6 added 361 characters in body
source | link

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description here

and one for 1x9:

14x14 = 196

enter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description here

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

enter image description here

1x12:

18x16 = 288

enter image description here

Here is the minimal solution for $2 \times 7$, which generalizes to $2 \times (10k + 7)$ and is just a little bit smaller than the one discovered by Jaap:

15x15 = 255 (generalized: $(20k + 15) \times (20k + 15)$)
enter image description here

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description here

and one for 1x9:

14x14 = 196

enter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description here

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

enter image description here

1x12:

18x16 = 288

enter image description here

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description here

and one for 1x9:

14x14 = 196

enter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description here

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

enter image description here

1x12:

18x16 = 288

enter image description here

Here is the minimal solution for $2 \times 7$, which generalizes to $2 \times (10k + 7)$ and is just a little bit smaller than the one discovered by Jaap:

15x15 = 255 (generalized: $(20k + 15) \times (20k + 15)$)
enter image description here

5 added 170 characters in body
source | link

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description here

and one for 1x9:

14x14 = 196

enter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description here

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

enter image description here

1x12:

18x16 = 288

enter image description here

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description here

and one for 1x9:

14x14 = 196

enter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description here

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

enter image description here

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description here

and one for 1x9:

14x14 = 196

enter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description here

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

enter image description here

1x12:

18x16 = 288

enter image description here

4 added 227 characters in body
source | link

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description hereenter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description hereenter image description here

and one for 1x9:

14x14 = 196

enter image description hereenter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description hereenter image description here

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

enter image description here

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description here

and one for 1x9:

14x14 = 196

enter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description here

Here's an attempt for 1x4:

11x5 = 55 squares

enter image description here

and another one for 1x5:

10x6 = 60 squares

enter image description here

and one for 1x9:

14x14 = 196

enter image description here

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

enter image description here

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

enter image description here

3 added 179 characters in body
source | link
2 added 134 characters in body
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1
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