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) ∨ (triangles) | green | |||
squares | r2 | b2 | ||
((squares) ∨ (triangles)) ∧ (triangles) | r1 | b1 | green | green |
CoLa
universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green}; property ¬(squares) ∨ (triangles) = {green}; property squares = {r2, b2}; property ((squares) ∨ (triangles)) ∧ (triangles) = {r1, b1, 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) ∨ (triangles) = 2]
Universe
(squares) ∨ (triangles) | r2 | b2 | r1 | b1 | green | green |
¬(squares) ∨ (triangles) | green | |||||
5 |
CoLa
universe squares = {r2, b2}; property (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green}; property ¬(squares) ∨ (triangles) = {green};
Configuration
1 | 2 |
CoLa
Obj 1: squares; Obj 2: squares;
Constraints
CoLa
Nr. (squares) ∨ (triangles) = 2;
$$\texttip{ \texttip{ 1 }{ Exchangeable choices } \cdot 2! }{ Nr. orders for all objects }$$
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);
$$\frac{\texttip{ \binom{ 2 }{ 0 } }{ Choose 0 of 2 (distinguishable) ??? for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 (squares) ∨ (triangles) }}{\texttip{ 1! }{ Extra permutations of (indist.) ??? }} + \frac{\texttip{ \binom{ 2 }{ 1 } }{ Choose 1 of 2 (distinguishable) ??? for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 (squares) ∨ (triangles) }}{\texttip{ 0! }{ Extra permutations of (indist.) ??? }}$$