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Results for "integer linear programming"
Search options not deleted
2
votes
Tiling a 16x16 square with 1x4 rectangles
Via integer linear programming, the maximum is...
1 1 1 1 2 2 2 2 37 38 3 3 3 3 39 40
4 4 4 4 5 5 5 5 37 38 6 6 6 6 39 40
7 7 7 7 8 8 8 8 37 38 41 42 43 44 39 40 …
- 15.7k
2
votes
Accepted
An 18-Letter Challenge-A: three 6-letter words, with limitations
Via integer linear programming, the unique solution is …
- 15.7k
4
votes
6x6 grid with no three cells of one colour in a line
Via integer linear programming, the minimum number of monochromatic lines is …
- 15.7k
3
votes
3x3 grid with no isosceles triangles of the same colour
Via integer linear programming, the minimum number of monochromatic isosceles triangles is …
- 15.7k
5
votes
Accepted
New maths puzzle
Here's the unique solution, obtained via integer linear programming:
I used SAS:
proc optmodel;
set ROWS = 1..12;
set COLS = ROWS;
num a {ROWS, COLS} = [
18 14 18 18 4 17 5 14 6 4 17 …
- 15.7k
7
votes
Splitting the integers 1 to 36
Via integer linear programming, the largest $|A|$ is
and the smallest $|A|$ is …
- 15.7k
2
votes
Accepted
Ying Yang 12x12 - Colombian Sudoku
Via integer linear programming, using the formulation described in my answer https://puzzling.stackexchange.com/a/128031/65277: …
- 15.7k
5
votes
Three white queens, two white knights, and one rook on a chess board
I used integer linear programming (and, sorry, a computer):
The solution is unique up to rotation and reflection. …
- 15.7k
5
votes
3 Colors of Chess Pieces Attacking Each Other Once Each
Via integer linear programming, the maximum for knights is
The maximum for queens is at least
Other maxima are …
- 15.7k
3
votes
Maximum number of kings that can exit
Via integer linear programming, I found a solution that uses
and all such kings can exit in
Initial configuration:
Covered squares:
Animation: …
- 15.7k
22
votes
Accepted
Three queens and two rooks covering the chess board... again!
I used integer linear programming to minimize the number of unattacked squares. Here is one optimal solution (unique up to symmetry), with …
- 15.7k
3
votes
Accepted
Scheduling Meetings
Via mixed integer linear programming, I found a solution that uses $76$ meetings and has a total waste of $4230 + 1900 + 45 = 6175$:
1 : 1516 3432
2 : 303 363 2339 3120 3400
3 : 4134
4 : 476 836 1567
5 …
- 15.7k
7
votes
General attacking chessboard squares
Via integer linear programming, as in https://puzzling.stackexchange.com/a/102587/65277,
here's another $8\times 8$, with
And another $9\times 9$, with …
- 15.7k
3
votes
Can you use all 26 letters across four 7-letter words?
Via integer linear programming (https://puzzling.stackexchange.com/a/123475/65277), I found that the maximum is
There are 515 such optimal solutions, such as: …
- 15.7k
15
votes
Accepted
A Perfect Diamond of Numbers
Four circles:
Five circles:
Six circles:
I used mixed integer linear programming to find these optimal solutions, and the first several optimal values are: …
- 15.7k