Langford's problem

The problem is to find integer sequences with special characteristics. See http://www.lclark.edu/~miller/langford.html. An example of a sequence is

I.e. we have 4 sets of 2 numbers 1,2,3,4 where between number k we have k other numbers.

For a MIP formulation see: http://www.amsterdamoptimization.com/pdf/langford.pdf

With Microsoft Solver Foundation it is easy to create a constraint programming version that solves much quicker and in addition it is easy to add a simple user interface.

Note that there are improved CP formulations. See e.g. http://4c.ucc.ie/~bms/Papers/ResearchReports/2000_18.ps