Aqre Minimize

Minimizing the number of black cells in Aqre

Use "Sugar" CSP solver for proof.

table: aqre number

1*1 0

2*2 0

3*3 0

4*4 7

5*5 9

6*6 13

7*7 15

8*8 27

9*9 33

10*10 41

11*11 47

12*12 〜61

6*6

13 (Proved)

https://gyazo.com/6ba1059208dc0c99bcefbe55f5f046c4

7*7

15 (Proved)

https://gyazo.com/500b37edbaa74eb77e858192df47e732

Only this and this rotation.

8*8

27 (Proved)

9*9

https://gyazo.com/bdbef10c5588e0d1f656a1f485586792

10*10

43 (Not Proved)

https://gyazo.com/91a3a27419c826b9f97cae903000776f

41 (semiexp)

※ Remove the black cells in R1C6.

40 doesn't exist.

11*11

47 (Proved by semiexp)

https://gyazo.com/ab27a7363c68eb8980767a74ec4b2177

46 doesn't exist

12*12

61 semiexp

※ Remove the black cells in R1C3.

n*m

n -> ∞

〜2/5

$ \frac{2}{5}nm+O(n+m)

(proved)