The unknotting number of a knot is defined to be the minimum number ofcrossings that must be switched in order to unknot it. (A knot isconsidered to be unknotted when it can be deformed into a circle.)Despite the simplicity of this definition, the unknotting number of a knot isa relatively intractable invariant of it.
Here is a diagram of a knot with 10 crossings (the minimum possible for thisknot). In this diagram, 3 crossings must be switched in order to unknot it.