There were ten people at the party. No one shook hands with his or her own partner (and couldn't have shaken with him/herself), so the maximum handshakes a person could have made was 8. The minimum is 0.
There are 9 numbers between 0 and 8, inclusive, and 9 different answers, so each number was used as an answer once.
The person who shook hands eight times shook with everyone but his partner, so none of them can be the person who did not shake at all, so she must be "8's"partner.
After eliminating "0" and "8", the same logic shows that "7" and "1" must be partners, then "6" and "2",followed by "5" and "3". "4's" partner must have also shaken 4 hands. But no two people answered the same. However, Bill did not answer the question, so he is the missing"4" Alice is his partner, so she is the other "4" |