You Do Need power plug adapter while traveling from Norway to Cayman Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cayman Islands are A and B and in Norway are C and F. This is how they look like.

Norway

In Norway, outlets of type C and F are in use.

Type C

Type F

Cayman Islands

In Cayman Islands, outlets of type A and B are in use.

Type A

Type B