August 2015
 

The problem is out...

[url]https://www.research.ibm.com/haifa/ponderthis/challenges/August2015.html[/url]

"Challenge: 02/08/2015 @ 12:00 PM EST"

This time is clearly wrong.
(in the past it was also wrong, in general came out earlier, there should be a much better policy on this)

Note that the July problem is still living!

[QUOTE=R. Gerbicz;406740]The problem is out...

[url]https://www.research.ibm.com/haifa/ponderthis/challenges/August2015.html[/url]

[/QUOTE]
Shouldn't there be a length for the string? Otherwise, how many points are you going to give?

Also, maybe some restriction on the values of the coordinates? Otherwise it would be trivially solvable (straight line).

[QUOTE=axn;406780]Shouldn't there be a length for the string? Otherwise, how many points are you going to give?

Also, maybe some restriction on the values of the coordinates? Otherwise it would be trivially solvable (straight line).[/QUOTE]

OK, you are tricky. So to restrict the problem:
find a simple, closed polygonal chain (ref. [url]https://en.wikipedia.org/wiki/Polygonal_chain[/url]), so p[0],p[1],...,p[n], where
p[i]==p[j] if and only if i=0,j=n or i=n,j=0. And n>1, the rest is the same p[i] is an integer point in 3D, in p[0],p[1],..,p[n] each (consecutive!) pair differs in exactly one coordinate and all three projections should be loop-free.

(You can see that you can get these simple closed polygonal chains by folding a loop.)

There is no given length for the string, so you can use any (finite) value of n. And no restriction for the coordinate values.

:doh!: Missed the "[B]loop[/B] of string" bit. So basically, starting point = end point.

I saw August 2015 problem yesterday,
and I tried to solve the problem with many different ways.
However, I could not figure out the solution.

If the loop is divided by two parts arbitrarily, then the two parts should be connected by at least two line segments.

In that case, I think that the two line segments always make a loop on at least one projection plane.

Therefore, I think that I misunderstood something...

How can I get close to the solution?

Never mind.

It was tricky and I solved.

:groupwave:

[url]https://www.research.ibm.com/haifa/ponderthis/solutions/August2015.html[/url]

My sent solution was:
"One solution:
[0,1,2],[0,0,2],[1,0,2],[1,1,2],[1,2,2],[0,2,2],[0,2,1],[1,2,1],[2,2,1],[2,2,2],[2,1,2],[2,1,1],[2,1,0],[2,2,0],[1,2,0],[1,1,0],[1,0,0],[2,0,0],[2,0,1],[1,0,1],[0,0,1],[0,0,0],[0,1,0],[0,1,1],[0,1,2]

To see the solution in Mathematica use:
Graphics3D[{Thick,
Line[{{0,1,2},{0,0,2},{1,0,2},{1,1,2},{1,2,2},{0,2,2},
{0,2,1},{1,2,1},{2,2,1},{2,2,2},
{2,1,2},{2,1,1},{2,1,0},{2,2,0},
{1,2,0},{1,1,0},{1,0,0},{2,0,0},
{2,0,1},{1,0,1},{0,0,1},{0,0,0},
{0,1,0},{0,1,1},{0,1,2}
}]}]

This was also a recent problem on Komal, see [url]http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=A638&l=hu[/url]

The book's picture shows the projections, one can easily verify that these projections are loop-free, so contains no cycle."

ps. for the English version see: [url]http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=A638&l=en[/url] (but it does not show the picture), there was only one solver on the competetion (it was on the math section), pretty hard problem.