This is a problem that's been troubling me recently. I'm neither a boy scout nor a knot theoretician, so I'm not sure how to progress. Is it possible for three pieces of string to be tied together without the knot being topologically equivalent to a knot tying two of the pieces together with the third string tied either around one of the other pieces or around the first knot itself? Oh dear, that wasn't very clear. Let's try again. Is it possible to construct a knot from three pieces of string where removing any of the pieces will cause the knot to collapse into an unknot? Help appreciated.