Tower Relay: move the small stack before the large disc
Break a five-disc transfer into two four-disc transfers. The middle move explains both the working tower and the familiar minimum-move count.
Worked examples use the Standard board unless a different size is stated. Hard and Expert may change the board dimensions or amount of information to track.
Make room for the disc you want to move
Tower Relay allows only the top disc of a tower to move. A larger disc cannot sit on a smaller one. These rules make an apparently direct goal depend on preparation: to move the largest disc from Tower 1 to Tower 3, first remove everything above it and keep the destination clear of smaller discs.
Tower 2 is therefore part of the plan rather than a place for mistakes. With five discs, the four smaller discs must form a legal stack on Tower 2 before the largest can move directly to Tower 3. The goal for that first stage is temporarily different from the final destination of the whole puzzle.
Understand the two-disc transfer first
Imagine only discs 1 and 2 on Tower 1, where 1 is the smaller disc. To transfer them to Tower 3, move disc 1 from Tower 1 to Tower 2, move disc 2 from Tower 1 to Tower 3, then move disc 1 from Tower 2 to Tower 3. All three moves are legal, and no shorter transfer can move disc 2 while keeping its destination available.
Notice how the small disc makes a detour. If you move it straight to Tower 3 first, disc 2 cannot follow until the small disc moves away again. The best immediate destination for the smallest disc depends on the larger transfer you are preparing. Looking only at whether a disc moved toward the final tower misses that dependency.
Use the same structure on a larger stack
For five discs, first transfer the top four discs from Tower 1 to Tower 2, using Tower 3 as working space. Then move disc 5 to Tower 3. Finally transfer the four-disc stack from Tower 2 to Tower 3, using Tower 1 as working space. The same three-stage description works inside each four-disc transfer, with one fewer disc and different tower roles.
Naming those roles prevents a common confusion. The working tower is not always Tower 2 during a smaller transfer. State the current subproblem explicitly: move this many top discs from this source to this destination, using the remaining tower. The rules stay fixed while source, destination and working space exchange roles.
Use the minimum as an explanation, not a deadline
Let the minimum moves for a stack of n discs be M(n). The smaller stack must move aside, the largest disc moves once, and the smaller stack returns onto it, giving M(n) = 2M(n−1) + 1. Starting with one disc taking one move produces 15 moves for four discs, 31 for five and 127 for seven. The counter shown here compares your current route with that theoretical minimum; it does not create a time limit.
You can still finish after taking extra legal moves. If a route becomes confusing, Undo restores the previous stack and move count. Selecting the current source again cancels a selection without moving a disc. Restart restores the same starting stack; it does not pretend to shuffle a different challenge. Work through a complete smaller transfer before stepping up to seven discs, and try to explain the role of each temporary tower rather than memorising a long sequence of clicks.
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