Problem 2. The anthropologist, her husband and another couple (M. Levine). (A dinner party with two couples only.)

An anthropologist went to a dinner party with her husband and another couple Always the scientist, the anthropologist could not help observing the curious ritual of introducing oneself to another person (that we did not meet before) with the handshaking

Before sitting at the table, the anthropologist recorded (in her head) each time two of the four people shook hands with one another. In this way, the anthropologist matched the names of the four people (including herself) with four numbers that kept track of how many people each person shook hands with.

At that point, first, she noted two obvious things: none of the four people had shaken hands with her or his respective spouse or partner and none of the four people had shaken hands twice with the same person. Second, she noted a curious incident: except for the number of hands that she shook, the other three numbers (that gave the number of handshakes of each of the other three people) were all different (they were, necessarily, the digits 0, 1, 2).

With how many people did the anthropologist's husband shake hands?

(Visualize who shook hands with whom making a 4x4 table.)

(Hint: Visualize the problem with a 4x4 matrix with checks for handshakes and crosses for no handshakes.)