Sr. John and his wife went to a party where four other married couples were present. Every person shook hands whit everyone he or she was no acquainted with. When the handshaking was over , Sir John asked everyone how many hands they shook.
Sir. John was surprised when he got nine different answers.
How many hands didi Sir. John's wife shake?
Assume that none of the couples knew each other, but hopefully each of the married people would be acquainted with their spouse
so Sir John's wife would shake hands with 8 other people (not with Sir John)
(My question to you:
How many different handshakes took place ? )
It appears Sir John did not answer the question (nine different answers) so if everyone knew their spouse, the answers were 0, 1, 2, 3, 4, 5, 6, 7, and 8. Since there is no indication of who knew whom, Sir John's wife could be any of 0 through 8. There were 36 handshakes in total.
To determine how many hands Sir John's wife shook, we need to analyze the information given in the problem.
We know that there were four other married couples present at the party, which means there were a total of nine couples at the party (including Sir John and his wife).
Since Sir John was able to get nine different answers when he asked everyone how many hands they shook, it means that each person shook a different number of hands.
Let's suppose Sir John and his wife are denoted by "J" and "W" respectively. The number of hands each person shook can be represented as follows:
J: a
W: b (our goal is to find the value of b)
Other couples: c, d, e, f, g, h, i
To get nine different answers, we can distribute the remaining numbers (a, c, d, e, f, g, h, i) such that each person shook a different number of hands.
One possible distribution could be as follows:
J shook hands with: b, c, d, e, f, g, h, i
W shook hands with: a, c, d, e, g, h
Since each person has a different number of hands shaken, we can see that b is one of the nine unique values obtained by Sir John.
Therefore, Sir John's wife shook b = 6 hands at the party.