@ -83,7 +83,7 @@ Finally we call @racket[solve], which finds a solution (if it exists):
(solve triples)
]
Perhaps we're curious to see how many of these triples exist. We use @racket[solve*] to find all 200 solutions:
Perhaps we're curious to see how many of these triples exist. We use @racket[solve*] to find all 20 solutions:
@examples[#:label #f #:eval my-eval
(solve* triples)
@ -96,14 +96,14 @@ Perhaps we're curious to see how many of these triples exist. We use @racket[sol
(add-constraint! triples coprime? '(a b c))
]
We @racket[solve*] again to see the 10 results:
We @racket[solve*] again to see the reduced set of 10 results:
@examples[#:label #f #:eval my-eval
(solve* triples)
]
``But really there's only five unique solutions —the values for @racket[a] and @racket[b] are swapped in the other two.'' Fair enough. We might say that this problem is @deftech{symmetric} relative to variables @racket[a] and @racket[b], because they have the same domains and are constrained the same way. We can break the symmetry by adding a constraint that forces @racket[a] to be less than or equal to @racket[b]:
``But really there's only five unique solutions —the values for @racket[a] and @racket[b] are swapped in the other five.'' Fair enough. We might say that this problem is @deftech{symmetric} relative to variables @racket[a] and @racket[b], because they have the same domains and are constrained the same way. We can break the symmetry by adding a constraint that forces @racket[a] to be less than or equal to @racket[b]:
