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Topic: You Can Turn but You Can't Hide (Read 909 times) |
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rloginunix
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You Can Turn but You Can't Hide
« on: Aug 27th, 2015, 8:06am » |
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You Can Turn but You Can't Hide
2N people located at the South-Western corner of a square grid start walking at a constant speed and at every intersection (including the initial one) the same process occurs:
- the group of people splits in half;
- one half turns and walks North;
- the other half turns and walks East;
What will the distribution of people be after all of them visit N intersections?
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towr
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Re: You Can Turn but You Can't Hide
« Reply #1 on: Aug 27th, 2015, 1:09pm » |
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Off the top of my head, pascal's triangle?
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rloginunix
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Re: You Can Turn but You Can't Hide
« Reply #2 on: Aug 27th, 2015, 2:46pm » |
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Dangit. Einstein was wrong - you guys are faster than light.
In terms of N - which row?
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pex
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Re: You Can Turn but You Can't Hide
« Reply #3 on: Aug 27th, 2015, 5:32pm » |
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on Aug 27th, 2015, 2:46pm, rloginunix wrote:| In terms of N - which row? |
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The one that sums to 2N 
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rmsgrey
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Re: You Can Turn but You Can't Hide
« Reply #4 on: Aug 28th, 2015, 6:03am » |
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on Aug 27th, 2015, 2:46pm, rloginunix wrote:Dangit. Einstein was wrong - you guys are faster than light.
In terms of N - which row? |
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Depends how you number the rows.
If you number the start row (1) as row 1, then row N+1; if you number the start row as 0, and the next row (1,1) as 1, then row N. I believe the latter is more standard since it means row n corresponds to the relevant power of the binomial expansion
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rloginunix
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Re: You Can Turn but You Can't Hide
« Reply #5 on: Aug 28th, 2015, 8:09am » |
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Minor detail of course but no C(2, 1) ways about it - pex++ for a shrewd observation and rmsgrey covered it thoroughly. The (1975) book gives (N + 1)-st row but I'd rather go with N-th.
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Grimbal
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Re: You Can Turn but You Can't Hide
« Reply #6 on: Aug 31st, 2015, 8:46am » |
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As a C and Java programmer I know 0-based ordinals is the most natural way to go. 
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rloginunix
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Re: You Can Turn but You Can't Hide
« Reply #7 on: Aug 31st, 2015, 3:17pm » |
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(Patterns, patterns. As a C/Java (Solaris/CentOS) programmer I concur)
Just a thought - a 3D extension:
3N people walk through a cubic lattice made up of unit cubes. At each intersection they split into three equally sized groups ...
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pex
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Re: You Can Turn but You Can't Hide
« Reply #8 on: Aug 31st, 2015, 8:11pm » |
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on Aug 31st, 2015, 3:17pm, rloginunix wrote:(Patterns, patterns. As a C/Java (Solaris/CentOS) programmer I concur)
Just a thought - a 3D extension:
3N people walk through a cubic lattice made up of unit cubes. At each intersection they split into three equally sized groups ... |
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Guess what: this is called Pascal's tetrahedron
on Aug 31st, 2015, 8:46am, Grimbal wrote:| As a C and Java programmer I know 0-based ordinals is the most natural way to go. |
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Ah, but does "natural" include zero...?
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towr
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Re: You Can Turn but You Can't Hide
« Reply #9 on: Aug 31st, 2015, 10:17pm » |
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on Aug 31st, 2015, 8:11pm, pex wrote:| Ah, but does "natural" include zero...? |
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Naturally. If convenient.
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rloginunix
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Re: You Can Turn but You Can't Hide
« Reply #10 on: Sep 1st, 2015, 10:45am » |
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Dangit again. No PhD in Pascal's anything.
nD? nN people walk ...
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Grimbal
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Re: You Can Turn but You Can't Hide
« Reply #12 on: Sep 2nd, 2015, 2:13am » |
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1N people located at the West end of a 1-dimensional grid start walking at a constant speed and at every grid point (including the initial one) the same process occurs:
- the group of people splits in one;
- the resulting group walks East;
What will the distribution of people be after all of them visit N intersections?
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rloginunix
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Re: You Can Turn but You Can't Hide
« Reply #13 on: Sep 2nd, 2015, 10:19am » |
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Absolutely cool but dangit3 - I either can not catch a break or great minds think alike, 
What is the date on the Potsdam article? Thanks.
Grimbal's problem:
- split 1N people into (n > 1)N elementary (hyper) particles;
- split the West end of a 1-dimensional grid into a crystalline (hypercubic) lattice;
- apply the previously obtained solutions;
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towr
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Re: You Can Turn but You Can't Hide
« Reply #14 on: Sep 2nd, 2015, 11:10am » |
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on Sep 2nd, 2015, 10:19am, rloginunix wrote:| What is the date on the Potsdam article? Thanks. |
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The document properties say the creation date was "11/4/2003, 4:31:15 PM", whether that's April 11th or November 4th, I don't know.
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