gavinksong

I'm not sure if this has been posted yet, but it is a nice puzzle. Can three lights always be placed outside of any convex solid such that the solid is completely illuminated? You can assume that: We are working in an otherwise empty three-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.

Oh.. Hmm...

Aand here's my second final answer... I probably still have [1] wrong...

Okay, I know I've made a lot of posts, but here's my final answer. I realized I made a mistake on the first problem, or at least the first problem as I understand it.

[2] is less nice.

[2] is less nice.

[2] is less nice.

Edit: fixed a typo

I need some clarifications: 1) Does every group of five squares share exactly two common points, or can they have more? 2) Are the squares solid?

Sorry, but Peter moves first.

You got it.

As TSLF said, Alice and the queen are unrestrained by how a queen normally moves on a chessboard. My understanding of it is that Alice can "jump" from anywhere on the board to any other unvisited square, without touching any of the squares in between.

Edit: I'm dumb.

That's not what I meant, but what you said afterwards made a lot of sense. It brought order to the muddled up thoughts in my mind. I guess what I meant was, is it possible to prove that no sufficient conditions exist?