(related to Problem: The Mouse-trap Puzzle)
If we interchange cards $6$ and $13$ and begin our count at $14,$ we may take up all the twenty-one cards — that is, make twenty-one "catches" — in the following order: $6,$ $8,$ $13,$ $2,$ $10,$ $1,$ $11,$ $4,$ $14,$ $3,$ $5,$ $7,$ $21,$ $12,$ $15,$ $20,$ $9,$ $16,$ $18,$ $17,$ $19.$ We may also exchange $10$ and $14$ and start at $16,$ or exchange $6$ and $8$ and start at $19.$
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