[Nocturnal]

Originally posted by Jack Simth:
It can be done with a single cut:
0: Undo clasp, so it is a line;
1: Cut link 3 and remove (one + two connected, four+five+six+seven connected)

Process:
First day: give single link. (you: 2+4, them: 1)
Second Day: retrieve single, give double (you: 1+4, them: 2)
Third day: give single (you: 4, them: 2+1)
Fourth day: retrieve all, give quad (you: 2+1, them: 4)
Fifth day: give single (you: 2, them: 4+1)
Sixth day: retrieve single, give double: (you: 1, them: 4+2)
Seventh (final) day: give single (you: none, them: 4+2+1)

It's disguised binary counting.

Very good. That is correct.