Mahjong Solitaire Computing the number of unique and solvable arrangements

This paper shows in how many ways n tiles can be arranged and provides a recurrence relation on this sequence and offers algorithms for generating all arrangements and calculating the number of arrangements that can be won. In this paper we will provide denitions on various aspects of the game Mahjong Solitaire. We will show in how many ways n tiles can be arranged and provide a recurrence relation on this sequence. We will also provide a recurrence relation on the number of ways we can divide these tiles over a various number of sets, and even a closed formula when we apply the constraint that each set may only contain two tiles. We will show that the product of these two sequences is not equal to the number of arrangements that can be created. We will provide algorithms for generating all arrangements and calculating the number of arrangements that can be won.

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