Why a torn treasure map?

A sliding puzzle needs a picture worth putting back together. Numbers work, but a map gives you a reason to finish. When the last piece slides home, a red X appears and a dotted line points to the next island. Thirty maps later, you’ve sailed a whole voyage.

Maps also suit the puzzle in a quieter way. You read a map by its landmarks: a hill here, a palm grove there, a compass in the corner. That is how you solve a picture slider too. Find the piece with the compass on it and work out where it belongs.

A bit of real 15 puzzle history

The sliding puzzle most people know has 15 numbered tiles in a four by four tray, with one empty space. Puzzle historians Jerry Slocum and Dic Sonneveld traced it to Noyes Palmer Chapman, a postmaster in Canastota, New York. He reportedly showed friends an early version as far back as 1874. By December 1879, a Boston woodworker named Matthias Rice was making it, and shops sold it as the Gem Puzzle.

Then came the craze. It started in the United States in January 1880, reached Europe by April, and was over by July. A dentist in Worcester, Massachusetts, named Charles Pevey offered a cash prize for a solution. Chapman applied for a patent in 1880, but it was turned down.

Puzzle maker Sam Loyd claimed from 1891 until his death in 1911 that he had invented it. He hadn’t. Loyd also offered a $1,000 prize for solving a version with the 14 and 15 swapped. Nobody could, and the math already said why. In 1879, William Woolsey Johnson and William E. Story published notes on the puzzle in the American Journal of Mathematics. Together they showed that only half of all starting arrangements can be solved. Swap two tiles in a finished tray and no amount of sliding will fix it.

That is why every map here is torn by sliding pieces around from the finished picture. Each one can always be mended.

The three seas

• The Shallows, islands 1 to 10: 3×3 maps with 8 pieces. Island 1 needs just 3 slides.
• Coral Sea, islands 11 to 20: 4×4 maps with 15 pieces, the classic size.
• Deep Sea, islands 21 to 30: 5×5 maps with 24 pieces. The last island needs at least 56 slides.

We had a computer find the shortest possible solution for every map, then set each goal a little above it. For scale, no 3×3 arrangement needs more than 31 moves, and no 4×4 needs more than 80.

How to play

• Tap a piece next to the gap to slide it in. Tap a piece further along the same row or column to slide several at once.
• You can also swipe on the map or use the arrow keys.
• Every piece that moves one space counts as one move.
• Mend the map and the X appears. The next island unlocks.
• Stuck? Turn on Numbers. Piece 1 goes top left, and the numbers count across each row.
• Stars: 3 for finishing within the goal, 2 for up to double the goal, 1 for any finish.
• Earn 3 stickers in this game for your QuickBOP sticker book.
• Sound is on to start. Tap 🔊 to mute, or 🎵 for music.

Tips

Finish the top row first. Put the top row of pieces in place, then the next row down. Once a row is done, leave it alone.

Do the last two rows a column at a time. When only two rows are left, work from left to right and place the top and bottom piece of each column as a pair.

Check the little map. The small picture beside the island name shows the whole map. Match the landmarks on a piece to find its spot.

Slide whole rows. Tapping the far end of a row moves every piece in between in one go. It saves taps, though each piece still counts as a move.

Your turn

The first map is waiting at the top of this page, torn into eight pieces. Mend it and see where the X lands.