The solution of 9 interlink the history of 9 interlink

Those who analyse Jie Jiulian annulus is complete write down a law, because move an annulus only every time, the expression of two paces also has reason only a number is different. An analysis is with 5 annulus below. The first 5 digit since left are the condition of 5 annulus, ordinal arrive by the first annulus the 5th annulus. The 2nd is express this to invert the 5 digit of order, it is binary number it seems that, but the binary number that can see with the 4th this is not pace number quite shows. The 3rd is the pace number that uses to this state institute from initiative condition. Most a binary system that just is pace number expresses right.

00000 - 00000 - 0 - 00000

10000 - 00001 - 1 - 00001

11000 - 00011 - 2 - 00010

01000 - 00010 - 3 - 00011

01100 - 00110 - 4 - 00100

11100 - 00111 - 5 - 00101

10100 - 00101 - 6 - 00110

00100 - 00100 - 7 - 00111

00110 - 01100 - 8 - 01000

10110 - 01101 - 9 - 01001

11110 - 01111 - 10 - 01010

01110 - 01110 - 11 - 01011

01010 - 01010 - 12 - 01100

11010 - 01011 - 13 - 01101

10010 - 01001 - 14 - 01110

00010 - 01000 - 15 - 01111

00011 - 11000 - 16 - 10000

10011 - 11001 - 17 - 10001

11011 - 11011 - 18 - 10010

01011 - 11010 - 19 - 10011

01111 - 11110 - 20 - 10100

11111 - 11111 - 21 - 10101

We discover, right is counted is the 0 case thunder that count to the binary system of 21 pile up decimal numeral fitly! This needs 21 paces of course. If count 5 binary systems ordinal write, namely

10111 - 11101 - 22 - 10110

00111 - 11100 - 23 - 10111

00101 - 10100 - 24 - 11000

10101 - 10101 - 25 - 11001

11101 - 10111 - 26 - 11010

01101 - 10110 - 27 - 11011

01001 - 10010 - 28 - 11100

11001 - 10011 - 29 - 11101

10001 - 10001 - 30 - 11110

00001 - 10000 - 31 - 11111

This explains, to having the 5 interlink of 5 annulus only, from initiative to condition 11111 those who use is not not be most, to condition 00001 ability are most, with 31 paces. Similar, to 9 interlink, from initiative to condition 111111111 those who use is not not be most, to condition 000000001 ability are most, with 511 paces. Because Grey is piled up 111111111 state the binary system is counted 101010101, express decimal numeral 341, reason goes up entirely to 9 annulus from initiative condition with 341 paces. This is the mathematical connotation of the contain in 9 interlink.

Note by the binary system several changeover are Grey to pile up: From right to left examination, if some number left is 0, this number is fixed; If be 1, this number is changed (0 turn into 1, 1 turn into 0) . Exemple, the binary system counts the Grey of 11011 to pile up is 10110.

By Grey the code expresses to turn into binary number: From right to left examination, if the left number of some number is mixed,be even, this number is fixed; If be odd, this number is changed.
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