Why ice blocks?

In a box-pushing puzzle you shove crates one square at a time until each one sits on a marked spot. We moved the whole thing onto the ice. The penguin still walks one tile at a time, but the blocks are made of ice, and a pushed block keeps sliding until something stops it.

That one change turns the puzzle around. In the classic, you can nudge a crate to exactly the square you want. Here you can’t stop a block halfway across open ice. You need a rock, the edge of the field or another block to catch it. There is one helper: a block that slides onto a snowflake stops right there.

A bit of real box-pushing history

The best-known box-pushing puzzle is Sokoban. Hiroyuki Imabayashi created it in 1981, and his company, Thinking Rabbit, released it in Japan in 1982 on the NEC PC-8801 and other home computers. The name means warehouse keeper. Spectrum HoloByte brought it to the United States in 1988 as Soko-Ban.

Computer scientists took it seriously. In 1997 Joseph Culberson of the University of Alberta showed that deciding whether a box-pushing level can be solved at all is PSPACE-complete. In plain words, nobody knows a fast method that works on every level, and most researchers believe there isn’t one.

Sliding blocks have their own paper trail. In a puzzle called PushPush, every pushed block slides as far as it can go. In 1999 Joseph O’Rourke and a problem-solving group at Smith College proved the 3D version NP-hard, and in 2000 Erik Demaine, Martin Demaine and O’Rourke proved the same for the flat 2D version. Our snowflakes, which catch a block mid-slide, are a small change to that rule.

The four ice fields

• Shore, levels 1 to 10: 5×5 ice with one or two blocks. Level 1 is a single push.
• Floe, levels 11 to 20: 6×6 ice, two blocks, and fewer rocks to lean on.
• Glacier, levels 21 to 30: 7×7 and 8×8 ice, mostly with three blocks.
• Aurora, levels 31 to 40: 9×9 ice under the night sky, with three or four blocks. The last one takes 89 moves at its shortest.

A computer search solved every level before it went in, and found its shortest solution. That number is the Fewest count above the board.

How to play

• Walk with the arrow keys or WASD, swipe on the ice, tap a spot to walk there, or use the arrow buttons.
• Walk into an ice block to push it. The penguin can push, but never pull.
• A pushed block slides until it hits a rock, the edge or another block, or until it lands on a snowflake.
• Get every block onto a snowflake to finish the level.
• Undo and Restart are free. Hint shows the next push, but a level finished with a hint tops out at 2 stars.
• Stars: 3 for finishing within 2 moves of the fewest, 2 for a few more, 1 for any finish.
• Earn 3 stickers in this game for your QuickBOP sticker book.

Tips

Find the brakes first. Before you push anything, look along the row and column of each block and ask what will stop it. If nothing useful is in the way, that push sends the block to the edge.

Work backward from each snowflake. A snowflake catches any block that slides onto it, so a block can arrive from any side with a clear run. Find the lines that lead into the snowflake, then work out how to get a block into one of them.

Park one block to stop another. A block resting on the ice works like a rock. Sometimes the right first move is to push a block somewhere it doesn’t belong, only so it can catch the next one.

Stay out of corners. A block pushed into a corner can never come out, and a block against the edge can only slide along it. The game warns you when a push leaves no way to finish, and Undo takes it back.

Walking counts. Stars go by moves, and every step is a move. When two plans both work, pick the one where the penguin walks less between pushes.

Your turn

Level 1 on the Shore has one block, one snowflake and a clear run between them. Push it and watch it slide.