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.
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
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