Hidato

Don't start at 1

The beginner's instinct in Hidato is to find the 1 and march forward, and it's the slowest possible way in. The grid must hold every number from 1 up to N, each sitting next to the following one horizontally, vertically, or diagonally, and a handful of numbers are printed to anchor you. The fast solvers work the gaps between those anchors instead. If you can see a 12 and a 15 with two empty cells between them, the path from 12 to 15 is short and heavily boxed in, so 13 and 14 usually have only one route that keeps both connected. Solvers call this bridging, and a well-made puzzle is basically a chain of bridges: close the short spans first, and the numbers you place become new anchors that shrink the longer spans into short ones.

Read the geometry, not just the numbers

Because moves include diagonals, each cell has up to eight neighbours, which sounds loose but tightens fast at the borders. A corner cell has only three neighbours and an edge cell five, so runs that pass near the rim have far fewer options than runs through the middle. Hunt for the most boxed-in cells first: an empty cell ringed by filled cells and walls sometimes has exactly one pair of numbers that can legally pass through it. Two more geometric facts do a lot of quiet work. First, 1 and N are special: every other number needs two free neighbours, one for the number before it and one for the number after, but the two endpoints only need one. If a pocket of the grid can only be entered from a single cell, one of the endpoints probably lives in there. Second, the chain may look like it crosses itself when two diagonal steps pass between the same four cells, and that's perfectly legal. Each cell is used once, but the drawn path can weave. Third, count pockets against spans. If the numbers 20 and 27 both sit on the border of a closed-off pocket containing exactly six empty cells, then the run 21 through 26 must fill that pocket completely, since six missing numbers need six cells and nothing else can reach in there. Matching the size of a gap in the count to the size of a gap in the grid is one of the most satisfying deductions the puzzle offers.

Place one number, learn three things

Keep an eye on both directions from any number you write. Placing a 20 immediately tells you where 19 and 21 must sit, adjacent to it, so one confident placement often pins down two more. When you're torn between two candidate paths, run the dead-end test: follow each option a couple of steps in your head and see whether it strands a cell with no way to continue the count. The route that creates the dead end is wrong, and in a puzzle with a single solution, proving one path bad is the same as proving the other good. Click a cell and type its number, or use the on-screen keys, and press Backspace to clear a mistake. The puzzle is done the instant 1 through N form one unbroken chain, and faster solves score better, which is why the bridging habit matters: deduction is quick, trial and error is slow, and erasing is slowest of all.

A riddle from Israel

Hidato was created by Gyora Benedek, an Israeli mathematician, and the name comes from the Hebrew word for riddle. He has said the idea came to him while diving, watching fish dart along a winding route he tried to reconstruct in his head afterwards. The puzzle spread through newspapers and books in the late 2000s, sometimes under the name Hidoku, and it sits in an interesting spot among number grids. Sudoku is about balancing many separate constraints at once; Hidato is about one single thread that must visit every cell of its run. That single-path rule gives it a different feel in the hand, closer to tracing a maze than filling a ledger, and it's why the geometry of corners, walls and bottlenecks matters here in a way Sudoku never asks of you. Every proper Hidato has exactly one solution, so every stuck moment has a logical way out. Look for the bridge you haven't closed yet.