Constraints in Girls and Pigs problem
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There are two constraints in problem that is not mentioned in problem statement:
- Obvious one: because number of breasts is always greater than number of legs, number of pigs is always greater than zero.
- Not obvious one: number of girls, too, should be greater than zero. With 32 legs and 176 breasts we have 6 solutions, including solution with 0 girls and 8 pigs with 22 breasts each, but checker disagrees and counts only 5 solutions.
I read many of other solutions and it seems that most people are not aware of second constraint.
Hoperfully this help someone to save hours debugging!
"..The girls are pasturing pigs at the field..." it seems like it's being said that there are girls on the field, so there are more than 0 of them))
Good point! Definitely there should be someone pasturing the pigs, or some of them may get lost, and my solutiong become wrong :).
Though I'm not quite sure about what was meant when writing the statement, I suspect that all the three unknown values should be non-negative integers.
When I proposed the problem to school kids I got various additional questions:
- are there only female pigs
- do all pigs have the same number of breasts
and even more wild ideas about possibly one-legged girls included into number of shepherdesses
not pondering on social and biological aspects of all those questions, I generally point out that any of them leads to problem becoming unsolvable (or allowing too large number of solutions) which, out of common sense, seems to be not our goal :)