Every rational unlink can be expressed by one of the following Conway symbols
 c0 c1 ... cr-1 cr (-1) 1 (cr-1) cr-1 ... c1 c0
 c0 c1 ... cr-1 (cr-1) 1 (-1) cr cr-1 ... c1 c0,
where ci ³ 0 for i = 0,...,r and cr ³ 2.

The LinKnot function RatKnotGenU0 (webMathematica RatKnotGenU0) gives the number and the list of Conway symbols of all rational unknots with n crossings, and the function RatLinkU0 (webMathematica RatLinkU0) gives the same result for rational unlinks. The number of such knots is given by the formula

 2[[(n-2)/ 2]]-2.
The number of such links is 0 for every even n, and for odd n it is given by the formula
 2[[(n-7)/ 2]].

Next figure represents a knot with the unknotting number 1. You can try to find the appropriate vertex for the crossing change that results in unknot. If you don't believe that such a point exists, you can check its unknotting number by putting its Conway symbol

 3 2 1 1 2 3 3 1 1 2 3 2 1 1 2
in the LinKnot function UnR. In a similar way for the unlink
 3 2 1 1 2 3 3 -1 1 2 3 2 1 1 2 3