Oxvo Cameron Browne (c) 2008

Oxvo is a solitaire puzzle in which the player slides knotwork tile segments around in order to complete closed paths.

Rules

Oxvo consists of 15 tiles showing knotwork segments initially set within a 4x4 grid as shown. The upper right cell is empty and no paths on any tile cross to neighbouring tiles at this point.

Starting position.

Each move involves sliding one, two or three tiles towards the empty cell, as per any other 15-puzzle. Two such moves are shown below.

Two typical opening moves.

If any move results in the formation of one or more closed paths then the score for that move is p the length of the longest closed path (squared) minus m the number of moves so far. Scores below 0 are not counted:

    score = max(0, p * p - m)

A path's length is given by the number of crossings along its length, where self-crossings count twice.

The game's final score is the best score achieved over the entire game.

Notes

The aim is to form the longest possible path in the shortest number of turns.

The longest possible path length is 32; one such maximal path is shown below.

A maximal path.

The maximum possible score is therefore 32 * 32 = 1,024 minus the number of moves required to form the path.

Oxvo rules and pieces copyright (c) Cameron Browne, April 2008.

Oxvo is a 15-puzzle played with Osbo dice, hence the name "OXVo" where XV = 15.