You and four other people (who coincendentally are all smarties) are in late testing room where you will take your test where there is a 6 by 6 grid of equally spaced desks with chairs in the same relative spot.

You go into the room after all four smarties have chosen their location. You have a test taking policy where you always want to sit at the midpoint between two smarties. The smarties in the room with you feel the exact opposite way, so their arrangement is always such that no smartie is at the midpoint of two other smarties

However, depending on where the smarties are sitting, you may not be able to sit at the midpoint since in all cases it would always be where there is no chair and desk. (There is a strict no moving desks or chairs rule too.) How many ways could the current 4 smarties sit such that you couldn't sit at the midpoint of two smarties if reflections and rotations count as well?

How many ways could you not find where you want to sit if there were 5 smarties other than you and reflections and rotations count as well?

(In reply to re(2): My new solution (Takes from previous solution) by Osi)

Your comment makes it obvious that your interpretation is so radically different from my interpretation, that I have no clue what you think the problem is asking.  All I have left to do is to explain my own interpretation very clearly.

Gamer tends to be a little unclear in wording (no offense to Gamer, he just thinks differently), so I'll try to explain it in my own words.

You and 4 smarties (you don't count as a smarty) are the only ones taking a test in a room.  There is a 6 by 6 grid of desks evenly spaced.

The 4 smarties take their seats before you do, and they sit in a way that none of them are at midpoints between two others.  You want to sit at the midpoint of two smarties, but it turns out to be impossible.  How many possible combinations of the 4 smarties positions are there so that you do not have a good seat?  How many combinations would there be if there were 5 smarties instead?

Does that help?

Posted by Tristan on 2004-11-06 16:15:54