Why critters and burrows?

A number-link puzzle gives you pairs of matching numbers on a grid. You join each pair with a line, and the lines can’t cross or share a square. We swapped the numbers for critters and their burrows, so every line is a path home. When a path is finished, its critter scampers along it and pops into its burrow. Fill every square and the meadow bursts into flower.

That last part matters. Every square of the meadow has to be on a path, and that rule is what gives each level here exactly one answer. A computer solver checked all 60 levels to make sure of it, and the levels are ordered by size and by how much searching the solver needed.

A bit of real number-link history

The idea is well over a hundred years old. In February 1897 the American puzzle maker Sam Loyd printed a puzzle in the Brooklyn Daily Eagle about quarrelsome neighbors: eight houses had to be joined to eight gates of a park, each by its own path, with no two paths crossing. It ran again in the British weekly Tit-Bits that October, and Loyd’s big 1914 collection, the Cyclopedia of Puzzles, has it too.

The grid version people play today comes from Japan. The puzzle magazine Puzzle Communication Nikoli first printed it in 1987, in issue 17, and the first book of them came out in 1989. Nikoli calls it Numberlink. Its rules say lines run through the middle of the squares and never cross or branch. Nikoli also published a version with pairs of letters, called Arukone.

Nikoli’s own rules don’t ask you to use every square. Many puzzle makers add that rule anyway, because it makes the puzzles tidier and helps each one have a single answer. This game uses it.

The six meadows

• Garden, levels 1 to 10: 5×5 meadows with 4 to 6 critters. A good place to learn.
• Hedge, levels 11 to 20: 6×6 with 5 to 7 critters.
• Orchard, levels 21 to 30: 7×7 with 7 or 8 critters.
• Woodland, levels 31 to 40: 8×8 with 7 to 9 critters.
• Riverbank, levels 41 to 50: 9×9 with 9 to 11 critters.
• Hilltop, levels 51 to 60: 10×10 with 10 to 12 critters. The last few are hard.

How to play

• Drag from a critter to the burrow ringed in its color. A small picture in each burrow shows whose home it is.
• Paths go up, down, left and right. They can’t cross or share a square.
• Drag over another path to cut it. Tap a critter or its burrow to clear its path. Undo takes back your last move.
• Fill every square. When all the critters are home and nothing is bare, the meadow blooms.
• Hint draws one correct path for you.
• Stars: 3 for no hints and no restarts, 2 for up to 1 hint, 1 for any solve.
• Earn 3 stickers in this game for your QuickBOP sticker book.

Tips

Start at the edges. A critter in a corner has only two ways out, and one on a wall has three. Fewer choices make those paths the easiest to place first.

Long paths hug the walls. When a critter and its burrow are far apart, the path usually runs around the outside of the meadow. Keeping to the wall leaves the middle open for the others.

Watch for dead ends. A bare square with only one open neighbor can never be filled, because a path needs a way in and a way out. If your path would leave a square like that, try another route.

Don’t box anyone in. Before you close off a corner, check that every critter inside it can still reach its burrow.

There is only one answer. If two routes both seem to work, one of them leaves a gap somewhere. Undo is free, so try one and see.

Your turn

The first Garden meadow at the top of this page has six critters on a 5×5 grid, with one of them tucked in a corner. Start with that one and see if you can fill the whole meadow without a hint.