During a game of hide-and-seek, Isabella hides behind a tree while Jack counts. Meanwhile, Kate watches from a distance as Isabella switches hiding spots to behind a bush. Unbeknownst to both girls, Luke sees Isabella move and decides to take her original spot behind the tree. When Jack finishes counting and starts searching, what do Isabella, Kate, and Luke think about each other's locations? Provide a short response.
Isabella believes she is the only one who knows she switched from the tree to the bush, assuming that neither Kate nor Jack saw her move. She thinks Jack will look for her at the tree and Kate will think she's still hiding there.

Kate observed Isabella move from the tree to the bush, so she knows where Isabella is actually hiding. However, she doesn't know that Luke saw Isabella and took her spot, so Kate thinks Isabella is safe behind the bush and Luke is somewhere else.

Luke saw Isabella switch her hiding spot, and he decided to hide behind the tree where Isabella was first hiding. He knows where Isabella is but he does not know that Kate witnessed Isabella's movements. Thus, he believes he has taken over a good hiding spot without being seen, and because he only saw Isabella move and not who was watching, he also thinks Kate does not know he is now behind the tree.