Consider a seven-segment LED display (used by many calculators). You wish to use one as an indicator in the dark. Because it will be dark, anyone reading it will not be able to distinguish between shapes that are shifted. For example, one can not distinguish between only the top-left or only the bottom-right segment being lit; they are the same shape, just shifted. Similarly, the top-left and top segments being lit can not be distinguished from the bottom-left and middle segments being lit. No segments lit can not be used either; you might not even be looking at the indicator.
Normally, there would be 128 possible lighting patterns. 1) In this scenario, how many are permitted? 2) What would be a simple way around this limitation?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, April 6, 2016 at noon Pacific Time. I will post the answer shortly after.