Root problem
Universe
| squares | r2 | b2 | |
| (triangles) ∧ (¬green) | r1 | b1 | |
| green | green | green | green |
CoLa
universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green};
property squares = {r2, b2};
property (triangles) ∧ (¬green) = {r1, b1};
property green = {green, green, green};
Configuration
| 1 | |||
| 1 | 2 | ||
| 1 | 2 | 3 | |
| 1 | 2 | 3 | 4 |
CoLa
permutation (size in [1,4]) of entity universe (perm)
Constraints
| 2 | green |
CoLa
Position 2: green; Nr. squares in [2, 7];
0
Configuration of size 1
Universe
| squares | r2 | b2 | |
| (triangles) ∧ (¬green) | r1 | b1 | |
| green | green | green | green |
CoLa
universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green};
property squares = {r2, b2};
property (triangles) ∧ (¬green) = {r1, b1};
property green = {green, green, green};
Configuration
| 1 |
CoLa
Obj 1: (squares) ∨ (triangles);
Constraints
| 2 | green |
CoLa
Position 2: green; Nr. squares in [2, 7];
$$\texttip{ 0 }{ Cannot satisfy Nr. squares in [2, 7] :( }$$
0
Configuration of size 2
Universe
| green | green | green | green |
| (triangles) ∧ (¬green) | r1 | b1 | |
| squares | r2 | b2 |
CoLa
universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green};
property green = {green, green, green};
property (triangles) ∧ (¬green) = {r1, b1};
property squares = {r2, b2};
Configuration
| 1 | 2 |
CoLa
Obj 1: (squares) ∨ (triangles); Obj 2: (squares) ∨ (triangles);
Constraints
| 2 | green |
CoLa
Position 2: green; Nr. squares in [2, 7];
$$\texttip{ 0 }{ No solution found }$$
2
Configuration of size 3
Universe
| (triangles) ∧ (¬green) | r1 | b1 | |
| squares | r2 | b2 | |
| green | green | green | green |
CoLa
universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green};
property (triangles) ∧ (¬green) = {r1, b1};
property squares = {r2, b2};
property green = {green, green, green};
Configuration
| 1 | 2 | 3 |
CoLa
Obj 1: (squares) ∨ (triangles); Obj 2: (squares) ∨ (triangles); Obj 3: (squares) ∨ (triangles);
Constraints
| 2 | green |
CoLa
Position 2: green; Nr. squares in [2, 7];
1
Left split: case 1 green are s.t. [Nr. squares = 0, Nr. green = 1, Nr. ¬green = 0]
Universe
| squares | r2 | b2 | |
| (triangles) ∧ (¬green) | r1 | b1 | |
| green | green | green | green |
CoLa
universe green = {green, green, green};
property squares = {r2, b2};
property (triangles) ∧ (¬green) = {r1, b1};
Configuration
| 1 |
CoLa
Obj 1: green;
Constraints
CoLa
Nr. squares = 0; Nr. green = 1; Nr. ¬green = 0;
$$\frac{\texttip{ \binom{ 0 }{ 0 } }{ Choose 0 of 0 (distinguishable) empty for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 green }}{\texttip{ 1! }{ Extra permutations of (indist.) green }}$$
2
Right split removing 1 green
Universe
| squares | r2 | b2 | |||
| triangles | r1 | b1 | green | green | green |
| 5 |
CoLa
universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green};
property squares = {r2, b2};
property triangles = {r1, b1, green, green, green};
Configuration
| 1 | 2 |
CoLa
Obj 1: (squares) ∨ (triangles); Obj 2: (squares) ∨ (triangles);
Constraints
CoLa
Nr. squares = 2;
$$\texttip{ \texttip{ 1 }{ Exchangeable choices } \cdot 2! }{ Nr. orders for all objects }$$
18
Configuration of size 4
Universe
| (triangles) ∧ (¬green) | r1 | b1 | |
| squares | r2 | b2 | |
| green | green | green | green |
CoLa
universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green};
property (triangles) ∧ (¬green) = {r1, b1};
property squares = {r2, b2};
property green = {green, green, green};
Configuration
| 1 | 2 | 3 | 4 |
CoLa
Obj 1: (squares) ∨ (triangles); Obj 2: (squares) ∨ (triangles); Obj 3: (squares) ∨ (triangles); Obj 4: (squares) ∨ (triangles);
Constraints
| 2 | green |
CoLa
Position 2: green; Nr. squares in [2, 7];
1
Left split: case 1 green are s.t. [Nr. squares = 0, Nr. green = 1, Nr. ¬green = 0]
Universe
| squares | r2 | b2 | |
| (triangles) ∧ (¬green) | r1 | b1 | |
| green | green | green | green |
CoLa
universe green = {green, green, green};
property squares = {r2, b2};
property (triangles) ∧ (¬green) = {r1, b1};
Configuration
| 1 |
CoLa
Obj 1: green;
Constraints
CoLa
Nr. squares = 0; Nr. green = 1; Nr. ¬green = 0;
$$\frac{\texttip{ \binom{ 0 }{ 0 } }{ Choose 0 of 0 (distinguishable) empty for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 green }}{\texttip{ 1! }{ Extra permutations of (indist.) green }}$$
18
Right split removing 1 green
Universe
| squares | r2 | b2 | |||
| triangles | r1 | b1 | green | green | green |
| 5 |
CoLa
universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green};
property squares = {r2, b2};
property triangles = {r1, b1, green, green, green};
Configuration
| 1 | 2 | 3 |
CoLa
Obj 1: (squares) ∨ (triangles); Obj 2: (squares) ∨ (triangles); Obj 3: (squares) ∨ (triangles);
Constraints
CoLa
Nr. squares in [2, 3];
2
Left split: case 2 squares are s.t. [Nr. squares = 2]
Universe
| squares | r2 | b2 | |||
| triangles | r1 | b1 | green | green | green |
| 5 |
CoLa
universe squares = {r2, b2};
property triangles = {r1, b1, green, green, green};
Configuration
| 1 | 2 |
CoLa
Obj 1: squares; Obj 2: squares;
Constraints
CoLa
Nr. squares = 2;
$$\texttip{ 2! }{ Nr. orders for all objects }$$
3
Right split removing 2 squares
Universe
| (squares) ∨ (triangles) | r1 | b1 | green | green |
CoLa
universe (squares) ∨ (triangles) = {r1, b1, green, green};
Configuration
| 1 |
CoLa
Obj 1: (squares) ∨ (triangles);
$$\frac{\texttip{ \binom{ 2 }{ 0 } }{ Choose 0 of 2 (distinguishable) ??? for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 (squares) ∨ (triangles) }}{\texttip{ 1! }{ Extra permutations of (indist.) ??? }} + \frac{\texttip{ \binom{ 2 }{ 1 } }{ Choose 1 of 2 (distinguishable) ??? for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 (squares) ∨ (triangles) }}{\texttip{ 0! }{ Extra permutations of (indist.) ??? }}$$