beginner is confused about rings

I would like to give some feedback about ...

In the extra check the given ring combination is:

break_rings(({3,4},{5,6},{2,7},{1,5},{2,6},{8,4},{1,7},{4,5},{9,5},{2,3},{8,2},{2,4},{9,6},{5,7},{3,6},{1,3},))

I tried to draw this combination on the paper to realize the situation. I can understand how it is possible to break rings in 5 steps to get them all lose. I think the answer should be 6:

first break ring number 5, then no.2, 3 and you got combination of ({8, 4}, {1, 7}, {9, 6}) which requires a removal of 3 rings. So total steps must be 6.

From: http://www.checkio.org/mission/break-rings/solve/

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