CS4341 Introduction to Artificial Intelligence. A97

Department of Computer Science
Worcester Polytechnic Institute

Homework 1

Puzzle:

This puzzle consists in finding a substitution of the letters F, O, R, T, Y, E, N, S, I, X by digits such that when each of these letters is replaced by the corresponding digit, the following sum is still arithmetically correct.

FORTY
+ TEN
+ TEN
-----
SIXTY

This puzzle has solutions. One of them is

F = 2, O = 9, R = 7, T = 8, Y = 6, E = 5, N = 0, S = 3, I = 1, X = 4

since:

29786
+ 850
+ 850
-----
31486

is arithmetically correct. Solutions to the puzzle should not repeat digits.

Homework 1

Your mission is to:

1. Write a computer program (preferably in Lisp, but C or scheme are also allowed for this assignment) that implements the generate-and-test strategy to solve this puzzle.
   • Your program must satisfy the following conditions:
     • It should find at least one solution to the puzzle.
     • The generator must be
       • complete, and
       • non-redundant
   • You will receive extra credit if:
     • your program produces a solution to the puzzle different to the one given above. (Extra points for each additional correct solution found).
     • your generator is informed.

2. You need to hand in the following material by 1:30 p.m. Thursday, Sept. 11, 1997:
   • A print out of:
     • your program code using the departmental documentation standard
     • the solutions found by your program.
   • A (mathematically sound) proof that your generator is:
     • complete, and
     • non-redundant
   • A precise count of how many different candidate solutions your generator would produce before exhausting all possibilities.
   • For the extra credit you need to include also:
     • A mathematically sound proof that your generator is informed.

About Lisp:

• You can find Ibuki Common Lisp (ibcl), Kyoto Common Lisp (kcl), or Scheme (scheme) on the CCC machines.

• Also, you can find the text software in the /cs/cs4341/ directory of the CCC machines. You are welcome to look at the code contained there but you cannot use it in your assignments. YOU MUST DEVELOP YOUR OWN CODE!!

• To run Kyoto Common Lisp in the CCC machines:

  • Type: kcl

  • You will get the message
    

    "AKCL (Austin Kyoto Common Lisp) Version(1.609) Thu Mar 12 17:14:07 EST 1992 Contains Enhancements by W. Schelter"

    followed by a prompt: " > "

  • Type: (help)
    to obtain help.

  • Type: (bye)
    to exit the shell.

  • Type: (load "foo")
    to load file "foo". By default the extension of the file will be assumed to be .lsp (lisp) or .o (compiled code)

  • Type: (compile-file "foo")
    to create a compiled file foo.o