How to plan moves ahead in a tile puzzle: six checks, and Millrace's Level 1 move by move

Millrace is a tile logic puzzle: build one exact number on the marked cell within a move limit, while tiles keep arriving one at a time at the arrival cell. The board is set and the queue of arriving tiles is fixed, so a level can be planned to the end.

The rules that matter for planning

Six checks before every swipe

1. Read the move limit. The “moves left” counter is your whole budget. Before your first swipe, sketch a line that fits inside it. After a solve, the result card shows the best possible, so a second attempt has a number to aim at.

2. Do the target arithmetic. Every tile is a power of two, so the target is built from pairs: a 32 is two 16s, a 16 is two 8s. Before moving, find the tiles that will become the target, including any still in the queue. Note anything that could merge with the finished value, too.

3. Never slide toward the arrival cell’s edge while a tile is due. When the arrival cell sits against an edge, as it does in Level 1, the newest tile lands there after every move. A slide toward that edge can’t move it off. It either stays put or absorbs an equal tile behind it, and either way the cell is still occupied when the next tile comes. So from move 2 on, while the queue isn’t empty, that swipe does nothing, loses, or wins. It can win because the goal is checked before the next arrival, so a slide that completes the delivery still counts.

4. Check the arrival cell’s own line on the other slides. Say the arrival cell is on the left edge. Left is check 3. Right moves the newest tile away, unless its row is still full after merging. Up and Down pack the arrival cell’s column toward one end, and if it holds enough tiles after merging to reach the arrival cell, one of them lands on it. Count before you swipe.

5. Count the queue. One tile arrives after each move until the queue is empty. Level 1 has three arrivals and a 7-move limit, so the arrival cell matters for the first three moves only. After that, the board is a pure delivery problem. When the queue holds at least as many tiles as the level has moves, the arrival cell never stops mattering.

6. Choose your finish early. A delivery ends in one of two ways. Either you build the value elsewhere and slide it onto the marked cell, or the final merge happens on the marked cell itself. Carrying needs an open lane to the marked cell; merging there needs the second tile to line up with it. The early moves build one or the other.

Level 1, move by move

Here is the first Warm-up level’s starting board:

The arrival cell is on the left edge, second row; the marked cell is directly below it. The target is exactly 16. The queue is 2, 2, 2, and the move limit is 7. The shortest solution is 5 moves, and only one five-move line exists.

Start with the arithmetic. 16 is 8 + 8, and the second 8 can come from the two 4s. The three queued 2s play no part in the target. They are the cost of the level: three tiles to keep off the arrival cell.

The 16 is built in the far corner, away from the arrivals, and carried to the marked cell only after the queue is empty. That is check 5 and check 6 working together.

Where it goes wrong:

• Move 2, Left or Up: Blocked. Two of the four swipes lose on the spot. Left pushes the 2 that just arrived against the edge (check 3). Up packs the left column, the 2 on the arrival cell and the 4 in the corner, into the top two cells, which puts the 4 on the arrival cell (check 4).
• Move 3, Up: lost, quietly. Up is legal and blocks nothing. It splits the two 8s: one goes to the top of the third column, the other to the second row of the fourth. With four moves left, no line brings a 16 to the marked cell. Nothing on screen says so, but if the run ends in a loss, the card reads “Position lost at move 3”.
• Move 3, Down: safe, but slower. It still wins, in six moves instead of five, so it costs one of the two spare moves.

Level 8: when the queue never runs out

Level 8, in Tactics, turns check 5 around. Nine tiles are queued against an 8-move limit, so a tile is due after every move the level allows. The arrival cell is in the top row, second column, and the marked cell sits right next to it in the third column. The target is exactly 32.

The only shortest line takes six moves: Right, Down, Left, Down, Right, Up. Its last swipe goes toward the arrival cell’s own edge with tiles still waiting. That’s the exception in check 3. Up carries a 32 from the third row onto the marked cell, and the goal is checked before the next tile is due. The same swipe one move earlier would have lost on the spot.

Why the checks are not enough on their own

Every check above looks one move ahead, and the levels are built so that one-move play rarely gets through; how Millrace’s levels are made explains the checks every level passes before it ships. The six checks keep you alive. Solving takes the next step: where the tile after next will land, and what the board must look like when it does.

When you get stuck

• Hint draws a move on a winning line from where you stand, with a one-line reason. It runs the same solver that proved the level, and it’s free.
• Undo inside a level is free and unlimited. After a loss, the card offers “Undo that move” and Retry. Undo tokens apply only to Freeplay, the endless board.
• The result card shows your move count, your best, and “Best possible is N moves”.

Millrace is free on iPhone and iPad, with no ads; the app page has the full rules. The comparisons with Threes, KAMI 2, and Flow Free set out what each of those games asks of you.