210.70 Lighting Outlets Required.
(A) Dwelling Units.
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(2) Additional Locations. Additional lighting outlets shall be installed in accordance with (A)(2)(a), (A)(2)(b), and (A)(2)(c).
(a) At least one wall switch?controlled lighting outlet shall be installed in hallways, stairways, attached garages, and detached garages with electric power.
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(c) Where one or more lighting outlet(s) are installed for interior stairways, there shall be a wall switch at each floor level, and landing level that includes an entryway, to control the lighting outlet(s) where the stairway between floor levels has six risers or more.
Exception to (A)(2)(a), (A)(2)(b), and (A)(2)(c): In hallways, in stairways, and at outdoor entrances, remote, central, or automatic control of lighting shall be permitted.
From 210.70(A)(2)(a) I get that any stairway (1 to n risers) requires a switch.
From 210.70(A)(2)(c) I get that a stairway with 6 or more risers requires two or more switches.
From the exception I get that no switch is required. I would ignore the exception as it specifies no riser count.
I would have answered 4 and contested the question, the grounds being the correct answer is 6 and not supplied. I would further note in the contest that, although the3-way switch are not specified in the code, only a code lawyer would claim they are not what should be installed.