This doesn't seem like a brain teaser to me. It sounds like an optics question. And a pretty basic one at that.
Mirrors will reflect a certain degree of whatever light is shone at them. So, if there's no light, they'll reflect nothing. If there is light, they'll reflect that light. Depending on the mirror's material, they may not reflect various wavelengths of light (like, say, X-rays or radio waves), but they should certainly reflect most visible light. Eventually, the light will also dissipate, such that nothing as reflected, as each subsequent reflection will decrease the intensity of the light by a certain amount. The amount of dissipation probably depends on the material being used for reflection (usually aluminum in common mirrors), and the specific wavelength of the light. And possibly other factors like ambient temperature, pressure, glass covering, material purity, etc.
DaveE