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Increase the square

Question

Four pegs begin at the corners of a unit square on a grid having integer coordinates. At any time one peg may jump a second peg along any straight line and land an equal distance on its other side. The jumped peg remains in place.

+    +    +    +    +    +         +    +    +    +    +    + 

+    +    +    +    +    +         +    +    +    +    +    + 

+    +    +    +    +    +         +    +    O    +    +    + 

+    +    +    O    O    +   ==>   +    +    +    O    O    +  

+    +    +    O    O    +         +    +    +    O    +    +  

+    +    +    +    +    +         +    +    +    +    +    +  

Is it possible to maneuver the pegs to the corners of a larger square?

+    +    +    +    +    +   

+    O    +    O    +    +   

+    +    +    +    +    +   

+    O    +    O    +    +   

+    +    +    +    +    +   

+    +    +    +    +    + 

 

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