Simple but not so simple

[tim-from-pa]

The answer is (10 choose 2) = 10 * 9 / 2 = 45. Each of the 10 people shakes hands with 9 others, but this counts every handshake twice, once for each person, so we need to divide 90 by 2.

Mathguy is correct. There are 45. In statistics, this is a classical problem of what they call "10 choose 2" or in everyday language, how many ways can you pair 10 objects (or people in this case ), and is mathematically written 10!/2!8!

Another way to think of this is: Line everyone up. The first guy gets out of the line and shakes hands with 9 others. That's 9. Now since he shook with everyone, drop him out. Now the next guy gets out of line and shakes hands with the remaining 8. Drop him out. Now the next one with the remaining 7, etc so this becomes 9+8+7+6+ ... +1=45.

The bible plays with such numbers as well. For example, Note that 153 and 666 are sums of consecutive numbers.

 

[Vanguard]

Mathguy is correct. There are 45. In statistics, this is a classical problem of what they call "10 choose 2" or in everyday language, how many ways can you pair 10 objects (or people in this case ), and is mathematically written 10!/2!8!

Another way to think of this is: Line everyone up. The first guy gets out of the line and shakes hands with 9 others. That's 9. Now since he shook with everyone, drop him out. Now the next guy gets out of line and shakes hands with the remaining 8. Drop him out. Now the next one with the remaining 7, etc so this becomes 9+8+7+6+ ... +1=45.

This, however, is based on knowing exact data. Let's look at the X factors:

1. What if they did a double hand shake with each person?
2. What if someone was missing a hand or arm?
3. Does a prosthetic hand or arm count, or are we talking about flesh only?
4. What time period are we in? Some people were not counted as a whole person.
5. What if someone had a multiple personality disorder?
6. What if someone has a genetic mutation and had two independent heads?

(queue the Twilight Zone music...or at least some Alfred Hitchcock)

 

[thisnumbersdisconnected]

1. What if they did a double hand shake with each person?

Unlikely, unless they are in the same fraternity.

2. What if someone was missing a hand or arm?

They usually shake with the opposite hand.

3. Does a prosthetic hand or arm count, or are we talking about flesh only?

A handshake is a handshake is a handshake.

4. What time period are we in? Some people were not counted as a whole person.

"People" does not indicate and half- or three-fifths of a person.

5. What if someone had a multiple personality disorder?

Only one personality can "come out" at a time (and it is now called dissociative disorder, and I still don't believe it).

6. What if someone has a genetic mutation and had two independent heads?

"They" still only got one set of hands.

(queue the Twilight Zone music...or at least some Alfred Hitchcock)

No, "Pop Goes the Weasel" came to my mind after reading your post.

 

[Classik]

Someone must win this today:bigfrown

 

[tim-from-pa]

Someone must win this today:bigfrown

Based on the OP, the (reasonable) assumption regarding the information given is that each person shakes hands with the other and the question can be regarded as how many handshaking combinations (or pairs) of persons are possible? Those of us who said 45 are correct, and thus won the question.

I trust you don't consider jokingly "x factors" as posted above, because then it ceases to be a brainteaser, but rather playful foolishness if such information was not given.

 

[Classik]

45? My goodness!!!

 

[Classik]

Matthew 13:20-21 *************20 The seed falling on rocky ground refers to someone who hears the word and at once receives it with joy. 21 But since they have no root, they last only a short time. When trouble or persecution comes because of the word, they quickly fall away.

 

[Classik]

90! Didn't someone say 90 before?;) :toofunny. Only the consistent minds eat from the classikalised dinning.

 

[Classik]

Actually any option outside this is totally fatal: A. 100 B. 20 C. 45 D. 50 E. 90