You Do Need power plug adapter while traveling from Greenland to Christmas Island.

Here is Why You Need An Adapter

The outlet and plug type used in Christmas Island is I and in Greenland are C, E, F and K. This is how they look like.

Greenland

In Greenland, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K

Christmas Island

In Christmas Island, outlets of type I are in use.

Type I