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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.

See The Solution Submitted by Jer    
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Solution No Subject | Comment 4 of 5 |

The diagram can form 21 squares:

9 with sides of unit 1 in length
4 with sides of unit SQRT(2) in length
2 with sides of unit SQRT(5) in length
4 with sides of unit 2*SQRT(2) in length
2 with sides of unit SQRT(13) in length

A minimum of 7 O's need to be eliminated so none of these 21 squares remains intact. Example below:

    0 0
    - 0
- - 0 - - 0
0 0 0 0 0 0
    - 0
    0 -


  Posted by Dej Mar on 2006-05-10 10:30:56
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