'Odd' Algorithms
Consider a Rubik's Cube.
A move is a 90 Degree turn on one of the faces of the cube.
An algorithm is a sequence of moves.
An identity algorithm is an algorithm which when applied on a particular state of the cube results in the exact same state.
How many identity algorithms are there which consist of an odd number of moves?
The answer is 0.
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1 solution
The problem has been discussed nicely over here .