My 14-week-old kitten just doesn't get it. She has to be in either a
cage, or a very small room with litterbox, toys, and food, in order to
understand that we USE THE BOX and not the corner for pooping. Her
health is fine and there are no introduction problems with other cats
(she's loving my playful neutered male, who is something like a giant
motorized teddy bear to her).

Every time I experimentally expand her domain a wee tad -- opening the
door to her happy kitty prison (the small room with the food, toys,
bed, and litterbox) and letting her go down the hall into the office --
she poops in the corner of the office. It's like out of sight, out of
mind with litter boxes. If there's a box within clear sight, she uses
it, but if not, she uses the corner.

So now I'm thinking I put about 20 boxes around the house to see if she
uses them, and if she does I start gradually removing them. And I do
mean 20 boxes. Let no man say I failed for lack of thoroughness. My
house isn't that big; I simply mean to see to it that there's a box
within her line of sight no matter where she is.

N.B. Coyotes prevent the outdoor solution.

Has anyone ever tried this 20-box idea successfully? Or heard of it?

Thanks.