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Squares in a cross (Posted on 2006-05-10) Difficulty: 3 of 5
In the diagram formed of twenty Os below, in how many ways may four be selected such that they form a square? What is the least number of Os that may be removed such that none of these squares remains intact?
O O
O O
O O O O O O
O O O O O O
O O
O O
Note: the horizontal and vertical spacing should be equal.

  Submitted by Jer    
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Solution: (Hide)
There are 21 squares (Taking the closest circles to have unit radius they are Nine 1x1's, Four sqrt(2)xsqrt(2)'s, Four, 2sqrt(2)x2sqrt(2)'s, Two sqrt(5)xsqrt(5)'s and Two sqrt(13)xsqrt(13)'s)

For the second part, one way is remove the SIX counters marked with an x:

  oo
  xo
xxoooo
oooxxo
  oo
  ox
				

Comments: ( You must be logged in to post comments.)
  Subject Author Date
MinimumJer2006-05-11 12:24:07
SolutionNo SubjectDej Mar2006-05-10 10:30:56
Some Thoughtsre(2): Solutiontomarken2006-05-10 09:57:58
re: SolutionFederico Kereki2006-05-10 09:08:52
SolutionSolutiontomarken2006-05-10 08:55:33
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