In the diagram formed of twenty O’s below, in how many ways may four be selected such that they form a square?
What is the least number of O’s 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.
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 20060510 10:30:56 