | 00000111 | 5 |
16: | 00001111 | 4 |
17: | 00011111 | 3 |
18: | 00111111 | 2 |
19: | 01111111 | 1 |
20: | 11111111 | |
Pattern 0001 |
| 12345678 | Move |
0: | 00000000 | 1 |
1: | 10000000 | 2 |
2: | 11000000 | 1 |
3: | 01000000 | 3 |
4: | 01100000 | 1 |
5: | 11100000 | 2 |
6: | 10100000 | 1 |
7: | 00100000 | 4 |
8: | 00110000 | 1 |
9: | 10110000 | 2 |
10: | 11110000 | 1 |
11: | 01110000 | 3 |
12: | 01010000 | 1 |
13: | 11010000 | 2 |
14: | 10010000 | 1 |
15: | 00010000 | 5 |
16: | 00011000 | 1 |
17: | 10011000 | 2 |
18: | 11011000 | 1 |
19: | 01011000 | 3 |
20: | 01111000 | 1 |
21: | 11111000 | 2 |
22: | 10111000 | 1 |
23: | 00111000 | 4 |
24: | 00101000 | 1 |
25: | 10101000 | 2 |
26: | 11101000 | 1 |
27: | 01101000 | 3 |
28: | 01001000 | 1 |
29: | 11001000 | 2 |
30: | 10001000 | 6 |
31: | 10001100 | 2 |
32: | 11001100 | 1 |
33: | 01001100 | 3 |
34: | 01101100 | 1 |
35: | 11101100 | 2 |
36: | 10101100 | 1 |
37: | 00101100 | 4 |
38: | 00111100 | 1 |
39: | 10111100 | 2 |
40: | 11111100 | 1 |
41: | 01111100 | 3 |
42: | 01011100 | 1 |
43: | 11011100 | 2 |
44: | 10011100 | 1 |
45: | 00011100 | 5 |
46: | 00010100 | 1 |
47: | 10010100 | 2 |
48: | 11010100 | 1 |
49: | 01010100 | 3 |
50: | 01110100 | 1 |
51: | 11110100 | 2 |
52: | 10110100 | 1 |
53: | 00110100 | 4 |
54: | 00100100 | 1 |
55: | 10100100 | 2 |
56: | 11100100 | 1 |
57: | 01100100 | 3 |
58: | 01000100 | 1 |
59: | 11000100 | 7 |
60: | 11000110 | 1 |
61: | 01000110 | 3 |
62: | 01100110 | 1 |
63: | 11100110 | 2 |
64: | 10100110 | 1 |
65: | 00100110 | 4 |
66: | 00110110 | 1 |
67: | 10110110 | 2 |
68: | 11110110 | 1 |
69: | 01110110 | 3 |
70: | 01010110 | 1 |
71: | 11010110 | 2 |
72: | 10010110 | 1 |
73: | 00010110 | 5 |
74: | 00011110 | 1 |
75: | 10011110 | 2 |
76: | 11011110 | 1 |
77: | 01011110 | 3 |
78: | 01111110 | 1 |
79: | 11111110 | 2 |
80: | 10111110 | 1 |
81: | 00111110 | 4 |
82: | 00101110 | 1 |
83: | 10101110 | 2 |
84: | 11101110 | 1 |
85: | 01101110 | 3 |
86: | 01001110 | 1 |
87: | 11001110 | 2 |
88: | 10001110 | 6 |
89: | 10001010 | 2 |
90: | 11001010 | 1 |
91: | 01001010 | 3 |
92: | 01101010 | 1 |
93: | 11101010 | 2 |
94: | 10101010 | 1 |
95: | 00101010 | 4 |
96: | 00111010 | 1 |
97: | 10111010 | 2 |
98: | 11111010 | 1 |
99: | 01111010 | 3 |
100: | 01011010 | 1 |
101: | 11011010 | 2 |
102: | 10011010 | 1 |
103: | 00011010 | 5 |
104: | 00010010 | 1 |
105: | 10010010 | 2 |
106: | 11010010 | 1 |
107: | 01010010 | 3 |
108: | 01110010 | 1 |
109: | 11110010 | 2 |
110: | 10110010 | 1 |
111: | 00110010 | 4 |
112: | 00100010 | 1 |
113: | 10100010 | 2 |
114: | 11100010 | 8 |
115: | 11100011 | 2 |
116: | 10100011 | 1 |
117: | 00100011 | 4 |
118: | 00110011 | 1 |
119: | 10110011 | 2 |
120: | 11110011 | 1 |
121: | 01110011 | 3 |
122: | 01010011 | 1 |
123: | 11010011 | 2 |
124: | 10010011 | 1 |
125: | 00010011 | 5 |
126: | 00011011 | 1 |
127: | 10011011 | 2 |
128: | 11011011 | 1 |
129: | 01011011 | 3 |
130: | 01111011 | 1 |
131: | 11111011 | 2 |
132: | 10111011 | 1 |
133: | 00111011 | 4 |
134: | 00101011 | 1 |
135: | 10101011 | 2 |
136: | 11101011 | 1 |
137: | 01101011 | 3 |
138: | 01001011 | 1 |
139: | 11001011 | 2 |
140: | 10001011 | 6 |
141: | 10001111 | 2 |
142: | 11001111 | 1 |
143: | 01001111 | 3 |
144: | 01101111 | 1 |
145: | 11101111 | 2 |
146: | 10101111 | 1 |
147: | 00101111 | 4 |
148: | 00111111 | 1 |
149: | 10111111 | 2 |
150: | 11111111 | |
Pattern 0010 |
| 12345678 | Move |
0: | 00000000 | 2 |
1: | 01000000 | 4 |
2: | 01010000 | 2 |
3: | 00010000 | 1 |
4: | 10010000 | 6 |
5: | 10010100 | 1 |
6: | 00010100 | 2 |
7: | 01010100 | 4 |
8: | 01000100 | 2 |
9: | 00000100 | 1 |
10: | 10000100 | 3 |
11: | 10100100 | 1 |
12: | 00100100 | 2 |
13: | 01100100 | 1 |
14: | 11100100 | 8 |
15: | 11100101 | 1 |
16: | 01100101 | 2 |
17: | 00100101 | 1 |
18: | 10100101 | 3 |
19: | 10000101 | 1 |
20: | 00000101 | 2 |
21: | 01000101 | 4 |
22: | 01010101 | 2 |
23: | 00010101 | 1 |
24: | 10010101 | 6 |
25: | 10010001 | 1 |
26: | 00010001 | 2 |
27: | 01010001 | 4 |
28: | 01000001 | 2 |
29: | 00000001 | 1 |
30: | 10000001 | 3 |
31: | 10100001 | 1 |
32: | 00100001 | 5 |
33: | 00101001 | 1 |
34: | 10101001 | 3 |
35: | 10001001 | 1 |
36: | 00001001 | 2 |
37: | 01001001 | 1 |
38: | 11001001 | 7 |
39: | 11001011 | 1 |
40: | 01001011 | 2 |
41: | 00001011 | 1 |
42: | 10001011 | 3 |
43: | 10101011 | 1 |
44: | 00101011 | 5 |
45: | 00100011 | 1 |
46: | 10100011 | 3 |
47: | 10000011 | 1 |
48: | 00000011 | 2 |
49: | 01000011 | 4 |
50: | 01010011 | 2 |
51: | 00010011 | 1 |
52: | 10010011 | 6 |
53: | 10010111 | 1 |
54: | 00010111 | 2 |
55: | 01010111 | 4 |
56: | 01000111 | 2 |
57: | 00000111 | 1 |
58: | 10000111 | 3 |
59: | 10100111 | 1 |
60: | 00100111 | 5 |
61: | 00101111 | 1 |
62: | 10101111 | 3 |
63: | 10001111 | 1 |
64: | 00001111 | 2 |
65: | 01001111 | 4 |
66: | 01011111 | 2 |
67: | 00011111 | 1 |
68: | 10011111 | 3 |
69: | 10111111 | 1 |
70: | 00111111 | 2 |
71: | 01111111 | 1 |
72: | 11111111 | |
Pattern 0011 |
| 12345678 | Move |
0: | 00000000 | 1 |
1: | 10000000 | 2 |
2: | 11000000 | 3 |
3: | 11100000 | 1 |
4: | 01100000 | 4 |
5: | 01110000 | 1 |
6: | 11110000 | 2 |
7: | 10110000 | 1 |
8: | 00110000 | 5 |
9: | 00111000 | 1 |
10: | 10111000 | 2 |
11: | 11111000 | 3 |
12: | 11011000 | 2 |
13: | 10011000 | 6 |
14: | 10011100 | 2 |
15: | 11011100 | 3 |
16: | 11111100 | 1 |
17: | 01111100 | 4 |
18: | 01101100 | 1 |
19: | 11101100 | 3 |
20: | 11001100 | 7 |
21: | 11001110 | 3 |
22: | 11101110 | 1 |
23: | 01101110 | 4 |
24: | 01111110 | 1 |
25: | 11111110 | 2 |
26: | 10111110 | 1 |
27: | 00111110 | 5 |
28: | 00110110 | 1 |
29: | 10110110 | 2 |
30: | 11110110 | 1 |
31: | 01110110 | 4 |
32: | 01100110 | 1 |
33: | 11100110 | 8 |
34: | 11100111 | 1 |
35: | 01100111 | 4 |
36: | 01110111 | 1 |
37: | 11110111 | 2 |
38: | 10110111 | 1 |
39: | 00110111 | 5 |
40: | 00111111 | 1 |
41: | 10111111 | 2 |
42: | 11111111 | |
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Pattern 0100 |
| 12345678 | Move |
0: | 00000000 | 2 |
1: | 01000000 | 5 |
2: | 01001000 | 2 |
3: | 00001000 | 3 |
4: | 00101000 | 2 |
5: | 01101000 | 1 |
6: | 11101000 | 8 |
7: | 11101001 | 1 |
8: | 01101001 | 2 |
9: | 00101001 | 3 |
10: | 00001001 | 2 |
11: | 01001001 | 5 |
12: | 01000001 | 2 |
13: | 00000001 | 1 |
14: | 10000001 | 4 |
15: | 10010001 | 1 |
16: | 00010001 | 2 |
17: | 01010001 | 1 |
18: | 11010001 | 7 |
19: | 11010011 | 1 |
20: | 01010011 | 2 |
21: | 00010011 | 1 |
22: | 10010011 | 4 |
23: | 10000011 | 1 |
24: | 00000011 | 3 |
25: | 00100011 | 1 |
26: | 10100011 | 6 |
27: | 10100111 | 1 |
28: | 00100111 | 3 |
29: | 00000111 | 2 |
30: | 01000111 | 5 |
31: | 01001111 | 2 |
32: | 00001111 | 1 |
33: | 10001111 | 4 |
34: | 10011111 | 1 |
35: | 00011111 | 3 |
36: | 00111111 | 2 |
37: | 01111111 | 1 |
38: | 11111111 | |
Pattern 0101 |
| 12345678 | Move |
0: | 00000000 | 1 |
1: | 10000000 | 2 |
2: | 11000000 | 1 |
3: | 01000000 | 3 |
4: | 01100000 | 1 |
5: | 11100000 | 2 |
6: | 10100000 | 4 |
7: | 10110000 | 2 |
8: | 11110000 | 1 |
9: | 01110000 | 3 |
10: | 01010000 | 5 |
11: | 01011000 | 3 |
12: | 01111000 | 1 |
13: | 11111000 | 2 |
14: | 10111000 | 4 |
15: | 10101000 | 6 |
16: | 10101100 | 4 |
17: | 10111100 | 2 |
18: | 11111100 | 1 |
19: | 01111100 | 3 |
20: | 01011100 | 5 |
21: | 01010100 | 1 |
22: | 11010100 | 7 |
23: | 11010110 | 1 |
24: | 01010110 | 5 |
25: | 01011110 | 3 |
26: | 01111110 | 1 |
27: | 11111110 | 2 |
28: | 10111110 | 4 |
29: | 10101110 | 6 |
30: | 10101010 | 2 |
31: | 11101010 | 8 |
32: | 11101011 | 2 |
33: | 10101011 | 6 |
34: | 10101111 | 4 |
35: | 10111111 | 2 |
36: | 11111111 | |
Pattern 0110 |
| 12345678 | Move |
0: | 00000000 | 2 |
1: | 01000000 | 1 |
2: | 11000000 | 4 |
3: | 11010000 | 1 |
4: | 01010000 | 2 |
5: | 00010000 | 1 |
6: | 10010000 | 3 |
7: | 10110000 | 6 |
8: | 10110100 | 3 |
9: | 10010100 | 1 |
10: | 00010100 | 2 |
11: | 01010100 | 1 |
12: | 11010100 | 4 |
13: | 11000100 | 1 |
14: | 01000100 | 2 |
15: | 00000100 | 1 |
16: | 10000100 | 3 |
17: | 10100100 | 1 |
18: | 00100100 | 2 |
19: | 01100100 | 5 |
20: | 01101100 | 1 |
21: | 11101100 | 8 |
22: | 11101101 | 1 |
23: | 01101101 | 5 |
24: | 01100101 | 2 |
25: | 00100101 | 1 |
26: | 10100101 | 3 |
27: | 10000101 | 1 |
28: | 00000101 | 2 |
29: | 01000101 | 1 |
30: | 11000101 | 4 |
31: | 11010101 | 1 |
32: | 01010101 | 2 |
33: | 00010101 | 1 |
34: | 10010101 | 3 |
35: | 10110101 | 6 |
36: | 10110001 | 3 |
37: | 10010001 | 1 |
38: | 00010001 | 2 |
39: | 01010001 | 1 |
40: | 11010001 | 4 |
41: | 11000001 | 1 |
42: | 01000001 | 2 |
43: | 00000001 | 1 |
44: | 10000001 | 3 |
45: | 10100001 | 1 |
46: | 00100001 | 2 |
47: | 01100001 | 5 |
48: | 01101001 | 2 |
49: | 00101001 | 1 |
50: | 10101001 | 3 |
51: | 10001001 | 1 |
52: | 00001001 | 2 |
53: | 01001001 | 1 |
54: | 11001001 | 4 |
55: | 11011001 | 7 |
56: | 11011011 | 4 |
57: | 11001011 | 1 |
58: | 01001011 | 2 |
59: | 00001011 | 1 |
60: | 10001011 | 3 |
61: | 10101011 | 1 |
62: | 00101011 | 2 |
63: | 01101011 | 5 |
64: | 01100011 | 2 |
65: | 00100011 | 1 |
66: | 10100011 | 3 |
67: | 10000011 | 1 |
68: | 00000011 | 2 |
69: | 01000011 | 1 |
70: | 11000011 | 4 |
71: | 11010011 | 1 |
72: | 01010011 | 2 |
73: | 00010011 | 1 |
74: | 10010011 | 3 |
75: | 10110011 | 6 |
76: | 10110111 | 3 |
77: | 10010111 | 1 |
78: | 00010111 | 2 |
79: | 01010111 | 1 |
80: | 11010111 | 4 |
81: | 11000111 | 1 |
82: | 01000111 | 2 |
83: | 00000111 | 1 |
84: | 10000111 | 3 |
85: | 10100111 | 1 |
86: | 00100111 | 2 |
87: | 01100111 | 5 |
88: | 01101111 | 2 |
89: | 00101111 | 1 |
90: | 10101111 | 3 |
91: | 10001111 | 1 |
92: | 00001111 | 2 |
93: | 01001111 | 1 |
94: | 11001111 | 4 |
95: | 11011111 | 1 |
96: | 01011111 | 2 |
97: | 00011111 | 1 |
98: | 10011111 | 3 |
99: | 10111111 | 1 |
100: | 00111111 | 2 |
101: | 01111111 | 1 |
102: | 11111111 | |
Pattern 0111 |
| 12345678 | Move |
0: | 00000000 | 1 |
1: | 10000000 | 2 |
2: | 11000000 | 3 |
3: | 11100000 | 4 |
4: | 11110000 | 1 |
5: | 01110000 | 5 |
6: | 01111000 | 1 |
7: | 11111000 | 2 |
8: | 10111000 | 6 |
9: | 10111100 | 2 |
10: | 11111100 | 3 |
11: | 11011100 | 7 |
12: | 11011110 | 3 |
13: | 11111110 | 4 |
14: | 11101110 | 8 |
15: | 11101111 | 4 |
16: | 11111111 | |
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Pattern 1000 |
| 12345678 | Move |
0: | 00000000 | 4 |
1: | 00010000 | 3 |
2: | 00110000 | 2 |
3: | 01110000 | 1 |
4: | 11110000 | 8 |
5: | 11110001 | 1 |
6: | 01110001 | 2 |
7: | 00110001 | 3 |
8: | 00010001 | 4 |
9: | 00000001 | 3 |
10: | 00100001 | 2 |
11: | 01100001 | 1 |
12: | 11100001 | 7 |
13: | 11100011 | 1 |
14: | 01100011 | 2 |
15: | 00100011 | 3 |
16: | 00000011 | 2 |
17: | 01000011 | 1 |
18: | 11000011 | 6 |
19: | 11000111 | 1 |
20: | 01000111 | 2 |
21: | 00000111 | 1 |
22: | 10000111 | 5 |
23: | 10001111 | 1 |
24: | 00001111 | 4 |
25: | 00011111 | 3 |
26: | 00111111 | 2 |
27: | 01111111 | 1 |
28: | 11111111 | |
Pattern 1001 |
| 12345678 | Move |
0: | 00000000 | 1 |
1: | 10000000 | 2 |
2: | 11000000 | 1 |
3: | 01000000 | 3 |
4: | 01100000 | 1 |
5: | 11100000 | 2 |
6: | 10100000 | 1 |
7: | 00100000 | 4 |
8: | 00110000 | 1 |
9: | 10110000 | 2 |
10: | 11110000 | 1 |
11: | 01110000 | 3 |
12: | 01010000 | 1 |
13: | 11010000 | 2 |
14: | 10010000 | 5 |
15: | 10011000 | 2 |
16: | 11011000 | 1 |
17: | 01011000 | 3 |
18: | 01111000 | 1 |
19: | 11111000 | 2 |
20: | 10111000 | 1 |
21: | 00111000 | 4 |
22: | 00101000 | 1 |
23: | 10101000 | 2 |
24: | 11101000 | 1 |
25: | 01101000 | 3 |
26: | 01001000 | 1 |
27: | 11001000 | 6 |
28: | 11001100 | 1 |
29: | 01001100 | 3 |
30: | 01101100 | 1 |
31: | 11101100 | 2 |
32: | 10101100 | 1 |
33: | 00101100 | 4 |
34: | 00111100 | 1 |
35: | 10111100 | 2 |
36: | 11111100 | 1 |
37: | 01111100 | 3 |
38: | 01011100 | 1 |
39: | 11011100 | 2 |
40: | 10011100 | 5 |
41: | 10010100 | 2 |
42: | 11010100 | 1 |
43: | 01010100 | 3 |
44: | 01110100 | 1 |
45: | 11110100 | 2 |
46: | 10110100 | 1 |
47: | 00110100 | 4 |
48: | 00100100 | 1 |
49: | 10100100 | 2 |
50: | 11100100 | 7 |
51: | 11100110 | 2 |
52: | 10100110 | 1 |
53: | 00100110 | 4 |
54: | 00110110 | 1 |
55: | 10110110 | 2 |
56: | 11110110 | 1 |
57: | 01110110 | 3 |
58: | 01010110 | 1 |
59: | 11010110 | 2 |
60: | 10010110 | 5 |
61: | 10011110 | 2 |
62: | 11011110 | 1 |
63: | 01011110 | 3 |
64: | 01111110 | 1 |
65: | 11111110 | 2 |
66: | 10111110 | 1 |
67: | 00111110 | 4 |
68: | 00101110 | 1 |
69: | 10101110 | 2 |
70: | 11101110 | 1 |
71: | 01101110 | 3 |
72: | 01001110 | 1 |
73: | 11001110 | 6 |
74: | 11001010 | 1 |
75: | 01001010 | 3 |
76: | 01101010 | 1 |
77: | 11101010 | 2 |
78: | 10101010 | 1 |
79: | 00101010 | 4 |
80: | 00111010 | 1 |
81: | 10111010 | 2 |
82: | 11111010 | 1 |
83: | 01111010 | 3 |
84: | 01011010 | 1 |
85: | 11011010 | 2 |
86: | 10011010 | 5 |
87: | 10010010 | 2 |
88: | 11010010 | 1 |
89: | 01010010 | 3 |
90: | 01110010 | 1 |
91: | 11110010 | 8 |
92: | 11110011 | 1 |
93: | 01110011 | 3 |
94: | 01010011 | 1 |
95: | 11010011 | 2 |
96: | 10010011 | 5 |
97: | 10011011 | 2 |
98: | 11011011 | 1 |
99: | 01011011 | 3 |
100: | 01111011 | 1 |
101: | 11111011 | 2 |
102: | 10111011 | 1 |
103: | 00111011 | 4 |
104: | 00101011 | 1 |
105: | 10101011 | 2 |
106: | 11101011 | 1 |
107: | 01101011 | 3 |
108: | 01001011 | 1 |
109: | 11001011 | 6 |
110: | 11001111 | 1 |
111: | 01001111 | 3 |
112: | 01101111 | 1 |
113: | 11101111 | 2 |
114: | 10101111 | 1 |
115: | 00101111 | 4 |
116: | 00111111 | 1 |
117: | 10111111 | 2 |
118: | 11111111 | |
Pattern 1010 |
| 12345678 | Move |
0: | 00000000 | 2 |
1: | 01000000 | 4 |
2: | 01010000 | 1 |
3: | 11010000 | 6 |
4: | 11010100 | 1 |
5: | 01010100 | 2 |
6: | 00010100 | 1 |
7: | 10010100 | 3 |
8: | 10110100 | 1 |
9: | 00110100 | 2 |
10: | 01110100 | 1 |
11: | 11110100 | 8 |
12: | 11110101 | 1 |
13: | 01110101 | 2 |
14: | 00110101 | 1 |
15: | 10110101 | 3 |
16: | 10010101 | 1 |
17: | 00010101 | 2 |
18: | 01010101 | 1 |
19: | 11010101 | 6 |
20: | 11010001 | 1 |
21: | 01010001 | 4 |
22: | 01000001 | 2 |
23: | 00000001 | 1 |
24: | 10000001 | 3 |
25: | 10100001 | 5 |
26: | 10101001 | 1 |
27: | 00101001 | 2 |
28: | 01101001 | 1 |
29: | 11101001 | 7 |
30: | 11101011 | 1 |
31: | 01101011 | 2 |
32: | 00101011 | 1 |
33: | 10101011 | 5 |
34: | 10100011 | 3 |
35: | 10000011 | 1 |
36: | 00000011 | 2 |
37: | 01000011 | 4 |
38: | 01010011 | 1 |
39: | 11010011 | 6 |
40: | 11010111 | 1 |
41: | 01010111 | 4 |
42: | 01000111 | 2 |
43: | 00000111 | 1 |
44: | 10000111 | 3 |
45: | 10100111 | 5 |
46: | 10101111 | 3 |
47: | 10001111 | 1 |
48: | 00001111 | 2 |
49: | 01001111 | 4 |
50: | 01011111 | 2 |
51: | 00011111 | 1 |
52: | 10011111 | 3 |
53: | 10111111 | 1 |
54: | 00111111 | 2 |
55: | 01111111 | 1 |
56: | 11111111 | |
Pattern 1011 |
| 12345678 | Move |
0: | 00000000 | 1 |
1: | 10000000 | 2 |
2: | 11000000 | 3 |
3: | 11100000 | 1 |
4: | 01100000 | 4 |
5: | 01110000 | 1 |
6: | 11110000 | 2 |
7: | 10110000 | 5 |
8: | 10111000 | 2 |
9: | 11111000 | 3 |
10: | 11011000 | 6 |
11: | 11011100 | 3 |
12: | 11111100 | 1 |
13: | 01111100 | 4 |
14: | 01101100 | 1 |
15: | 11101100 | 7 |
16: | 11101110 | 1 |
17: | 01101110 | 4 |
18: | 01111110 | 1 |
19: | 11111110 | 2 |
20: | 10111110 | 5 |
21: | 10110110 | 2 |
22: | 11110110 | 8 |
23: | 11110111 | 2 |
24: | 10110111 | 5 |
25: | 10111111 | 2 |
26: | 11111111 | |
|
Pattern 1100 |
| 12345678 | Move |
0: | 00000000 | 2 |
1: | 01000000 | 1 |
2: | 11000000 | 5 |
3: | 11001000 | 1 |
4: | 01001000 | 2 |
5: | 00001000 | 1 |
6: | 10001000 | 4 |
7: | 10011000 | 1 |
8: | 00011000 | 3 |
9: | 00111000 | 2 |
10: | 01111000 | 1 |
11: | 11111000 | 8 |
12: | 11111001 | 1 |
13: | 01111001 | 2 |
14: | 00111001 | 3 |
15: | 00011001 | 1 |
16: | 10011001 | 4 |
17: | 10001001 | 1 |
18: | 00001001 | 2 |
19: | 01001001 | 1 |
20: | 11001001 | 5 |
21: | 11000001 | 1 |
22: | 01000001 | 2 |
23: | 00000001 | 1 |
24: | 10000001 | 4 |
25: | 10010001 | 1 |
26: | 00010001 | 3 |
27: | 00110001 | 2 |
28: | 01110001 | 1 |
29: | 11110001 | 7 |
30: | 11110011 | 1 |
31: | 01110011 | 2 |
32: | 00110011 | 3 |
33: | 00010011 | 1 |
34: | 10010011 | 4 |
35: | 10000011 | 1 |
36: | 00000011 | 3 |
37: | 00100011 | 2 |
38: | 01100011 | 1 |
39: | 11100011 | 6 |
40: | 11100111 | 1 |
41: | 01100111 | 2 |
42: | 00100111 | 3 |
43: | 00000111 | 2 |
44: | 01000111 | 1 |
45: | 11000111 | 5 |
46: | 11001111 | 1 |
47: | 01001111 | 2 |
48: | 00001111 | 1 |
49: | 10001111 | 4 |
50: | 10011111 | 1 |
51: | 00011111 | 3 |
52: | 00111111 | 2 |
53: | 01111111 | 1 |
54: | 11111111 | |
Pattern 1101 |
| 12345678 | Move |
0: | 00000000 | 1 |
1: | 10000000 | 2 |
2: | 11000000 | 1 |
3: | 01000000 | 3 |
4: | 01100000 | 1 |
5: | 11100000 | 2 |
6: | 10100000 | 4 |
7: | 10110000 | 2 |
8: | 11110000 | 1 |
9: | 01110000 | 3 |
10: | 01010000 | 1 |
11: | 11010000 | 5 |
12: | 11011000 | 1 |
13: | 01011000 | 3 |
14: | 01111000 | 1 |
15: | 11111000 | 2 |
16: | 10111000 | 4 |
17: | 10101000 | 2 |
18: | 11101000 | 6 |
19: | 11101100 | 2 |
20: | 10101100 | 4 |
21: | 10111100 | 2 |
22: | 11111100 | 1 |
23: | 01111100 | 3 |
24: | 01011100 | 1 |
25: | 11011100 | 5 |
26: | 11010100 | 1 |
27: | 01010100 | 3 |
28: | 01110100 | 1 |
29: | 11110100 | 7 |
30: | 11110110 | 1 |
31: | 01110110 | 3 |
32: | 01010110 | 1 |
33: | 11010110 | 5 |
34: | 11011110 | 1 |
35: | 01011110 | 3 |
36: | 01111110 | 1 |
37: | 11111110 | 2 |
38: | 10111110 | 4 |
39: | 10101110 | 2 |
40: | 11101110 | 6 |
41: | 11101010 | 2 |
42: | 10101010 | 4 |
43: | 10111010 | 2 |
44: | 11111010 | 8 |
45: | 11111011 | 2 |
46: | 10111011 | 4 |
47: | 10101011 | 2 |
48: | 11101011 | 6 |
49: | 11101111 | 2 |
50: | 10101111 | 4 |
51: | 10111111 | 2 |
52: | 11111111 | |
Pattern 1110 |
| 12345678 | Move |
0: | 00000000 | 2 |
1: | 01000000 | 1 |
2: | 11000000 | 4 |
3: | 11010000 | 1 |
4: | 01010000 | 2 |
5: | 00010000 | 1 |
6: | 10010000 | 3 |
7: | 10110000 | 1 |
8: | 00110000 | 2 |
9: | 01110000 | 1 |
10: | 11110000 | 6 |
11: | 11110100 | 1 |
12: | 01110100 | 2 |
13: | 00110100 | 1 |
14: | 10110100 | 3 |
15: | 10010100 | 1 |
16: | 00010100 | 2 |
17: | 01010100 | 1 |
18: | 11010100 | 4 |
19: | 11000100 | 1 |
20: | 01000100 | 2 |
21: | 00000100 | 1 |
22: | 10000100 | 3 |
23: | 10100100 | 1 |
24: | 00100100 | 2 |
25: | 01100100 | 1 |
26: | 11100100 | 5 |
27: | 11101100 | 1 |
28: | 01101100 | 2 |
29: | 00101100 | 1 |
30: | 10101100 | 3 |
31: | 10001100 | 1 |
32: | 00001100 | 2 |
33: | 01001100 | 1 |
34: | 11001100 | 4 |
35: | 11011100 | 1 |
36: | 01011100 | 2 |
37: | 00011100 | 1 |
38: | 10011100 | 3 |
39: | 10111100 | 1 |
40: | 00111100 | 2 |
41: | 01111100 | 1 |
42: | 11111100 | 8 |
43: | 11111101 | 1 |
44: | 01111101 | 2 |
45: | 00111101 | 1 |
46: | 10111101 | 3 |
47: | 10011101 | 1 |
48: | 00011101 | 2 |
49: | 01011101 | 1 |
50: | 11011101 | 4 |
51: | 11001101 | 1 |
52: | 01001101 | 2 |
53: | 00001101 | 1 |
54: | 10001101 | 3 |
55: | 10101101 | 1 |
56: | 00101101 | 2 |
57: | 01101101 | 1 |
58: | 11101101 | 5 |
59: | 11100101 | 1 |
60: | 01100101 | 2 |
61: | 00100101 | 1 |
62: | 10100101 | 3 |
63: | 10000101 | 1 |
64: | 00000101 | 2 |
65: | 01000101 | 1 |
66: | 11000101 | 4 |
67: | 11010101 | 1 |
68: | 01010101 | 2 |
69: | 00010101 | 1 |
70: | 10010101 | 3 |
71: | 10110101 | 1 |
72: | 00110101 | 2 |
73: | 01110101 | 1 |
74: | 11110101 | 6 |
75: | 11110001 | 1 |
76: | 01110001 | 2 |
77: | 00110001 | 1 |
78: | 10110001 | 3 |
79: | 10010001 | 1 |
80: | 00010001 | 2 |
81: | 01010001 | 1 |
82: | 11010001 | 4 |
83: | 11000001 | 1 |
84: | 01000001 | 2 |
85: | 00000001 | 1 |
86: | 10000001 | 3 |
87: | 10100001 | 1 |
88: | 00100001 | 2 |
89: | 01100001 | 1 |
90: | 11100001 | 5 |
91: | 11101001 | 1 |
92: | 01101001 | 2 |
93: | 00101001 | 1 |
94: | 10101001 | 3 |
95: | 10001001 | 1 |
96: | 00001001 | 2 |
97: | 01001001 | 1 |
98: | 11001001 | 4 |
99: | 11011001 | 1 |
100: | 01011001 | 2 |
101: | 00011001 | 1 |
102: | 10011001 | 3 |
103: | 10111001 | 1 |
104: | 00111001 | 2 |
105: | 01111001 | 1 |
106: | 11111001 | 7 |
107: | 11111011 | 1 |
108: | 01111011 | 2 |
109: | 00111011 | 1 |
110: | 10111011 | 3 |
111: | 10011011 | 1 |
112: | 00011011 | 2 |
113: | 01011011 | 1 |
114: | 11011011 | 4 |
115: | 11001011 | 1 |
116: | 01001011 | 2 |
117: | 00001011 | 1 |
118: | 10001011 | 3 |
119: | 10101011 | 1 |
120: | 00101011 | 2 |
121: | 01101011 | 1 |
122: | 11101011 | 5 |
123: | 11100011 | 1 |
124: | 01100011 | 2 |
125: | 00100011 | 1 |
126: | 10100011 | 3 |
127: | 10000011 | 1 |
128: | 00000011 | 2 |
129: | 01000011 | 1 |
130: | 11000011 | 4 |
131: | 11010011 | 1 |
132: | 01010011 | 2 |
133: | 00010011 | 1 |
134: | 10010011 | 3 |
135: | 10110011 | 1 |
136: | 00110011 | 2 |
137: | 01110011 | 1 |
138: | 11110011 | 6 |
139: | 11110111 | 1 |
140: | 01110111 | 2 |
141: | 00110111 | 1 |
142: | 10110111 | 3 |
143: | 10010111 | 1 |
144: | 00010111 | 2 |
145: | 01010111 | 1 |
146: | 11010111 | 4 |
147: | 11000111 | 1 |
148: | 01000111 | 2 |
149: | 00000111 | 1 |
150: | 10000111 | 3 |
151: | 10100111 | 1 |
152: | 00100111 | 2 |
153: | 01100111 | 1 |
154: | 11100111 | 5 |
155: | 11101111 | 1 |
156: | 01101111 | 2 |
157: | 00101111 | 1 |
158: | 10101111 | 3 |
159: | 10001111 | 1 |
160: | 00001111 | 2 |
161: | 01001111 | 1 |
162: | 11001111 | 4 |
163: | 11011111 | 1 |
164: | 01011111 | 2 |
165: | 00011111 | 1 |
166: | 10011111 | 3 |
167: | 10111111 | 1 |
168: | 00111111 | 2 |
169: | 01111111 | 1 |
170: | 11111111 | |
Pattern 1111 |
| 12345678 | Move |
0: | 00000000 | 1 |
1: | 10000000 | 2 |
2: | 11000000 | 3 |
3: | 11100000 | 4 |
4: | 11110000 | 5 |
5: | 11111000 | 6 |
6: | 11111100 | 7 |
7: | 11111110 | 8 |
8: | 11111111 | |
|