In Trifles, how is it significant that the men and women problem-solve in different ways?
The men and women approach the crime scene with different mindsets. The men are looking for a purposeful, exact motive, something that explains the murder without any loose ends. Because of that, they spend their time looking for "clues" that do not exist; no broken windows or footprints in the garden. In contrast, the women look to the functional things in the kitchen, the things that Minnie was likely to have touched or moved in the last few days before the murder; they are not directly looking for clues, but find them anyway.
COUNTY ATTORNEY: You mean that they didn't get on very well?
MRS. HALE: No, I don't mean anything. But I don't think a place'd be any cheerfuller for John Wright's being in it.
COUNTY ATTORNEY: I'd like to talk more of that a little later. I want to get the lay of things upstairs now.
(Glaspell, Trifles, etext.virginia.edu)
This exchange shows how the County Attorney is looking for exact facts, for real things that might lead to an epiphany moment. He wants to look upstairs because he is expecting to find a confession note or a diary with evil thoughts, but those obvious clues can't exist. In contrast, the women are more aware of the emotional problems in the marriage, and so when they discover the dead canary, things fall into place; the men can't figure how a woman's emotional status could lead to murder, while the women understand it because they can see past the explicit into the implicit.