[Matt Q]

Carl,

Here's my thinking: Two perpendicular mirrors produce three images, that's one image per mirror and one "composite" image across the join.

If you have three mirrors, then you have, in effect 3 sets of paired mirrors. So presumably, each of those pairs will produce a composite image across the join, since we know that's what a pair of mirrors do. So that's 3 composite images.

Plus each of the 3 mirrors will produce a whole reflection. So, that would make 6 reflections in total. So, at least 6 is what I thought.

I have since looked on the internet, and as you say the answer given is 7 reflections, though I'm not clear how that works (no one gives a clear diagram). I guess the 7th reflection must be bounced off all three mirrors, and possibly is seen in the corner (where the three mirrors join).

As to whether we should also count the real iPhone or not, well, the question doesn't specify whether or not it's visible to me when I look in the mirror, only that it's in my hand. So, I guess it's up to us.

Matt