3 views

Skip to first unread message

May 22, 2020, 11:44:16 AM5/22/20

to

The Sandwich Sudoku also called Between 1 and 9 Sudoku follows the same rules of

classic sudoku but has extra clues outside the grid. The clues are the sum of

the digits between 1 and 9 in that row or column. When you have eg. 0, then

there are NO cells between 1 and 9.

Constraints for a standard Sudoku are well known. However, I can't find anything

for a sandwich sudoku, and I'm having trouble formulating contraints.

The usual formulation is Vxyd where x and y are the rows and columns, d is the

digit in that cell and takes a (0,1) value.

I can create a new variable that is (0,1) if the cell is in the sandwich

Consider a row

3 4 2 1 5 6 9 7 8

We have the 1 and 9 values as

Value 1 - 0 0 0 1 0 0 0 0 0

Value 9 - 0 0 0 0 0 0 1 0 0

You can now easily create effectively 4 new rows

There are two cases to consider. 1 comes before 9. The second is 9 comes before 1

It's easy to create an After 1, After and including 9, Before and including 1 and Before 9

Te first case constraint a binary variable where its 1 if comes after the 1, else is zero

Create a second variable where its 1 if it comes after and including the 9

After 1 - 0 0 0 0 1 1 1 1 1

After including 9 - 0 0 0 0 0 0 1 1 1

We then take the difference and we have

Difference - 0 0 0 0 1 1 0 0 0

This shows the cells that are in the sandwich

Two problems.

It doesn't work the other way where 9 comes before 1. You can create a rule similar to the above, but I can't get a combination working

Secondly I need the sum of the values where its true and this isn't linear

It's a product of the value in the cell, which is a variable, and another variable.

Any ideas?

It feels like their should be an expression that is linear.

classic sudoku but has extra clues outside the grid. The clues are the sum of

the digits between 1 and 9 in that row or column. When you have eg. 0, then

there are NO cells between 1 and 9.

Constraints for a standard Sudoku are well known. However, I can't find anything

for a sandwich sudoku, and I'm having trouble formulating contraints.

The usual formulation is Vxyd where x and y are the rows and columns, d is the

digit in that cell and takes a (0,1) value.

I can create a new variable that is (0,1) if the cell is in the sandwich

Consider a row

3 4 2 1 5 6 9 7 8

We have the 1 and 9 values as

Value 1 - 0 0 0 1 0 0 0 0 0

Value 9 - 0 0 0 0 0 0 1 0 0

You can now easily create effectively 4 new rows

There are two cases to consider. 1 comes before 9. The second is 9 comes before 1

It's easy to create an After 1, After and including 9, Before and including 1 and Before 9

Te first case constraint a binary variable where its 1 if comes after the 1, else is zero

Create a second variable where its 1 if it comes after and including the 9

After 1 - 0 0 0 0 1 1 1 1 1

After including 9 - 0 0 0 0 0 0 1 1 1

We then take the difference and we have

Difference - 0 0 0 0 1 1 0 0 0

This shows the cells that are in the sandwich

Two problems.

It doesn't work the other way where 9 comes before 1. You can create a rule similar to the above, but I can't get a combination working

Secondly I need the sum of the values where its true and this isn't linear

It's a product of the value in the cell, which is a variable, and another variable.

Any ideas?

It feels like their should be an expression that is linear.

Jun 16, 2020, 1:22:32 PM6/16/20

to

El 22/5/20 a las 17:44, nic...@gmail.com escribió:

Really, I can't understand you.

A simple sudoku it's only a big binary linear program - glpk is ok.

So, want to add more restrictions???

You can.

Best regards.

--

http://gamo.sdf-eu.org/

“Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer

in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is

taht the frist and lsat ltteer be at the rghit pclae. The rset can be

a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae

the huamn mnid deos not raed ervey lteter by istlef, but the wrod as

a wlohe.”

A simple sudoku it's only a big binary linear program - glpk is ok.

So, want to add more restrictions???

You can.

Best regards.

--

http://gamo.sdf-eu.org/

“Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer

in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is

taht the frist and lsat ltteer be at the rghit pclae. The rset can be

a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae

the huamn mnid deos not raed ervey lteter by istlef, but the wrod as

a wlohe.”

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu