Source: Wikipedia article on Peg Solitaire
Problem:
The European version of the popular game "Brainvita" (or "Peg Solitaire") looks as follows:
Y Y O O O Y Y
Y O O O O O Y
O O O O O O O
O O O T O O O
O O O O O O O
Y O O O O O Y
Y Y O O O Y Y
Prove that the initial configuration as shown in the representation is not solvable.
Background:
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.
Similar Problems:
Rubik's Cube
Sam Loyd Puzzle Solvability
Update:
Solution posted by Pritish Kamath (CSE IITB 2012 Alumnus, Assistant Researcher MSR Bangalore) in comments!