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The party (Posted on 2002-06-20) Difficulty: 4 of 5
Alice and Bill threw a party and invited four other couples. As each couple arrived there were greetings, including handshakes.

Later in the evening, Bill asked everyone, including Alice how many people they shook hand with. Every answer was different. No one shook hands with his or her own partner.

How many hands did Alice shake?

See The Solution Submitted by TomM    
Rating: 3.6923 (13 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
hmm.. | Comment 1 of 16
there are 9 people to assign handshakes to, since bill
does not ask himself.

each person can shake hands with 10 - 1 - 1
people at most, 8. so we have to distribute the
numbers 0-8 among 9 people, works out.

we can describe the process in the usual
"state machine" way.. in this case
{previous handshakes .. new handshakes}

eg, at first we have {0, 0}
letting bill be first {Bill, Alice}

if the first meeting is

{0, 0, .. 2, 0}

well get the best spread of numbers, with no conflicts:

{B, 1, 2, 0} (remember, bill doesnt matter)

next we do

{B, 1, 2, 0, .. 4, 0} -> {B, 2, 3, 1, 4, 0}
{B, 2, 3, 1, 4, 0, .. 6, 0} -> {B, 3, 4, 2, 5, 1, 6, 0}
{B, 3, 4, 2, 5, 1, 6, 0 .. 8, 0}
-> {B, 4, 5, 3, 6, 2, 7, 1, 8, 0}

the numbers are distributed.

so my answer is 4
  Posted by Cheradenine on 2002-06-20 00:43:37
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