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Four Way Smarties (Posted on 2004-11-05) Difficulty: 3 of 5
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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(4): My new solution (Takes from previous solution)Gamer2004-11-08 15:42:21
re(2): Minor difference in interpretation + Computer solutionDavid Shin2004-11-06 17:37:44
re(4): My new solution (Takes from previous solution)Osi2004-11-06 16:52:37
re(3): My new solution (Takes from previous solution)Tristan2004-11-06 16:15:54
re: Minor difference in interpretation + Computer solutionOsi2004-11-06 12:14:30
re(2): My new solution (Takes from previous solution)Osi2004-11-06 12:10:03
re: My new solution (Takes from previous solution)Tristan2004-11-06 10:30:26
My new solution (Takes from previous solution)Osi2004-11-06 09:24:57
re: SpecificationsOsi2004-11-06 09:00:05
re(5): Part B (Correction and Full Solutions--Possibly)Osi2004-11-06 08:58:36
SpecificationsGamer2004-11-05 23:14:28
re(4): Part B (Correction and Full Solutions--Possibly)Tristan2004-11-05 19:33:21
SolutionIndependent solutionTristan2004-11-05 19:23:28
re(2): Part B (Full Solutions--with six smarties (including myself)Osi2004-11-05 18:19:41
re(3): Part B (Correction and Full Solutions--Possibly)Osi2004-11-05 18:05:41
re(2): Part B (Correction and Full Solutions--Possibly)Gamer2004-11-05 17:30:23
Eating CrowSteve Herman2004-11-05 16:50:26
re: Part B (Correction and Full Solutions--Possibly)Osi2004-11-05 15:46:57
Part BOsi2004-11-05 15:05:34
SolutionFull Solution (Part b)Steve Herman2004-11-05 14:40:47
SolutionMinor difference in interpretation + Computer solutionDavid Shin2004-11-05 14:38:07
SolutionFull SolutionJer2004-11-05 13:00:36
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