Mythic squares/rectangles - Page 6

Till · 2018-09-03, 15:30

Quote:

Originally Posted by science_man_88

if my counting is correct an absolute upper bound on 10 by 10 is 647 but that's likely unreachable. edit: okay plugging the math in PARI/GP gives 675 but that's still not 4 digits. 11 by 11 gives 819, 12 by 12 gives 979, and 13 by 13 breaks 1100 but again duplicates will.lower these.

I also get 675 for best packings in 10x10 base 10, not considering palindromes:
* rows -> 8*10 = 80, counting reverses -> 160
* same for columns -> 160
* diagonals -> (1+2+...+8) + (1+2+...+7) = (72/2 + 56/2) = 64, counting reverses -> 128
* same for antidiagonals -> 128
------------------------------------------------
sum = 576

the first 99 scores are free -> total = 576 + 99 = 675

But now we still need to subtract the number of palindromes > 100 in the range.

So I think your first number (647) looks better.

science_man_88 · 2018-09-03, 15:36

Quote:

Originally Posted by Till

I also get 675 for best packings in 10x10 base 10, not considering palindromes:
* rows -> 8*10 = 80, counting reverses -> 160
* same for columns -> 160
* diagonals -> (1+2+...+8) + (1+2+...+7) = (72/2 + 56/2) = 64, counting reverses -> 128
* same for antidiagonals -> 128
------------------------------------------------
sum = 576

the first 99 scores are free -> total = 576 + 99 = 675

But now we still need to subtract the number of palindromes > 100 in the range.

So I think your first number (647) looks better.

50 palindromes under 600 but above 100 gives 625 which then has 2 more palindromes under it so 623 is closer. 11 by 11 falls to 755, 12 by 12 to 899, 13 by 13 to 1065 (1437 if you include 4 digits)

Till · 2018-09-03, 16:57

Yep, looks better

But as you mentioned, probably the upper bounds are still far too high...

science_man_88 · 2018-09-03, 17:39

Quote:

Originally Posted by Till

Yep, looks better

But as you mentioned, probably the upper bounds are still far too high...

Yeah , another consideration is the earlier bounds minus 99, work for all bases because all they count, is the number of sets of three that are on diagonal or straight across/(up/down) . There may be 61440 three hexit, hexadecimal numbers only 576 of these will fit into a 10 by 10 square at most. Wonder if pigeonhole principle can help eliminate duplicates in it's probabilistic form perhaps.

R. Gerbicz · 2018-09-03, 20:15

Quote:

Originally Posted by Till

I also get 675 for best packings in 10x10 base 10, not considering palindromes:.

My best upper bound is much better: 505 for m=n=10;base=10.
The simple idea is that we need a new "line" (row/column/diagonal) for x, if
x%base=0 or x<=reverse(x,base), when we consider the x numbers from [10^(L-1),10^L) interval in increasing order.

science_man_88 · 2018-09-03, 20:38

Quote:

Originally Posted by R. Gerbicz

My best upper bound is much better: 505 for m=n=10;base=10.
The simple idea is that we need a new "line" (row/column/diagonal) for x, if
x%base=0 or x<=reverse(x,base), when we consider the x numbers from [10^(L-1),10^L) interval in increasing order.

yeah I wasn't really considering reversal for my bound but I know there's only 504 numbers you need under 1000 for all the reversals to be there as well. partly how I did my checking actually.

Till · 2018-09-04, 20:25

Here is my update. I found new base 10 top scores for many entries with m>=6, nothing new for m<6.

Summary of best base 10 results: (increment on Robert's table)

Code:

 x |    1    2    3    4    5    6    7    8    9   10
---+--------------------------------------------------
 1 |    1    2    3    4    5    6    7    8    9   10
 2 |         4    6    8   10   21   32   37   46   54
 3 |              9   26   38   48   66   78   98  104
 4 |                  43   65   88  104  116  125  132
 5 |                       98  108  126  136  149  161
 6 |                           128  142  157  171  184
 7 |                                157  176  193  207
 8 |                                     194  211  234
 9 |                                          237  256
10 |                                               284

m=1;n=1;base=10;score=1;
1

m=1;n=2;base=10;score=2;
1 2

m=1;n=3;base=10;score=3;
2 1 3

m=1;n=4;base=10;score=4;
3 1 4 2

m=1;n=5;base=10;score=5;
1 3 5 4 2

m=1;n=6;base=10;score=6;
5 1 4 2 6 3

m=1;n=7;base=10;score=7;
7 3 2 5 4 6 1

m=1;n=8;base=10;score=8;
8 7 2 1 5 4 6 3

m=1;n=9;base=10;score=9;
1 4 6 2 9 5 3 7 8

m=1;n=10;base=10;score=10;
6 8 7 4 3 1 0 2 5 9

m=2;n=2;base=10;score=4;
2 3
1 4

m=2;n=3;base=10;score=6;
6 5 1
2 4 3

m=2;n=4;base=10;score=8;
5 3 1 6
7 4 8 2

m=2;n=5;base=10;score=10;
7 5 0 1 4
9 8 2 3 6

m=2;n=6;base=10;score=21;
9 1 0 7 4 5
6 2 8 3 1 1

m=2;n=7;base=10;score=32;
8 1 0 3 4 2 5
6 2 1 9 2 1 7

m=2;n=8;base=10;score=37;
3 1 2 6 3 7 2 8
4 2 1 0 3 5 1 9

m=2;n=9;base=10;score=46;
1 7 2 5 4 0 3 2 1
1 8 3 6 1 4 2 3 9

m=2;n=10;base=10;score=54;
2 0 1 4 6 3 4 7 3 2
3 5 4 1 9 2 1 8 2 3

m=3;n=3;base=10;score=9;
1 9 5
3 7 4
6 8 2

m=3;n=4;base=10;score=26;
9 6 5 2
8 1 2 3
7 4 1 0

m=3;n=5;base=10;score=38;
3 5 4 7 3
1 3 2 1 6
1 0 8 2 9

m=3;n=6;base=10;score=48;
5 3 4 6 2 5
8 4 0 3 1 2
1 2 7 1 3 9

m=3;n=7;base=10;score=66;
1 3 3 7 1 2 5
6 0 5 4 2 1 8
2 6 4 5 9 3 4

m=3;n=8;base=10;score=78;
5 8 2 2 1 4 8 3
1 5 6 3 0 7 4 9
9 1 3 6 7 5 2 6

m=3;n=9;base=10;score=98;
3 4 7 7 9 2 4 8 5
3 0 4 8 3 5 2 6 5
6 9 1 1 8 0 1 7 6

m=3;n=10;base=10;score=104;
8 2 3 9 9 2 2 1 9 7
6 8 4 6 5 7 0 0 1 8
6 1 0 4 7 3 3 1 5 5

m=4;n=4;base=10;score=43;
8 2 5 3
2 1 0 7
9 4 1 2
8 3 3 6

m=4;n=5;base=10;score=65;
9 2 8 1 1
5 4 3 5 9
4 6 7 3 5
0 1 2 2 0

m=4;n=6;base=10;score=88;
9 3 0 6 9 1
2 5 3 4 7 1
6 1 8 7 4 5
6 8 0 2 2 5

m=4;n=7;base=10;score=104;
3 7 6 3 3 1 6
0 9 2 4 5 8 6
1 0 4 2 8 5 0
1 0 1 7 7 9 9

m=4;n=8;base=10;score=116;
3 3 4 8 6 7 2 4
5 4 9 0 1 3 7 2
6 9 1 0 1 0 8 5
7 6 2 1 1 1 5 8

m=4;n=9;base=10;score=125;
4 8 6 6 5 1 7 7 4
5 2 1 0 1 1 0 4 6
5 7 1 1 0 2 1 3 9
9 3 8 8 9 1 2 3 9

m=4;n=10;base=10;score=132;
7 6 1 1 3 1 1 1 1 1
8 1 0 2 1 3 0 1 2 5
8 0 1 1 2 4 5 7 6 9
3 9 9 4 8 5 4 6 7 3

m=5;n=5;base=10;score=98;
7 7 9 2 3
5 4 2 5 1
5 0 6 8 1
1 7 8 6 9
4 4 3 3 0

m=5;n=6;base=10;score=108;
3 1 2 5 6 1
3 0 5 2 8 0
1 0 1 7 9 8
1 0 7 9 3 4
4 4 6 6 5 2

m=5;n=7;base=10;score=126;
7 6 1 1 8 8 1
7 1 2 0 1 4 2
4 2 1 1 0 9 5
4 3 0 1 7 8 9
6 6 5 5 3 3 6

m=5;n=8;base=10;score=136;
5 6 7 1 3 4 4 7
4 5 2 3 1 2 0 1
9 8 1 1 2 1 0 1
7 8 0 1 3 0 2 0
7 3 6 6 9 5 9 9

m=5;n=9;base=10;score=149;
6 6 9 9 8 6 7 9 5
2 0 1 3 2 1 4 3 1
1 4 1 2 1 1 0 1 1
4 2 1 4 0 0 1 3 3
5 5 7 7 8 8 5 6 1

m=5;n=10;base=10;score=161;
1 6 7 8 8 5 1 3 7 9
6 4 3 1 2 6 3 2 4 8
1 1 5 1 0 1 1 1 4 1
1 5 0 1 5 3 2 4 0 1
7 7 6 9 9 2 1 0 8 2

m=6;n=6;base=10;score=128;
4 7 3 3 4 4
8 6 0 1 2 0
6 8 1 1 0 1
3 5 0 1 2 8
5 9 2 2 9 6
4 7 7 1 1 9

m=6;n=7;base=10;score=142;
6 1 1 4 6 7 7 
6 0 4 2 9 8 3 
5 3 1 0 8 1 1 
5 1 1 2 1 3 3 
9 2 0 1 2 4 1 
9 3 1 0 7 5 8 

m=6;n=8;base=10;score=157;
9 9 7 7 6 8 8 7 
3 0 1 4 3 1 2 5 
1 3 1 1 5 1 4 1 
2 4 1 2 3 1 0 4 
9 2 0 0 1 5 5 8 
6 1 1 3 6 6 1 9 

m=6;n=9;base=10;score=171;
1 3 7 9 9 5 1 2 7
7 4 3 1 6 0 2 5 7
1 1 5 1 4 1 1 1 8
6 5 1 1 2 6 1 4 4
1 0 3 0 6 3 1 2 9
8 8 1 1 0 7 1 6 8

m=6;n=10;base=10;score=184;
5 1 9 9 1 1 9 1 5 1 
7 2 4 1 7 1 6 5 3 9 
1 4 1 6 0 2 1 8 1 0 
1 0 1 6 1 2 1 4 0 1 
3 7 8 5 3 7 3 1 5 7 
9 8 4 1 3 1 8 2 1 7 

m=7;n=7;base=10;score=157;
9 9 7 6 1 4 7
4 2 8 5 9 3 8
1 2 4 1 1 0 8
1 1 1 4 0 1 1
4 2 3 1 1 5 5
6 1 0 6 3 2 1
6 7 7 1 1 3 9

m=7;n=8;base=10;score=176;
8 9 0 1 2 1 3 1 
9 3 7 0 2 3 1 4 
4 6 1 7 1 5 7 8 
1 1 1 3 4 1 5 1 
0 1 6 1 0 1 4 1 
8 6 2 5 1 2 0 4 
1 8 1 9 1 3 9 6 

m=7;n=9;base=10;score=193;
0 9 1 0 2 1 1 9 2 
1 6 5 1 4 7 7 1 9 
3 1 2 2 6 1 3 2 4 
9 8 1 1 8 4 1 3 1 
1 6 6 3 1 4 1 5 1 
8 0 1 0 5 0 7 8 5 
1 8 7 1 9 1 0 1 8 

m=7;n=10;base=10;score=207;
1 2 5 1 2 1 5 1 8 2 
1 4 0 2 0 5 1 7 0 0 
1 9 1 6 1 8 8 2 1 7 
1 5 6 1 3 7 1 1 9 5 
4 1 3 1 9 1 6 0 3 1 
8 4 9 2 7 8 4 1 0 3 
1 9 7 4 1 7 1 4 2 2 

m=8;n=8;base=10;score=194;
1 3 1 8 5 1 4 7
0 3 1 3 4 5 5 1
2 1 6 4 1 1 6 6
1 2 8 1 0 0 7 1
1 1 1 3 5 1 6 2
9 9 4 7 1 9 1 5
4 3 2 1 8 0 7 1
1 1 1 1 8 1 7 1

m=8;n=9;base=10;score=211;
1 1 1 8 9 1 2 1 7 
1 5 8 1 7 0 7 0 2 
0 1 6 7 9 5 1 4 1 
6 3 7 1 1 5 4 1 1 
1 3 1 9 3 1 2 0 2 
1 2 9 1 4 8 3 0 2 
2 0 6 6 1 0 1 2 5 
4 8 1 1 8 1 4 9 1 

m=8;n=10;base=10;score=234;
8 2 2 9 5 1 1 8 1 9
2 0 8 1 7 4 3 5 4 0
9 2 1 8 4 1 2 1 0 3
1 0 7 9 1 2 6 2 2 2
0 8 1 1 9 3 1 7 0 2
1 9 6 6 1 2 5 7 1 3
5 8 1 0 5 4 5 1 3 4
1 3 3 2 1 1 6 4 0 1

m=9;n=9;base=10;score=237;
8 7 1 1 9 6 2 2 5 
2 3 4 3 1 2 0 3 2 
5 2 1 9 7 1 2 2 6 
1 3 0 1 5 5 8 2 1 
3 1 6 4 9 8 1 0 4 
1 5 1 6 1 2 1 8 7 
1 9 1 6 7 2 0 7 1 
9 4 8 1 3 1 0 5 7 
4 1 8 3 4 1 2 9 1 

m=9;n=10;base=10;score=256;
1 3 5 6 0 1 2 9 1 8
1 5 2 0 6 1 3 7 0 2
2 2 6 3 2 1 9 1 0 2
7 4 5 2 3 4 1 0 3 1
1 6 2 0 2 1 7 5 1 6
1 3 2 4 0 1 1 1 8 4
5 2 4 1 8 8 6 1 9 1
9 4 5 2 3 7 1 9 4 7
1 5 1 2 1 2 1 8 1 7

m=10;n=10;base=10;score=284;
1 1 6 9 1 9 1 8 1 9 
7 7 2 2 5 4 2 5 8 9 
0 2 4 2 3 1 6 1 0 1 
2 0 3 1 1 6 0 2 9 1 
6 5 2 8 1 4 1 3 6 0 
2 6 5 6 1 2 5 7 2 8 
3 7 2 1 7 9 1 1 5 2 
2 2 4 8 1 1 3 7 0 1 
8 4 7 0 4 3 8 2 7 9 
2 1 0 2 2 1 9 4 2 8

Uncwilly · 2018-09-05, 02:23

I posted the latest 10x10 as an image on FB as a challenge for friends to try to find out how far it goes. In a few days I will post the current best 20x20. I will credit the creators as 'number nerd friends'.

Till · 2018-09-05, 14:12

Quote:

Originally Posted by Uncwilly

I posted the latest 10x10 as an image on FB as a challenge for friends to try to find out how far it goes. In a few days I will post the current best 20x20. I will credit the creators as 'number nerd friends'.

Fine for me. Here is a 20x20 base 10 square with score 1287:

Code:

7 4 9 1 1 7 1 1 1 1 9 5 7 2 1 8 1 1 3 9 
5 0 6 2 1 0 9 2 2 0 9 1 3 2 0 6 8 2 1 4 
9 3 6 7 7 1 1 6 7 3 6 5 2 2 1 2 7 6 5 3 
4 9 4 4 8 0 5 2 7 8 8 6 1 1 1 1 1 4 7 9 
6 6 8 6 7 9 1 3 7 7 5 2 1 2 4 2 9 0 5 9 
3 9 4 9 8 7 7 5 5 3 9 8 1 3 8 2 4 9 3 0 
1 2 0 6 0 1 0 8 4 9 6 8 2 2 9 4 5 9 0 1 
1 2 4 1 1 1 0 2 4 0 1 2 5 0 1 3 8 9 4 9 
1 1 0 3 0 1 1 1 6 0 0 4 8 1 1 7 5 7 3 8 
0 0 2 0 6 3 3 8 6 1 5 1 1 0 0 0 1 2 4 4 
1 2 8 7 2 7 4 4 7 5 6 0 1 5 4 1 1 0 7 7 
9 1 9 9 9 5 0 1 8 1 8 4 1 5 4 2 1 1 4 6 
1 2 2 1 6 1 1 8 2 8 0 1 0 9 4 5 0 5 6 7 
0 2 2 5 2 0 1 0 9 3 8 1 0 8 3 4 9 7 9 3 
0 3 2 3 5 7 4 1 6 8 0 6 2 6 2 0 1 2 6 7 
6 1 4 0 2 8 2 7 3 3 1 1 4 1 9 1 1 2 5 3 
2 7 1 1 5 5 6 6 6 5 1 1 1 2 6 1 1 1 6 5 
3 5 4 3 1 0 6 8 3 3 0 2 0 9 4 0 1 0 7 6 
1 8 2 2 1 1 0 4 0 7 0 1 0 3 3 2 1 9 5 0 
3 8 1 1 1 1 3 8 5 5 5 3 3 3 7 0 7 0 2 1

Till · 2018-09-05, 18:34

Found a new 7x7 base 10 top score -> updated table:

Code:

 x |    1    2    3    4    5    6    7    8    9   10
---+--------------------------------------------------
 1 |    1    2    3    4    5    6    7    8    9   10
 2 |         4    6    8   10   21   32   37   46   54
 3 |              9   26   38   48   66   78   98  104
 4 |                  43   65   88  104  116  125  132
 5 |                       98  108  126  136  149  161
 6 |                           128  142  157  171  184
 7 |                                158  176  193  207
 8 |                                     194  211  234
 9 |                                          237  256
10 |                                               284

m=1;n=1;base=10;score=1;
1

m=1;n=2;base=10;score=2;
1 2

m=1;n=3;base=10;score=3;
2 1 3

m=1;n=4;base=10;score=4;
3 1 4 2

m=1;n=5;base=10;score=5;
1 3 5 4 2

m=1;n=6;base=10;score=6;
5 1 4 2 6 3

m=1;n=7;base=10;score=7;
7 3 2 5 4 6 1

m=1;n=8;base=10;score=8;
8 7 2 1 5 4 6 3

m=1;n=9;base=10;score=9;
1 4 6 2 9 5 3 7 8

m=1;n=10;base=10;score=10;
6 8 7 4 3 1 0 2 5 9

m=2;n=2;base=10;score=4;
2 3
1 4

m=2;n=3;base=10;score=6;
6 5 1
2 4 3

m=2;n=4;base=10;score=8;
5 3 1 6
7 4 8 2

m=2;n=5;base=10;score=10;
7 5 0 1 4
9 8 2 3 6

m=2;n=6;base=10;score=21;
9 1 0 7 4 5
6 2 8 3 1 1

m=2;n=7;base=10;score=32;
8 1 0 3 4 2 5
6 2 1 9 2 1 7

m=2;n=8;base=10;score=37;
3 1 2 6 3 7 2 8
4 2 1 0 3 5 1 9

m=2;n=9;base=10;score=46;
1 7 2 5 4 0 3 2 1
1 8 3 6 1 4 2 3 9

m=2;n=10;base=10;score=54;
2 0 1 4 6 3 4 7 3 2
3 5 4 1 9 2 1 8 2 3

m=3;n=3;base=10;score=9;
1 9 5
3 7 4
6 8 2

m=3;n=4;base=10;score=26;
9 6 5 2
8 1 2 3
7 4 1 0

m=3;n=5;base=10;score=38;
3 5 4 7 3
1 3 2 1 6
1 0 8 2 9

m=3;n=6;base=10;score=48;
5 3 4 6 2 5
8 4 0 3 1 2
1 2 7 1 3 9

m=3;n=7;base=10;score=66;
1 3 3 7 1 2 5
6 0 5 4 2 1 8
2 6 4 5 9 3 4

m=3;n=8;base=10;score=78;
5 8 2 2 1 4 8 3
1 5 6 3 0 7 4 9
9 1 3 6 7 5 2 6

m=3;n=9;base=10;score=98;
3 4 7 7 9 2 4 8 5
3 0 4 8 3 5 2 6 5
6 9 1 1 8 0 1 7 6

m=3;n=10;base=10;score=104;
8 2 3 9 9 2 2 1 9 7
6 8 4 6 5 7 0 0 1 8
6 1 0 4 7 3 3 1 5 5

m=4;n=4;base=10;score=43;
8 2 5 3
2 1 0 7
9 4 1 2
8 3 3 6

m=4;n=5;base=10;score=65;
9 2 8 1 1
5 4 3 5 9
4 6 7 3 5
0 1 2 2 0

m=4;n=6;base=10;score=88;
9 3 0 6 9 1
2 5 3 4 7 1
6 1 8 7 4 5
6 8 0 2 2 5

m=4;n=7;base=10;score=104;
3 7 6 3 3 1 6
0 9 2 4 5 8 6
1 0 4 2 8 5 0
1 0 1 7 7 9 9

m=4;n=8;base=10;score=116;
3 3 4 8 6 7 2 4
5 4 9 0 1 3 7 2
6 9 1 0 1 0 8 5
7 6 2 1 1 1 5 8

m=4;n=9;base=10;score=125;
4 8 6 6 5 1 7 7 4
5 2 1 0 1 1 0 4 6
5 7 1 1 0 2 1 3 9
9 3 8 8 9 1 2 3 9

m=4;n=10;base=10;score=132;
7 6 1 1 3 1 1 1 1 1
8 1 0 2 1 3 0 1 2 5
8 0 1 1 2 4 5 7 6 9
3 9 9 4 8 5 4 6 7 3

m=5;n=5;base=10;score=98;
7 7 9 2 3
5 4 2 5 1
5 0 6 8 1
1 7 8 6 9
4 4 3 3 0

m=5;n=6;base=10;score=108;
3 1 2 5 6 1
3 0 5 2 8 0
1 0 1 7 9 8
1 0 7 9 3 4
4 4 6 6 5 2

m=5;n=7;base=10;score=126;
7 6 1 1 8 8 1
7 1 2 0 1 4 2
4 2 1 1 0 9 5
4 3 0 1 7 8 9
6 6 5 5 3 3 6

m=5;n=8;base=10;score=136;
5 6 7 1 3 4 4 7
4 5 2 3 1 2 0 1
9 8 1 1 2 1 0 1
7 8 0 1 3 0 2 0
7 3 6 6 9 5 9 9

m=5;n=9;base=10;score=149;
6 6 9 9 8 6 7 9 5
2 0 1 3 2 1 4 3 1
1 4 1 2 1 1 0 1 1
4 2 1 4 0 0 1 3 3
5 5 7 7 8 8 5 6 1

m=5;n=10;base=10;score=161;
1 6 7 8 8 5 1 3 7 9
6 4 3 1 2 6 3 2 4 8
1 1 5 1 0 1 1 1 4 1
1 5 0 1 5 3 2 4 0 1
7 7 6 9 9 2 1 0 8 2

m=6;n=6;base=10;score=128;
4 7 3 3 4 4
8 6 0 1 2 0
6 8 1 1 0 1
3 5 0 1 2 8
5 9 2 2 9 6
4 7 7 1 1 9

m=6;n=7;base=10;score=142;
6 1 1 4 6 7 7 
6 0 4 2 9 8 3 
5 3 1 0 8 1 1 
5 1 1 2 1 3 3 
9 2 0 1 2 4 1 
9 3 1 0 7 5 8 

m=6;n=8;base=10;score=157;
9 9 7 7 6 8 8 7 
3 0 1 4 3 1 2 5 
1 3 1 1 5 1 4 1 
2 4 1 2 3 1 0 4 
9 2 0 0 1 5 5 8 
6 1 1 3 6 6 1 9 

m=6;n=9;base=10;score=171;
1 3 7 9 9 5 1 2 7
7 4 3 1 6 0 2 5 7
1 1 5 1 4 1 1 1 8
6 5 1 1 2 6 1 4 4
1 0 3 0 6 3 1 2 9
8 8 1 1 0 7 1 6 8

m=6;n=10;base=10;score=184;
5 1 9 9 1 1 9 1 5 1 
7 2 4 1 7 1 6 5 3 9 
1 4 1 6 0 2 1 8 1 0 
1 0 1 6 1 2 1 4 0 1 
3 7 8 5 3 7 3 1 5 7 
9 8 4 1 3 1 8 2 1 7 

m=7;n=7;base=10;score=158;
1 0 6 1 3 9 9 
5 9 2 3 1 4 2 
8 1 1 0 0 2 1 
8 0 5 1 1 4 8 
9 7 1 5 4 3 1 
8 4 3 2 1 5 6 
6 1 1 1 7 7 6 

m=7;n=8;base=10;score=176;
8 9 0 1 2 1 3 1 
9 3 7 0 2 3 1 4 
4 6 1 7 1 5 7 8 
1 1 1 3 4 1 5 1 
0 1 6 1 0 1 4 1 
8 6 2 5 1 2 0 4 
1 8 1 9 1 3 9 6 

m=7;n=9;base=10;score=193;
0 9 1 0 2 1 1 9 2 
1 6 5 1 4 7 7 1 9 
3 1 2 2 6 1 3 2 4 
9 8 1 1 8 4 1 3 1 
1 6 6 3 1 4 1 5 1 
8 0 1 0 5 0 7 8 5 
1 8 7 1 9 1 0 1 8 

m=7;n=10;base=10;score=207;
1 2 5 1 2 1 5 1 8 2 
1 4 0 2 0 5 1 7 0 0 
1 9 1 6 1 8 8 2 1 7 
1 5 6 1 3 7 1 1 9 5 
4 1 3 1 9 1 6 0 3 1 
8 4 9 2 7 8 4 1 0 3 
1 9 7 4 1 7 1 4 2 2 

m=8;n=8;base=10;score=194;
1 3 1 8 5 1 4 7
0 3 1 3 4 5 5 1
2 1 6 4 1 1 6 6
1 2 8 1 0 0 7 1
1 1 1 3 5 1 6 2
9 9 4 7 1 9 1 5
4 3 2 1 8 0 7 1
1 1 1 1 8 1 7 1

m=8;n=9;base=10;score=211;
1 1 1 8 9 1 2 1 7 
1 5 8 1 7 0 7 0 2 
0 1 6 7 9 5 1 4 1 
6 3 7 1 1 5 4 1 1 
1 3 1 9 3 1 2 0 2 
1 2 9 1 4 8 3 0 2 
2 0 6 6 1 0 1 2 5 
4 8 1 1 8 1 4 9 1 

m=8;n=10;base=10;score=234;
8 2 2 9 5 1 1 8 1 9
2 0 8 1 7 4 3 5 4 0
9 2 1 8 4 1 2 1 0 3
1 0 7 9 1 2 6 2 2 2
0 8 1 1 9 3 1 7 0 2
1 9 6 6 1 2 5 7 1 3
5 8 1 0 5 4 5 1 3 4
1 3 3 2 1 1 6 4 0 1

m=9;n=9;base=10;score=237;
8 7 1 1 9 6 2 2 5 
2 3 4 3 1 2 0 3 2 
5 2 1 9 7 1 2 2 6 
1 3 0 1 5 5 8 2 1 
3 1 6 4 9 8 1 0 4 
1 5 1 6 1 2 1 8 7 
1 9 1 6 7 2 0 7 1 
9 4 8 1 3 1 0 5 7 
4 1 8 3 4 1 2 9 1 

m=9;n=10;base=10;score=256;
1 3 5 6 0 1 2 9 1 8
1 5 2 0 6 1 3 7 0 2
2 2 6 3 2 1 9 1 0 2
7 4 5 2 3 4 1 0 3 1
1 6 2 0 2 1 7 5 1 6
1 3 2 4 0 1 1 1 8 4
5 2 4 1 8 8 6 1 9 1
9 4 5 2 3 7 1 9 4 7
1 5 1 2 1 2 1 8 1 7

m=10;n=10;base=10;score=284;
1 1 6 9 1 9 1 8 1 9 
7 7 2 2 5 4 2 5 8 9 
0 2 4 2 3 1 6 1 0 1 
2 0 3 1 1 6 0 2 9 1 
6 5 2 8 1 4 1 3 6 0 
2 6 5 6 1 2 5 7 2 8 
3 7 2 1 7 9 1 1 5 2 
2 2 4 8 1 1 3 7 0 1 
8 4 7 0 4 3 8 2 7 9 
2 1 0 2 2 1 9 4 2 8

science_man_88 · 2018-09-05, 19:14

Quote:

Originally Posted by Till

Fine for me. Here is a 20x20 base 10 square with score 1287:

Code:

7 4 9 1 1 7 1 1 1 1 9 5 7 2 1 8 1 1 3 9 
5 0 6 2 1 0 9 2 2 0 9 1 3 2 0 6 8 2 1 4 
9 3 6 7 7 1 1 6 7 3 6 5 2 2 1 2 7 6 5 3 
4 9 4 4 8 0 5 2 7 8 8 6 1 1 1 1 1 4 7 9 
6 6 8 6 7 9 1 3 7 7 5 2 1 2 4 2 9 0 5 9 
3 9 4 9 8 7 7 5 5 3 9 8 1 3 8 2 4 9 3 0 
1 2 0 6 0 1 0 8 4 9 6 8 2 2 9 4 5 9 0 1 
1 2 4 1 1 1 0 2 4 0 1 2 5 0 1 3 8 9 4 9 
1 1 0 3 0 1 1 1 6 0 0 4 8 1 1 7 5 7 3 8 
0 0 2 0 6 3 3 8 6 1 5 1 1 0 0 0 1 2 4 4 
1 2 8 7 2 7 4 4 7 5 6 0 1 5 4 1 1 0 7 7 
9 1 9 9 9 5 0 1 8 1 8 4 1 5 4 2 1 1 4 6 
1 2 2 1 6 1 1 8 2 8 0 1 0 9 4 5 0 5 6 7 
0 2 2 5 2 0 1 0 9 3 8 1 0 8 3 4 9 7 9 3 
0 3 2 3 5 7 4 1 6 8 0 6 2 6 2 0 1 2 6 7 
6 1 4 0 2 8 2 7 3 3 1 1 4 1 9 1 1 2 5 3 
2 7 1 1 5 5 6 6 6 5 1 1 1 2 6 1 1 1 6 5 
3 5 4 3 1 0 6 8 3 3 0 2 0 9 4 0 1 0 7 6 
1 8 2 2 1 1 0 4 0 7 0 1 0 3 3 2 1 9 5 0 
3 8 1 1 1 1 3 8 5 5 5 3 3 3 7 0 7 0 2 1

change that to a 1 and you get higher unless 1184, is only once in the puzzle ( I'll double check for more I may have missed) 554 may be a deal breaker as well.

2018-09-03, 16:57	#58
Till "Tilman Neumann" Jan 2016 Germany 448₁₀ Posts	Yep, looks better But as you mentioned, probably the upper bounds are still far too high... Last fiddled with by Till on 2018-09-03 at 16:59 Reason: note on still too wide bounds

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2018-09-05, 02:23	#63
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2×3×7×233 Posts	I posted the latest 10x10 as an image on FB as a challenge for friends to try to find out how far it goes. In a few days I will post the current best 20x20. I will credit the creators as 'number nerd friends'.