If the number of discs is even, try moving the first disc to the middle peg. If the number of discs is odd, try moving the first disc to the right peg.

In general, the minimum number of moves required to move n discs to the right peg (or even the middle peg) is 2⁰ + 2¹ + 2² + 2³ + ... + 2^(n-1). This can be expressed by the formula (2ⁿ) -1. [ This proof can be found in Mathematics Teacher, vol. 45, page 522, 1952. ] Thus 2 discs can be transferred to another peg in 3 moves, 3 in 8, 4 in 15, and so on.