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A Tighter Fit (Posted on 2004-07-29) Difficulty: 3 of 5
A 10x10 square can obviously hold 100 unit circles (diameter=1) when arranged in rows and columns. What is the maximum number of non-overlapping unit circles a 10x10 square can hold if the circles are packed closer together?

  Submitted by Brian Smith    
Rating: 2.0000 (4 votes)
Solution: (Hide)
106 circles can fit in a 10x10 square.

8 rows of row/column packed circles (which take up 8 units of space) can be replaced by 9 hexagonally packed rows (which take up 1+8*sqrt(3)/2 = 7.928 units of space.) This leaves 2 more units of space in the square which can be filled with two complete rows of 10 circles. Altogether, there are 4 rows with 9 circles and 7 rows with 10 circles.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsPuzzle ThoughtsK Sengupta2023-04-30 23:52:46
SolutionsolutionDej Mar2008-05-30 08:38:03
re: SolutionBrian Smith2004-08-27 08:13:36
SolutionMissy2004-08-26 14:30:50
QuestionCorrection and solutionHugo2004-08-02 15:04:14
re: another direction (circles, not coins)rixar2004-08-01 08:45:13
another directionLarry2004-07-31 23:33:03
re(2): hmmm... (I think I got it this time)Vee-Liem Veefessional2004-07-31 22:57:29
re(3): hmmm...Vee-Liem Veefessional2004-07-31 22:52:36
one morerixar2004-07-31 08:28:12
I think it might workPuneeth2004-07-30 20:40:55
Solutioni think i have itrixar2004-07-30 20:12:41
Solutionre: hmmm... (I think I got it this time)Thalamus2004-07-30 13:03:09
110 or moreHugo2004-07-30 08:55:47
Close but no cigarBrian Smith2004-07-30 08:05:41
re(2): hmmm...ThoughtProvoker2004-07-30 05:38:23
re: hmmm...Vee-Liem Veefessional2004-07-30 02:20:32
Hmm, just a wild guess.Vee-Liem Veefessional2004-07-30 02:04:13
SolutionSolution...Henry2004-07-29 17:38:32
Hints/Tipshmmm...Thalamus2004-07-29 13:15:38
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