Red Christmas Island crabs scuttle about Her Majesty’s feet, and over on the grass, an indigenous man plays the didgeridoo.

It this meant to be an average day chez the PM?

What goes on in the minds of architects when they’re envisioning a new home, specifically one designed for Australia’s Prime Minister to live and work in?

Surely designing a house with a home office is no big deal, but add to that a 600-person dining hall, room for security and private lodgings befitting the leader of our nation, and things get fun.

It was an unusual challenge for many of the 242 designs submitted for the Lodge on the Lake competition, a Centenary initiative designed to get people thinking about the kind of digs our prime minister should live in, should the day ever come when he or she is able to move out of the decades-old “temporary” accommodation on Adelaide Avenue.

A new exhibition at the Gallery of Australian Design is showcasing 26 of the 242 designs pitched as the new lakeside home.

From a “snow dome” approach, to a house that “floods”, may of the designs embrace the landscape; one entry, that placed the Lodge on an island, even predicted the future by putting Kevin Rudd in the design drawings.

Another shows a grand reception, at which Rudd and his wife, Therese Rein (again, prescient) mingle among their guests. Paul Keating is there, albeit in black and white, and, if you look closer, rock legend Nick Cave is loitering in the background.

Again, just another day at the Lodge.