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 Four Way Smarties (Posted on 2004-11-05)
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?

 See The Solution Submitted by Gamer Rating: 4.2000 (5 votes)

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 Subject Author Date re(4): My new solution (Takes from previous solution) Gamer 2004-11-08 15:42:21 re(2): Minor difference in interpretation + Computer solution David Shin 2004-11-06 17:37:44 re(4): My new solution (Takes from previous solution) Osi 2004-11-06 16:52:37 re(3): My new solution (Takes from previous solution) Tristan 2004-11-06 16:15:54 re: Minor difference in interpretation + Computer solution Osi 2004-11-06 12:14:30 re(2): My new solution (Takes from previous solution) Osi 2004-11-06 12:10:03 re: My new solution (Takes from previous solution) Tristan 2004-11-06 10:30:26 My new solution (Takes from previous solution) Osi 2004-11-06 09:24:57 re: Specifications Osi 2004-11-06 09:00:05 re(5): Part B (Correction and Full Solutions--Possibly) Osi 2004-11-06 08:58:36 Specifications Gamer 2004-11-05 23:14:28 re(4): Part B (Correction and Full Solutions--Possibly) Tristan 2004-11-05 19:33:21 Independent solution Tristan 2004-11-05 19:23:28 re(2): Part B (Full Solutions--with six smarties (including myself) Osi 2004-11-05 18:19:41 re(3): Part B (Correction and Full Solutions--Possibly) Osi 2004-11-05 18:05:41 re(2): Part B (Correction and Full Solutions--Possibly) Gamer 2004-11-05 17:30:23 Eating Crow Steve Herman 2004-11-05 16:50:26 re: Part B (Correction and Full Solutions--Possibly) Osi 2004-11-05 15:46:57 Part B Osi 2004-11-05 15:05:34 Full Solution (Part b) Steve Herman 2004-11-05 14:40:47 Minor difference in interpretation + Computer solution David Shin 2004-11-05 14:38:07 Full Solution Jer 2004-11-05 13:00:36

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