Rigor mortis: It is the post-mortem stiffening of the muscles after death due to chemical changes in the muscle tissues. This occurs after the primary relaxation and is characterized by fixed muscle contractions.
Livor mortis: Refers to the pooling of blood in the dependent parts of the body due to gravity, leading to a purple discoloration of the skin.
Cadaveric spasm: This is an involuntary muscle contraction that occurs immediately after death, before rigor mortis sets in. It is most commonly seen in cases of violent deaths or intense physical activity before death. The contraction is permanent and is most often observed in the hands, as described in the question.
Algor mortis: Refers to the cooling of the body post-mortem and does not involve muscle contractions.
Thus, the correct answer is Cadaveric spasm (3) because it specifically refers to the muscular contractions immediately after death, observed in the hands in this case.