You have 36 playing cards that are to be arranged in a 6x6 array. Each card is to be placed initially face up into one of the 36 positions allocated, not necessarily adjacent to any previously placed card.

When a newly placed card, though, is in fact adjacent edge-to-edge (not diagonally), to a previously placed card, the previously placed card is flipped: face-up to face-down, or vice versa. A card may then be flipped more than once as additional cards are placed next to it. And a newly placed card may cause this to happen in more than one previously placed card, if more than one occupy orthogonally adjacent positions.

The goal is to have the completed 6x6 array consist of all face-up cards.

What is the placement order to make this happen? Or prove it's impossible.

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Based on "Not over easy", Enigma No. 1767, by Bob Walker, New Scientist, 21 September 2013, page 30.