Odd person out
I was at a party with a friend one evening where he got bored and started keeping track of the number of handshakes made by people. A person was called "odd person" if he made an odd number of handshakes, otherwise he was called "even person".
After some time my bored friend said to me, "Hey, do you know that there are an even number of odd persons?" I replied, "Big deal ! there will be always an even number of odd persons". But still he seemed confused ?
Can you explain in one line , why this is so ?
After some time my bored friend said to me, "Hey, do you know that there are an even number of odd persons?" I replied, "Big deal ! there will be always an even number of odd persons". But still he seemed confused ?
Can you explain in one line , why this is so ?
Labels: thinktank, trickofmind
posted by Rajesh Lal at
9:15 AM
32 Comments:
test
because theirs only two people.
not because there are only two people, but because it takes two people for a handshake.
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2 odds make an even in addition
anonymous guy one above looks more confused than rajesh's friend who is counting the handshakes hahahaha !
odd personS, it is plural meaning more then one.. besides, it takes two p/p to shake hands
3rd Anonymous comment is right:
Everyone starts at zero handshakes, 2 people shake giving 2 'odd people'. Carrying on to infinity, there will always be an even number of odd people since it will always be +2, -2, or +0 'odd people'
Oh, and in answer to the real question: No, I can't do it on one line.
Here's the concept: two people shake hands, both shook ONE hand, you end up with two "odd people".
there is an even number of ppl in room, each person shakes odd amount of hands, if theres 4, then 4ppl shake 3 hands
what if he shakes hands with himself????????
Then he becomes a 'very odd person'.
Ha! That's rich! I can't explain it in one line. But...when an odd person shakes with an odd person, they both become even, so the number of odd people decrease by two. When an even person shakes with an even person, they both become odd so the number of odd people increase by two. When an odd person shakes with an even person, the odd becomes even and the even becomes odd, so the total number of odd people stay the same.
The comment about 'very odd person' was very good, though!
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(It didn't come out right in the above post so let me try again)
If I am in a room with 9 other people, that makes 10 of us, an even number of people. We all shake hands with the other 9 people in the room, making an odd number of handshakes.
And this would be reversed if the number of people in the room was an even number. Then there would be an odd number of handshakes.
is he asking why he was confused?
because an even number of odd people is a hard sentence to wrap your mind around?
foochaz
What if one person in the room didn't shake hands with everyone else???
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(Again, I find something wrong in my initial post and have to do it again...sort of odd number of posters with even number of posts! LOL)
Now don't go confusing the issue Anonymous. ;-D
This could go either way. I tried it a couple ways, using 10 people...here goes.
10 ppl in room and 1 person shakes 4 hands...all others shake all remaining hands
1 > 4 (odd # of evens)
5 > 8 (odd # of evens)
4 > 9 (even # of odds)
Also,
10 ppl in room and 1 person shakes 3 hands...all others shake all remaining hands
1 > 3 (odd # of odds)
3 > 9 (odd # of odds)
6 > 8 (even # of evens)
So I supposed if you 'insist' on making things difficult, you could probably make it any combination...but basing it on 10 ppl shaking everyone else's hand, the even # of odds still stands.
But, the correct answer is still supposed to be in ONE LINE, so my answer is incorrect either way you look at it. :-(
odd numbers added always equal even numbers
It takes two people to make a handshake.
This is becasue x is an even number and y is the amount of handshakes they can make, y has to equal x-1!
there has to be 2 people to shake hands
I didn't really take the time to go through and read all of the comments, so forgive me if I'm repeating someone's answer.
That said, there will always be an even number of odd persons, in any room:
There are three types of handshakes:
Even-even, Odd-odd, and Even-odd.
In an even-even handshake, two people who are "even people" shake each other's hand, both becoming "odd people", thus increasing the number of "odd people" by two, and not changing the evenness of the number.
In an odd-odd handshake, the opposite happens, both odd people become even people, and the number of odd people decreases by two, still not changing the evenness of the number.
And finally in an odd-even handshake, the two people switch roles, giving zero net change.
In review, after every handshake the number of "odd people" in the room can only change +2, -2, or +0 with a single handshake.
Since at the start of the event all people are "even people" (0 handshakes) and there are zero "odd people," the number will always be even.
D'oh! Can you explain it in one line?
At the start of the party the number of "odd people" is even, and through every subsequent handshake the number increases by two, decreases by two, or stays the same and all these three changes maintain evenness.
Sorry about that :)
ANSWER
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Total Number of handshakes (EVEN) = Sum of Handshakes of Even Persons (EVEN) by definition + Sum of Handshakes by ODD Persons (Has to be EVEN)* ,because EVEN = EVEN + EVEN
Detail
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* Because you cannot add odd numbers, odd number of time to get an even number, So the total number of Odd persons has to be EVEN to make the sum of handshakes EVEN, Only assumption here is you are not counting the handshake with yourself
GOT RIGHT
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A FEW OF you were close, the question was a bit tricky to capture in one line
Chuma, judy and daniel's analysis were reasonabaly close
Daniel has it right, just over explained.
you cant shake your own hand.
if there are 20ppl then they each shake 19 hands.
it's not necessarily true.
You, him and me in the party. I shake your hand:
2 odd people, 1 even person
I leave because the party is not going to get any better than this..
1 odd person, 1 even person
-Peji
nice catch peji. but if u wanna look at the other side of it lol, the guy thats at a party with only one other person is pretty odd himself, unless its a bedroom party with a secret password.
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