1. The Puzzle
Tyson Kendon © 2007

2. Search Control 2
ffield,2 – choose a field on the matrix that is connected to the existing pieces and has the smallest number of options for pieces to place
fpiece,2 – choose a piece that ‘fits’ in the field chosen
fremove,2- choose a field that has a piece that can be removed without breaking up the puzzle
Tyson Kendon © 2007

3. ( ) Search Control 2 Rest0 A0 S0= , ffield,2 (s0)= (1,1)
(0,-)
S0=
(1, 2, 3, 4, 5, 6, 7, 8) ,
ffield,2 (s0)= (1,1)
fpiece,2 ((A0, Rest0), 1, 1) = (1, u), (3, r) (6, r), (7,u)
Tyson Kendon © 2007

4. ( ) Search Control 2 Rest1 A1 S1= ,
(7,u)
(0,-)
S1=
(1, 2, 3, 4, 5, 6, 8) ,
ffield,2 (s1)= (2,1) ((2,1) has 1 fitting piece, (1,2) has 2 pieces (2 or 5))
fpiece,2 ((A1, Rest1), 2, 1) = (3, d)
Tyson Kendon © 2007

5. ( ) Search Control 2 Rest2 A2 S2= , ffield,2 (s2)= (1,2)
(7,u)
(0,-)
(3,d)
S2=
(1, 2, 4, 5, 6, 8) ,
ffield,2 (s2)= (1,2)
fpiece,2 ((A2, Rest2), 1, 2) = (5, u) or (2, u)
Tyson Kendon © 2007

6. ( ) Search Control 2 Rest3 A3 S3= , ffield,2 (s3)= (1,3)
(7,u)
(5,u)
(0,-)
(3,d)
S3=
(1, 2, 4, 6, 8) ,
ffield,2 (s3)= (1,3)
fpiece,2 ((A3, Rest3), 1, 3) = (6, u) – no other options!
Tyson Kendon © 2007

7. ( ) Search Control 2 Rest4 A4 S4= , ffield,2 (s4)= (2,3)
(7,u)
(5,u)
(6,u)
(0,-)
(3,d)
S4=
(1, 2, 4, 8) ,
ffield,2 (s4)= (2,3)
fpiece,2 ((A4, Rest4), 2, 3) = (8, d) or (1, d)
Tyson Kendon © 2007

8. ( ) Search Control 2 Rest5 A5 S5= ,
(7,u)
(5,u)
(6,u)
(0,-)
(3,d)
(1,d)
S5=
(2, 4, 8) ,
fremove,2 ((A5, Rest5)) = (2, 3) or (2, 1)
Any other combination results in islands
Tyson Kendon © 2007

9. ( ) Search Control 2 Rest6 A6 S6= , ffield,2 (s6)= (2,3)
(7,u)
(5,u)
(6,u)
(0,-)
(3,d)
S6=
(1, 2, 4, 8) ,
ffield,2 (s6)= (2,3)
fpiece,2 ((A6, Rest6), 2, 3) = (8, d)
Tyson Kendon © 2007

10. ( ) Search Control 2 Rest7 A7 S7= ,
(7,u)
(5,u)
(6,u)
(0,-)
(3,d)
(8,d)
S7=
(1, 2, 4) ,
fremove,2 ((A7, Rest7)) = (2, 3) or (2, 1)
Any other combination results in islands
Tyson Kendon © 2007

11. ( ) Search Control 2 Rest8 A8 S8= ,
(7,u)
(5,u)
(6,u)
(0,-)
(3,d)
S8=
(1, 2, 4, 8) ,
fremove,2 ((A8, Rest8)) = (1, 3) or (2, 1)
Any other combination results in islands
Tyson Kendon © 2007

12. ( ) Search Control 2 Rest9 A9 S9= ,
(7,u)
(5,u)
(0,-)
(3,d)
S9=
(1, 2, 4, 6, 8) ,
fremove,2 ((A9, Rest9)) = (1, 2) or (2, 1)
Any other combination results in islands
Tyson Kendon © 2007

13. ( ) Search Control 2 Rest10 A10 S10= , ffield,2 (s10)= (1,2)
(7,u)
(0,-)
(3,d)
S10=
(1, 2, 4, 5, 6, 8) ,
ffield,2 (s10)= (1,2)
fpiece,2 ((A10, Rest10), 1, 2) = (2, u) – since (5,u) has all ready been tried
Tyson Kendon © 2007

14. ( ) Search Control 2 Rest11 A11 S11= , ffield,2 (s11)= (1,3)
(7,u)
(2,u)
(0,-)
(3,d)
S11=
(1, 4, 5, 6, 8) ,
ffield,2 (s11)= (1,3)
fpiece,2 ((A11, Rest11), 1, 2) = (5, u) – again this is the only option now
Tyson Kendon © 2007

15. ( ) Search Control 2 Rest12 A12 S12= , ffield,2 (s12)= (2,3)
(7,u)
(2,u)
(5,u)
(0,-)
(3,d)
S12=
(1, 4, 6, 8) ,
ffield,2 (s12)= (2,3)
fpiece,2 ((A12, Rest12), 2, 3) = (4, d)
Tyson Kendon © 2007

16. ( ) Search Control 2 Rest13 A13 S13= ,
(7,u)
(2,u)
(5,u)
(0,-)
(3,d)
(4,d)
S13=
(1, 6, 8) ,
ffield,2 (s13)= (1,4) – at this point we could go with any of the 3
fpiece,2 ((A13, Rest13), 1, 4) = (6, u)
Tyson Kendon © 2007

17. ( ) Search Control 2 Rest14 A14 S14= , ffield,2 (s14)= (2,4)
(7,u)
(2,u)
(5,u)
(6,u)
(3,d)
(0,-)
(4,d)
S14=
(1, 8) ,
ffield,2 (s14)= (2,4)
fpiece,2 ((A14, Rest14), 2, 4) = (1, d)
Tyson Kendon © 2007

18. ( ) Search Control 2 Rest15 A15 S15= , ffield,2 (s15)= (2,2)
(7,u)
(2,u)
(5,u)
(6,u)
(3,d)
(0,-)
(4,d)
(1,d)
S15=
(8) ,
ffield,2 (s15)= (2,2)
fpiece,2 ((A15, Rest15), 2, 4) = (8, d)
Tyson Kendon © 2007

19. ( ) Search Control 2 Rest16 A16 S16= , Gpuzzle1(s16) = yes
(3,d)
(8,d)
(4,d)
(1,d)
S16= () ,
Gpuzzle1(s16) = yes
Since |Rest16| = 0
Tyson Kendon © 2007

20. Search Control 3 Change our definition of a ‘fitting’ piece
Change ffield to ignore positions that put straight sides facing inside the matrix
Change fpiece to ignore pieces/orientations that put straight sides facing inside the matrix
Tyson Kendon © 2007

21. ( ) Search Control 3 Rest0 A0 S0= , ffield,3 (s0)= (1,1)
(0,-)
S0=
(1, 2, 3, 4, 5, 6, 7, 8) ,
ffield,3 (s0)= (1,1)
fpiece,3 ((A0, Rest0), 1, 1) = (1, u), (3, r) (6, r), (7,u)
Tyson Kendon © 2007

22. ( ) Search Control 3 Rest1 A1 S1= , ffield,3 (s1)= (2,1)
(7,u)
(0,-)
S1=
(1, 2, 3, 4, 5, 6, 8) ,
ffield,3 (s1)= (2,1)
fpiece,3 ((A1, Rest1), 2, 1) = (3, d)
Tyson Kendon © 2007

23. ( ) Search Control 3 Rest2 A2 S2= , ffield,3 (s2)= (1,2)
(7,u)
(0,-)
(3,d)
S2=
(1, 2, 4, 5, 6, 8) ,
ffield,3 (s2)= (1,2)
fpiece,3 ((A2, Rest2), 1, 2) = (2,u), (5,u)
Tyson Kendon © 2007

24. ( ) Search Control 3 Rest3 A3 S3= ,
(7,u)
(5,u)
(0,-)
(3,d)
S3=
(1, 2, 4, 6, 8) ,
Can’t put down (5,u) because it no longer ‘fits’
fremove,3 ((A3, Rest3)) = (1, 2) or (2, 1)
Tyson Kendon © 2007

25. ( ) Search Control 3 Rest4 A4 S4= , ffield,3 (s4)= (1,2)
(7,u)
(0,-)
(3,d)
S4=
(1, 2, 4, 5, 6, 8) ,
ffield,3 (s4)= (1,2)
fpiece,3 ((A4, Rest4), 1, 2) = (2,u)
Tyson Kendon © 2007

26. ( ) Search Control 3 Rest5 A5 S5= , ffield,3 (s5)= (1,3)
(7,u)
(2,u)
(0,-)
(3,d)
S5=
(1, 4, 5, 6, 8) ,
ffield,3 (s5)= (1,3)
fpiece,3 ((A5, Rest5), 1, 3) = (5,u)
Tyson Kendon © 2007

27. ( ) Search Control 3 Rest6 A6 S6= , ffield,3 (s6)= (2,3)
(7,u)
(2,u)
(5,u)
(0,-)
(3,d)
S6=
(1, 4, 6, 8) ,
ffield,3 (s6)= (2,3)
fpiece,3 ((A6, Rest6), 2, 3) = (4,d)
Tyson Kendon © 2007

28. ( ) Search Control 3 Rest7 A7 S7= , ffield,3 (s7)= (1,4) – arbitrarily
(7,u)
(2,u)
(5,u)
(0,-)
(3,d)
(4,d)
S7=
(1, 6, 8) ,
ffield,3 (s7)= (1,4) – arbitrarily
fpiece,3 ((A7, Rest7), 1, 4) = (6,u)
Tyson Kendon © 2007

29. ( ) Search Control 3 Rest8 A8 S8= , ffield,3 (s8)= (2,4) – arbitrarily
(7,u)
(2,u)
(5,u)
(6,u)
(3,d)
(0,-)
(4,d)
S8=
(1, 8) ,
ffield,3 (s8)= (2,4) – arbitrarily
fpiece,3 ((A8, Rest8), 2, 4) = (1,d)
Tyson Kendon © 2007

30. ( ) Search Control 3 Rest9 A9 S9= , ffield,3 (s9)= (2,2)
(7,u)
(2,u)
(5,u)
(6,u)
(3,d)
(0,-)
(4,d)
(1,d)
S9=
(8) ,
ffield,3 (s9)= (2,2)
fpiece,3 ((A9, Rest9), 2, 2) = (8,d)
Tyson Kendon © 2007

31. ( ) Search Control 3 Rest10 A10 S10= , Gpuzzle1(s10) = yes
(3,d)
(8,d)
(4,d)
(1,d)
S10= () ,
Gpuzzle1(s10) = yes
Since |Rest10| = 0
Tyson Kendon © 2007