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Magic square An example of how to represent a problem

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# Magic square An example of how to represent a problem - PowerPoint PPT Presentation

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

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Magic square

An example of how to represent a problem

An idea from Chris Beck

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

• 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

Use sumVars(x) = sumVars(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?

2nd stab

• 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

Use allDiff (must have Iceberg for claire!)

But what is k?

How does model perform?

Magic square on the web

http://mathworld.wolfram.com/MagicSquare.html

http://mathforum.org/alejandre/magic.square.html