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No: 04       November 09, 2022



Two circles of the same size and different colors are placed randomly on a computer screen. These circles can be in one of 4 different states:


1. The circles are not touching.
2. The circles are tangent, i.e. touching at a single point.
3. The circles are overlapping, the first one is on top.
4. The circles are overlapping, the second one is on top.

How many different states are there for 3 circles with different colors?

*All three circles should be seen on the screen and considered two-dimensional.
*The circles have a well defined order (top/bottom), e.g. if the first circle is on top of the second and the second circle is on top of the third, the third circle cannot be on top of the first.

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