There are four pegs, numbered from 0 to 3. A stack of n white disks, is initially on peg 0, and a stack of n black disks, initially on peg 2. The destination pegs for the white stack and the black stack are pegs 2 and 0, respectively. In other words, the goal is to interchange the two stacks, using pegs 1 and 3 as temporary holding pegs.
The basic way to solve is that first we move the white disks initially to peg 1 using peg 3 as temporary holding peg (using regular tower of Hanoi problem). And then move black disks to peg 0 using peg 3, finally move white disks from peg 1 to peg 2. Is there any better way to solve this in lesser number of steps? The above approach gives $3*2^n -3$ steps.