The European version of the popular game "Brainvita" (or "Peg Solitaire") looks as follows:
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The game fills the entire board with pegs except for the central hole. The objective is, making valid moves, to empty the entire board except for a solitary peg. A valid move is to jump a peg orthogonally over an adjacent peg into a hole two positions away and then to remove the jumped peg.
Solution posted by Pritish Kamath (CSE IITB 2012 Alumnus, Assistant Researcher MSR Bangalore) in comments!