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Results are presented from an exhaustive search on the odd permutations of Square-1 in its solved shape. A maximum of 31 turns (U, D and /) are needed to solve these positions, which may be a new lower bound on the length of God's Algorithm for Square-1, in this metric.

The method I used was suggested by Tom and Silviu's coset searches for the Rubik's Cube: Starting from a cube-shaped, odd-parity position of Square-1, an iterated depth-first search was made for all even-parity cube-shaped positions, with the search being pruned on [shape]x[parity].