The solution is written at the first door with the sets of colors being: Orange, Purple and Blue; Orange; Red, Bright green (not yellow!) and Purple; Light green and green; Dark red, Purple and orange. You have to press the correct paintings from the room in the correct order.
UPDATE: I Found the solution and deciphered the code! Here are the colors that you have to tap per each stage (as indicated near the door) in order to complete this 100 Rooms Level 13:
And this was the walthrough for Room 13 in 100 Rooms! Check back soon for the rest of the levels or check out the 100 Rooms Room 12 Walkthrough.