How does a number path puzzle work?
A number path puzzle is a grid to fill with 1, 2, 3 and so on up to the number of squares, so that each number touches the next: across, down or diagonally. Some numbers are already in place, always including 1 and the last one. The path has to pass through each of them at its turn, and it visits every square exactly once.
Choose 5 × 5, 6 × 6 or 7 × 7, numbers 1 to 25 up to 1 to 49. Tap a square that touches the end of your path and the next number goes there; squares you can move to are outlined. Tap a square already on the path to go back to it.
How is your Number Path Puzzle time calculated?
Your result is the time from Start until the path reaches the last number. Next to it are the times you pressed Check, which marks numbers that are in the wrong square, and Hint, which takes the path back to the last right number and places the next one. There is no rating, because no published typical time exists for puzzles built like these.
At least 10 of the 25 numbers are shown on a 5 × 5, about 40%, which keeps a puzzle to a few minutes. Puzzles with fewer numbers shown need much longer chains of reasoning.
How do you solve a number path puzzle?
- Measure the gaps. If 8 is shown and 12 is shown, the path has 4 steps to get from one to the other. When they are exactly 4 king moves apart, every step must bring the path one move closer to 12.
- Watch the corners. A corner square touches only 3 others, an edge square 5, and a middle one 8. A square with few free neighbours left must be visited soon, or it will be cut off.
- Look for squares with one way in. An empty square with a single free neighbour can only be the end of the path. If it isn't the last number's square, a step before it was wrong.
- Work from both sides of a gap. The numbers just after one shown number and just before the next narrow each other down.
Does every Number Path puzzle have exactly one answer?
Yes. Each puzzle starts as a random path through every square. Numbers are then hidden one at a time, in random order, and one stays hidden only if a search of every possible path still finds exactly one that fits. The site's tests check hundreds of puzzles this way, and confirm the 5 × 5 ones with a plain search that tries every path from 1.
Is this the same as Hidato?
It is the same kind of puzzle. Hidato was invented by the Israeli mathematician Gyora Benedek, and the name is a registered trademark, so this page uses a plain one; the puzzle is also published as Hidoku and Number Snake. Numbrix, Marilyn vos Savant's version in Parade, is the variant without diagonal steps.
To visit every square with a chess knight instead, try the Knight's Tour; to join numbers in order against the clock, the Trail Making Test.