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        riddles >> easy >> You Can Turn but You Can't Hide
        
(Message started by: rloginunix on Aug 27^th, 2015, 8:06am)

Title: You Can Turn but You Can't Hide
Post by rloginunix on Aug 27^th, 2015, 8:06am

You Can Turn but You Can't Hide
2^N 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?

Title: Re: You Can Turn but You Can't Hide
Post by towr on Aug 27^th, 2015, 1:09pm

[hide]Off the top of my head, pascal's triangle?[/hide]

Title: Re: You Can Turn but You Can't Hide
Post by rloginunix on Aug 27^th, 2015, 2:46pm

Dangit. Einstein was wrong - you guys are faster than light.

In terms of N - which row?

Title: Re: You Can Turn but You Can't Hide
Post by pex on Aug 27^th, 2015, 5:32pm

on 08/27/15 at 14:46:15, rloginunix wrote:

In terms of N - which row?

The one that sums to 2^N 8)

Title: Re: You Can Turn but You Can't Hide
Post by rmsgrey on Aug 28^th, 2015, 6:03am

on 08/27/15 at 14:46:15, rloginunix wrote:

Dangit. Einstein was wrong - you guys are faster than light.

In terms of N - which row?

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

Title: Re: You Can Turn but You Can't Hide
Post by rloginunix on Aug 28^th, 2015, 8:09am

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.

Title: Re: You Can Turn but You Can't Hide
Post by Grimbal on Aug 31^st, 2015, 8:46am

As a C and Java programmer I know 0-based ordinals is the most natural way to go. :P

Title: Re: You Can Turn but You Can't Hide
Post by rloginunix on Aug 31^st, 2015, 3:17pm

(Patterns, patterns. As a C/Java (Solaris/CentOS) programmer I concur)

Just a thought - a 3D extension:

3^N people walk through a cubic lattice made up of unit cubes. At each intersection they split into three equally sized groups ...

Title: Re: You Can Turn but You Can't Hide
Post by pex on Aug 31^st, 2015, 8:11pm

on 08/31/15 at 15:17:28, rloginunix wrote:

Guess what: this is called [hide]Pascal's tetrahedron (https://en.wikipedia.org/wiki/Pascal's_tetrahedron)[/hide]

on 08/31/15 at 08:46:39, Grimbal wrote:

As a C and Java programmer I know 0-based ordinals is the most natural way to go. :P

Ah, but does "natural" include zero...?

Title: Re: You Can Turn but You Can't Hide
Post by towr on Aug 31^st, 2015, 10:17pm

on 08/31/15 at 20:11:36, pex wrote:

Ah, but does "natural" include zero...?

Naturally (http://mathworld.wolfram.com/NaturalNumber.html). If convenient.

Title: Re: You Can Turn but You Can't Hide
Post by rloginunix on Sep 1^st, 2015, 10:45am

Dangit again. No PhD in [hide]Pascal's[/hide] anything.

nD? n^N people walk ...

Title: Re: You Can Turn but You Can't Hide
Post by towr on Sep 1^st, 2015, 1:00pm

Sure, let's get hyper (http://arxiv.org/ftp/math/papers/0311/0311035.pdf)

Title: Re: You Can Turn but You Can't Hide
Post by Grimbal on Sep 2^nd, 2015, 2:13am

1^N 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?

:P

Title: Re: You Can Turn but You Can't Hide
Post by rloginunix on Sep 2^nd, 2015, 10:19am

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 1^N 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;

Title: Re: You Can Turn but You Can't Hide
Post by towr on Sep 2^nd, 2015, 11:10am

on 09/02/15 at 10:19:22, rloginunix wrote:

What is the date on the Potsdam article? Thanks.

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.