This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
references: | |
https://www.facebook.com/groups/391950357895182/permalink/1748946985528839/ | |
https://www.puzzlefun.online/problems | |
https://erich-friedman.github.io/mathmagic/0802.html | |
For each N, try to pack 1 1x1 square, 2 2x2 squares, 3 3x3 squares, 4 4x4 squares, ..., N NxN squares into a N*(N+1)/2xN*(N+1)/2 square | |
The goal is to omit as little area as possible. (e.g. omitting 1 2x2 and 2 3x3s means that a total area of 4+9+9 is omitted) | |
Here are the optimal results for small N: |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
FILN;PUXY;TVWZ | |
.000002. | |
22212221 | |
20111021 | |
20010011 | |
00220221 | |
11120122 | |
10122112 | |
.000011. |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
FIL;NPVWX;TUYZ | |
00000112 | |
11121122 | |
12221002 | |
120..012 | |
000..011 | |
10221021 | |
11211121 | |
11221222 |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
basis = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 } | |
46 PTs with legs < 10^9 are listed below. | |
{0,1,0,1,1,1,1,1,0,1,0,0} -- this coloring scheme avoids mono-coloring all 46 PTs | |
(parity of [dot product of this with vector-form of number] determines the number's color) | |
--- | |
12 {2,1,0,0,0,0,0,0,0,0,0,0} | |
35 {0,0,1,1,0,0,0,0,0,0,0,0} |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
primitive pythagorean triples using only factors of { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41 } | |
and legs < 10^9 | |
12 35 37 | |
12 5 13 | |
132 475 493 | |
84 187 205 | |
84 13 85 | |
156 133 205 | |
204 253 325 |
This file has been truncated, but you can view the full file.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
01 {33,56,65} * {15,8,17} + 1073 {264,448,495,520,561,840,952,975,1105,1073} | |
11 {13,84,85} * {9,40,41} + 925 {117,520,533,756,765,3360,3400,3444,3485,925} | |
01 {153,104,185} * {13,84,85} + 9061 {1352,1989,2405,8736,8840,12852,13005,15540,15725,9061} | |
10 {161,240,289} * {187,84,205} + 38675 {13524,20160,24276,30107,33005,44880,49200,54043,59245,38675} | |
01 {297,304,425} * {105,208,233} + 77393 {31185,31920,44625,61776,63232,69201,70832,88400,99025,77393} | |
01 {153,104,185} * {105,88,137} + 21473 {9152,10920,13464,14248,16065,16280,19425,20961,25345,21473} | |
00 {185,672,697} |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
reference: https://dustingmixon.wordpress.com/2021/02/01/polymath16-seventeenth-thread-declaring-victory/#comment-46997 | |
mono-edge densities for n: (tentative) | |
3 - 0.333333 (or no solution) | |
4 - 0.416667 | |
5 - 0.538462 | |
6 - 0.571429 | |
7 - 0.633333 | |
8 - 0.666667 | |
9 - 0.701149 -- I only tried like 5 shapes |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
On the A2 lattice (triangular lattice -- each vertex has 6 neighbors), color the vertices | |
such that the density of mono edges is maximized. An edge is "mono" if its neighbors are | |
the same color. | |
A "forbidden shape" is also provided. No set of vertices in this shape can be all-the-same-color. | |
https://dustingmixon.wordpress.com/2021/02/01/polymath16-seventeenth-thread-declaring-victory/#comment-46576 | |
O O . . . . . |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
class PrimeSieve | |
{ | |
public: | |
PrimeSieve( int64_t n ) | |
{ | |
m.resize( n, true ); | |
m[0] = m[1] = false; | |
for ( int64_t i = 2; i * i < n; i++ ) if ( isPrime( i ) ) | |
for ( int64_t j = i*2; j < n; j += i ) | |
m[j] = false; |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
FLVX;IPYZ;NTUW | |
.001122. | |
00211122 | |
10200002 | |
12202221 | |
12011211 | |
10001201 | |
12021101 | |
.222000. |
NewerOlder