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?

Your solution looks great to me, Jer.
The second part of the problem asks about 5 other Smarties.
The 4th smartie to sit leaves no seats for the 5th smartie which wouldn't create a midpoint opportunity, so the answer to part (b) is 0!

Edited on November 5, 2004, 2:41 pm

Edited on November 5, 2004, 4:40 pm

Posted by Steve Herman on 2004-11-05 14:40:47