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Search: Posts Made By: EdPeggJr
Forum: Puzzles 2017-01-07, 00:22
Replies: 44
Views: 10,644
Posted By EdPeggJr
Your solution for a(26) here uses each rectangle...

Your solution for a(26) here uses each rectangle exactly twice, with all in different orientations. I have a similar solution for a(10), and no others.
Forum: Puzzles 2017-01-05, 17:56
Replies: 44
Views: 10,644
Posted By EdPeggJr
Many of those are unexpectedly wild. I didn't...

Many of those are unexpectedly wild. I didn't foresee the variant solution for 18 to have such a range.

I imagine the ranges for the standard problem will be much tamer by comparison.
Forum: Puzzles 2017-01-04, 16:23
Replies: 44
Views: 10,644
Posted By EdPeggJr
If it would be easy, for values up to 24 or so...

If it would be easy, for values up to 24 or so (or whatever is easy), could you post solutions optimized for the most rectangles instead of the least rectangles?

For example, in the Variant for...
Forum: Puzzles 2017-01-02, 18:05
Replies: 44
Views: 10,644
Posted By EdPeggJr
Very interesting solutions. This time, I already...

Very interesting solutions. This time, I already managed to find some of those optimal solutions already, but it's good to have all of them. Which one of those required the most time to find?
Forum: Puzzles 2016-12-30, 02:36
Replies: 44
Views: 10,644
Posted By EdPeggJr
Thanks for the note. I've updated a(101). ...

Thanks for the note. I've updated a(101).

Any chance you can beat my a(99) = 27? That's my only value under 100 that goes past my upper bound. Another that might be easy to beat is a(60)=18.
Forum: Puzzles 2016-12-28, 21:45
Replies: 44
Views: 10,644
Posted By EdPeggJr
The new solutions amaze me. Mostly because I...

The new solutions amaze me. Mostly because I came so close to the correct solutions with my non-optimal code. For 45-57, you gave improvements of 1,2,3,1,4,2,1,3,2,1,1,1,1 over my best solutions. ...
Forum: Puzzles 2016-12-16, 04:03
Replies: 44
Views: 10,644
Posted By EdPeggJr
https://oeis.org/A279596

https://oeis.org/A279596
Forum: Puzzles 2016-12-14, 05:32
Replies: 44
Views: 10,644
Posted By EdPeggJr
Great! I did find some of these earlier, and I...

Great! I did find some of these earlier, and I found 5 and 12 today while I was doing some polishing, but I was far from getting the optimal results for quite a few of them. The current best...
Forum: Puzzles 2016-12-12, 16:49
Replies: 44
Views: 10,644
Posted By EdPeggJr
In the variant problem, divide a square of size N...

In the variant problem, divide a square of size N into rectangles so that no rectangles are translations of each other. Minimize the difference between the largest area and smallest area. Basically,...
Forum: Puzzles 2016-12-08, 16:49
Replies: 44
Views: 10,644
Posted By EdPeggJr
What a difference a good overnight run can make. ...

What a difference a good overnight run can make. I've found a good solution for square 61, and many other squares. Current values to a(120) are as follows:

x, x, 4, 2, 3, 2, 2, 1, 2, 0, 2, 1, 1,...
Forum: Puzzles 2016-12-08, 04:25
Replies: 44
Views: 10,644
Posted By EdPeggJr
Sequence https://oeis.org/A278970 is known up to...

Sequence https://oeis.org/A278970 is known up to a(44). Here are currently known best values up to 120.
x, x, 4, 2, 3, 2, 2, 1, 2, 0,
2, 1, 1, 3, 1, 1, 2, 2, 2, 1,
1, 2, 3, 2, 1, 2, 2, 3,...
Forum: Puzzles 2016-12-02, 20:34
Replies: 44
Views: 10,644
Posted By EdPeggJr
One amusing method for tackling large squares...

One amusing method for tackling large squares occurred to me.

1. Compile a catalog of perfect k-rectangle Blanche dissections of the unit square for various k from 7 to 16. Each rectangle in a...
Forum: Puzzles 2016-12-02, 19:36
Replies: 44
Views: 10,644
Posted By EdPeggJr
So far, we seem to have the sequence 2, 4,...

So far, we seem to have the sequence
2, 4, 4, 5, 5, 6, 6, 8, 6, 7, 8, 6, 8, 8, 8, 8, 8, 9, 9, 9, 8, 9, 10, 9, 10, 9, 9, 11, 11, 10, 12, 12, 11, 12, 11, 10, 11, 12, 13, 12, 12

I also have...
Forum: Puzzles 2016-12-02, 17:29
Replies: 44
Views: 10,644
Posted By EdPeggJr
The new solutions look great. I'll need to...

The new solutions look great. I'll need to incorporate them.

I made a poster out of solutions to size 32. http://community.wolfram.com/groups/-/m/t/973362

In talks with Hannes Bassen,...
Forum: Puzzles 2016-12-01, 05:12
Replies: 44
Views: 10,644
Posted By EdPeggJr
I've posted an update of my own results to 999 at...

I've posted an update of my own results to 999 at
http://demonstrations.wolfram.com/MondrianArtProblem/

My method for these high numbers is to create perfect Blanche dissections using some of...
Forum: Puzzles 2016-11-29, 19:44
Replies: 44
Views: 10,644
Posted By EdPeggJr
Many thanks for the improved solutions. I found...

Many thanks for the improved solutions. I found a few bugs in my coding. I'll be posting an update at http://demonstrations.wolfram.com/MondrianArtProblem/ in the near future.
Showing results 1 to 16 of 16

 
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