1. PROLOG
MORE PROBLEMS

2. MAGIC PUZZLE 3 X 3 3 X 3 square Digits 1 to 9 All rows are equal to 15
All columns are equal to 15
Both diagonals are equal to 15

3. MAGIC PUZZLE 3 X 3
3 X 3 square
X1 X2 X3
X4 X5 X6
X7 X8 X9

4. MAGIC PUZZLE 3 X 3 Basically only one solution (+symmetries) 2 7 6
Check it out: all totals are 15

5. MAGIC PUZZLE 3 X 3 All digits should be different
All digits are between 1 and 9
Set of equations:
X1 + X2 + X3 = 15 (1st row)
X4 + X5 + X6 = 15 (2nd row) …
X3 + X5 + X7 = 15 (opposite diagonal)

6. MAGIC PUZZLE 3 X 3 solve(X1,X2,X3,X4,X5,X6,X7,X8,X9) :-
member(X1,[1,2,3,4,5,6,7,8,9]), ..
alldifferent([X1,X2,X3,….,X6,X7,X8,X9]),
X1 + X2 + X3 =:= 15,
X3 + X5 + X7 =:= 15.

7. MAGIC PUZZLE 3 X 3 Would take about 7 minutes to generate the solution
Intuitively
The average number is 5
There are 3 numbers in each row, column, diagonal
Average number (5) * # numbers/row .. (3) = 15
 5 is probably in the middle (it is)
 hard code 5 in the middle to speed up the code.

8. TOWERS OF HANOI 3 Towers: left, center, right N disks on left tower
All disks have a different diameter
A smaller disk must be on top of a bigger disk; it can be alone too
We want to move the N disks to the center tower

9. TOWERS OF HANOI
Starting position with 3 disks

10. TOWERS OF HANOI Solution (general case: N >= 2):
To move N disks from A to B using C
Move (N-1) disks from A to C using B (recursive call)
Move 1 disk from A to B
Move (N-1) disks from C to B using A (recursive call)
Base Case (only 1 disk to move from A to B; no need for C here):

11. TOWERS OF HANOI
Problem: Can we move N disks from tower A to tower B using tower C?
Yes or No answer + printing out all the steps
Predicate move takes 4 arguments: the number of disks, and 3 towers

12. TOWERS OF HANOI Base case: Move 1 disk from A to B move(1,A,B,_) :-
write(‘Move top disk from ‘),
write(A),
write(‘ to ‘),
write(B),
nl.

13. TOWERS OF HANOI General case: Move N disks from A to B using C
move(N,A,B,C) :-
N > 1,
M is N – 1,
move(M,A,C,B),
move(1,A,B,_),
move(M,C,B,A).