==> induction/handshake.s <==
Assume there were 2n people (including host and hostess)
in the party.

1. When the host asked the question he must have got
   2n-1 responses (including from his wife).

2. All of the responses were different.

The responses have to be (0, 1, 2, 3, ..., 2n-2)
to satisfy the above requirements. As 2n-2 is the maximum
possible handshakes any person in this party could have made.

/**   Below,
      P{x} - means a person who shook x hands.
      H    - means the host
 **/

H: <-------->2n-2   0
	   2n-3        1
          2n-4          2
	  2n-5          3
          .             .
           .           .
             .       .
	      n  n-1 n-2

		(There are 2n-1 on the circle.)

P{2n-2} must have handshaked with H (because in the circle he
can handshake with only 2n-3. He has to exclude himself also.)

P{2n-3} must have handshaked with H (because in the circle he
can handshake with only 2n-4.)

P{2n-4} must have handshaked with H (because in the circle he
can handshake with only 2n-5.)

P{n} must have handshaked with H (because in the circle he
can handshake with only n-1.)

from P{n-1} to P{0} nobody  handshakes with H, because, for them
the handshake numbers are satisfied on the circle itself.

This leaves H with (n-1) handshakes.
----------------------------------

P{0} must be the spouse of P{2n-2} (since P{2n-2} handshakes with
everbody else.)
.
.
.
same logic till P{n-2}

leaving the Hostess to be P{n-1}.

----------------------------------------
So,
Host    - made (n-1) handshakes.
Hostess - made (n-1) handshakes.

where n is the number of couple including
the host couple.
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