gavinksong

Wow. I had seriously overthunk. I literally just realized that plasmid's proof is a finished solution. Silly old me thought that we also had to prove 2 being false implies 1 being true.

This UTM seems pretty foolproof... I know this isn't exactly what the OP is asking for, but it seems that's as close as I can get it.

I decided this post needs some love. I failed to account for the case where two squares share part of a side or sides.

I decided this post needs some love.

Is this claim for any nxm table or only when n = m ? Does OP ask for every nxm, or a particular nxm? Fair question! The way I wrote the OP, I only asked if one exists. I am seeking to extend the OP to see if the above conjecture(s) extends to any nxm and if not, what nxm does it work for? Hmm. So is k-man's answer not correct?

k-man always has such elegant solutions to these problems. I'm sorry but I couldn't contain myself.

Does this account for all 1000 patrons? Ohhhhhh, wait. I missed the part where it says that each patron pays $100.

BMAD, I like this series of puzzles you've posted. Do you come up with them yourself, or did you get them from somewhere?

Can you prove it?

This is a follow-up to do not know the answer to this problem. How many lights are necessary to completely illuminate a convex solid in N dimensions? Same conditions as before: We are working in an otherwise empty N-dimensional space. The lights are point sources. The solid is illuminated at every point on its surface where a straight line can be drawn uninterrupted between it and a light source. Let me also add: Lights cannot be placed "at infinity".