1. Magic square An example of how to represent a problem An idea from Chris Beck

2. put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal

12. Back to CP

14. put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal 1st stab Use sum(x) = sum(y) where x and y are - different rows - different columns - different diagonals Every element of the array is different - represent as a clique of not equals How does it go? For propagation and search?

15. put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal 2nd stab Use allDiff But what is k? How does model perform?

16. Magic

17. Could edit this

18. Magic What is k?

19. Magic Just a counter

20. Magic S is actual square v is S flattened

21. Magic Create S, its transpose TS and S flattened into v

22. Magic That’s why we flattened S

23. Magic Transpose is neat (thanks Neil Moore)

28. Is this solution unique?

29. Magic square on the web http://mathforum.org/alejandre/magic.square.html http://mathworld.wolfram.com/MagicSquare.html

30. Is there an order 3 magic square with the number 5 in one of the outer corners?

32. Thanks to Chris Beck