Sheet 1

Task 1

Model and solve in MiniZinc problem 028 from the CSPLib: “Balanced Incomplete Block Designs”.

Task 2

Consider the SEND + MORE = MONEY cryptarythm problem seen in the classes.

• Implement the model saw in class and experiments with different heuristics for the search changing:
  • the criterion for selecting which variable to assign first and
  • the criterion for selecting which value to assign first.

• Formulate another model for the problem (hint: model the arithmetic constraint by means of rest variables)

• Implement in MiniZinc the alternative models that you have conceived. Compare their solutions. Which is fastest? (print search statistics and compare them).

• Visualize the search tree

• Find all solutions for the problem. How many solutions are there? Do all models yield the same number?

• Model, implement and solve the optimization version in which you have to maximize the value that MONEY gets.

• Repeat the analysis for the cryptarythm: ten + ten + forty = sixty or the one proposed in the assignments of the course in coursera

• Compare using lexicographic and first-fail search. Which of the two search strategies is the best in the two problems? Is the conclusion the same?

Task 3

Model and solve in MiniZinc the following problem. A kid goes to a store and buys four items. The cashier: “that makes $7.11”. The kid pays and when he is about to leave the store, the Cashier says: “Hold on, I multiplied! let me add! wow, the sum is also $7.11”. Which are the prices of the four items?