Planning
Puzzles

A planning puzzle gives you a starting state, a set of legal actions and a goal that cannot usually be reached well by treating each move in isolation. Progress depends on preserving or creating options for later.

What makes a puzzle about planning?

Many puzzles involve decisions, but not every decision is a plan. In a target hunt, the useful action is attached to what you see now: find a matching symbol and select it. In a planning puzzle, the board after your action becomes part of the decision. A move can be locally attractive and still damage the route.

Three ingredients make that possible. The state must change, the consequences of an action must be predictable, and the order of actions must affect whether the goal is reached efficiently. Sliding blocks, river crossings, Towers of Hanoi and switch puzzles express those ingredients in different ways.

A practical planning loop

1. Name the goal exactly. “Improve the board” is too vague. Decide what must be true at the finish and which restrictions must remain true on the way.
2. List the effect of one action. Separate what the move changes directly from the neighbouring pieces, routes or resources it changes indirectly.
3. Protect scarce options. Do not block an exit, consume the only free space or move the only useful connector until its later role is complete.
4. Work backwards from forced states. Ask which move could create the final position. That often reveals what the previous position must contain.
5. Commit, then compare. After a move, check the actual state against the one you predicted. If they differ, revise the model rather than repeating the same trial.

Forward planning and backward planning

Forward planning begins with the current state: “If I move this piece, what happens next?” It is natural and useful when consequences are short. The difficulty is branching. If five moves are legal now and five more follow each of them, an unstructured search grows quickly.

Backward planning begins with the goal: “What must be true immediately before the last move?” It works well when the final step is constrained. In Tower Transfer, the goal peg must be clear before a large disk arrives, while the smaller disks need an ordered temporary home. In Toggle Grid, moving down the board progressively narrows the remaining repair routes.

Why undo does not erase the plan

Undo is useful feedback, not a substitute for consequences. It lets you test whether your prediction matched the board and recover without reconstructing the initial state by hand. Both games count the reversal in move efficiency, so exploration remains visible in the result.

A reset is broader: it restores the starting position but retains the move count for that round. This makes the interface forgiving without allowing a long unsuccessful route to disappear from the score.

Double Up takes the opposite position and has no undo at all. Its planning tool is the preview of the next tile, and a taken-back drop would falsify the tile count that its score is built on.

How Double Up creates fair queues

Double Up’s queue of number tiles is fixed by the seed before play begins. Before the queue is shown, a search places every tile itself, keeping the most promising board positions after each drop. If it cannot place the whole queue, or its best finish leaves too many tiles for that level, the queue is discarded and another is drawn.

The route the search found is shown as the reference during play. It is a strong route rather than a proven minimum, and it could see the entire queue where a player sees one or two tiles ahead, so finishing close to it is good planning and beating it is possible.

How Tower Transfer creates fair routes

Every legal Tower Transfer state records which of three pegs holds each disk. The exact breadth-first solver explores that complete graph in distance order, so its first path to the goal is guaranteed to be shortest. Even the five-disk Hard game has at most 243 states.

Easy uses the familiar full three-disk tower with par seven. Standard and Hard select reproducible legal split layouts only after the solver proves that their route depths land inside the published 10–15 and 22–31 move ranges.

How Toggle Grid creates fair boards

The generator creates only reachable states by applying legal presses to a solved board. An independent exact solver then tests every possible first-row pattern, chases its consequences down the remaining rows and selects the shortest complete route. A board is used only when its true optimum falls inside the difficulty range.

This matters because surface busyness is not a reliable difficulty measure. A board with many lights can collapse in two presses, while a sparse arrangement may require a longer sequence. Difficulty should follow the actual route, not the screenshot.

What Planning Workout scores mean

All three games put completion and efficiency ahead of pace. Tower Transfer uses a 70/25/5 split and Toggle Grid 72/23/5, both measured against an exact optimum. Double Up weights completing the queue 35%, tile efficiency against its reference route 55% and pace 10%, because merging well matters more than merely surviving. Those balances are specific to planning games; they are deliberately different from the accuracy-led recipe used for multiple-choice puzzles. Difficulty records remain separate.

A score describes one recreational puzzle session. It does not measure executive function, intelligence, decision-making quality or neurological health. Improvement can reflect familiarity with this particular rule as much as any broader change.

Planning puzzle questions