A plain white cube has gone through 4 steps to become what it is now. The steps (not necessarily in order) are:
a) The whole cube being painted red
b) A white circle being painted on every face except for the top and back
c) The front and back faces being painted black
d) The top, back, and bottom being painted blue
All of the following facts about painting the cube are true:
1. After the last of the four steps, the top face was all purple, the left and right faces were red with a pink circle in each of their centers, the front black with a gray circle, the bottom purple with a light blue circle, and the back completely dark blue.
2. Color mixing goes as follows:
3. Once black is added to a face, it will mix with the colors on the face if possible, but it cannot be changed at all afterwards. This is not true with white.
4. Any area where two colors have been mixed cannot change color.
5. Exactly one of the following is true:
-Black was added first.
-Red was added before blue.
-Blue was added after white.
-White was added last.
In what order were the colors added?
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