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Stand behind your friend

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There is a crowd of people in a room. Each person is asked to select some other person in the room (without telling anyone). At a signal, every person tries to approach the selected person and stand behind his/her back. What patter would emerge when "the dust settles"?

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16 answers to this question

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Posted · Report post

The more attractive people would have more people behind their backs

:blink:
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Posted · Report post

Two of them may be continuously moving in circle

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Posted · Report post

Two of them may be continuously moving in circle

Or possibly standing back to back.

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Posted · Report post

Two of them may be continuously moving in circle

Or possibly standing back to back.

on the right track. think of how stasis would look (the steady state).

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Posted · Report post

If more than two people are involved in a loop, then you might have people standing in a triangle or higher order polygon, each pointing their back toward another.

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Posted · Report post

A tree structure.

Some people would not have been chosen.
They would be the leaf nodes of the tree branches.

Note, since they have chosen someone, there are not isolated persons.

Some people would have been chosen by more than one other person.
They would be branch points.

Everyone else would have been chosen by exactly one other person.
They would form the body of each branch.

Some branches will be re-entrant (cyclical.).

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Posted · Report post

At least if you only need to stand anywhere along the line behind the chosen person, and not necessarily immediately behind them and having to squeeze in with multiple people.

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Posted · Report post

At least if you only need to stand anywhere along the line behind the chosen person, and not necessarily immediately behind them and having to squeeze in with multiple people.

Yes, it's a different result then. I took the "directly behind" interpretation.

It also took a second to see "patter" meant "pattern"

I'm thinking there is further richness (or simplicity) in the solution,

my answer was in the manner of first thoughts.

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Posted (edited) · Report post

At least if you only need to stand anywhere along the line behind the chosen person, and not necessarily immediately behind them and having to squeeze in with multiple people.

Yes, it's a different result then. I took the "directly behind" interpretation.

It also took a second to see "patter" meant "pattern"

I'm thinking there is further richness (or simplicity) in the solution,

my answer was in the manner of first thoughts.

Yes, the OP intended the individuals to move directly behind the person they identified.

The answer has been given by one of the participants here but i will hold off a little longer in siding with a particular answer to allow some additional thinking on the problem.

Edited by BMAD
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Posted · Report post

Suppose someone near the "root" decided to stand behind someone on a "branch".

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Posted (edited) · Report post

I got sort of a combination of the answers given thus far. There will be several "islands" of people, each composed of a circle of people (or just two people standing back to back) and then trees branching off the circle.

Edited by gavinksong
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Posted · Report post

tradingpit20.jpg

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Posted · Report post

:thumbsup: k-man, do you have an equation for that?

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:thumbsup: k-man, do you have an equation for that?

Yeah, but It took me a while to find it...

3equations.jpg

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hahaha.

Essentially what Bonanova and some others have noted about this puzzle is pretty much correct. If one were to run repeated simulations you would see this kind of hive/honeycomb formations occur with an occasional loose pieces.

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I think gavinksong's description was best.

k-man, the guy should insert a tat saying "What about" above, and "don't you understand?" below.

Looks like a proof of the Riemann Hypothesis.

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