Ascent

Place each number once, so they form a path from 1 to the highest, each in a square neighboring the one before. Some are given. Which squares are neighbors depends on the game mode:

Orthogonal: Squares side by side, never diagonally.
Hex: Hexagons that share a side.
Classic: Squares side by side or diagonal; corners are cut off to show the path may cross them.

Classic may add a rule:

Edges: a number in an arrow round the grid points along the row, column or diagonal it lies on.

Controls

On a touch screen, a tap does what a click does, and a long press what a right-click does (more ways to right-click). A key the puzzle’s controls show as a button can be pressed there instead of on a keyboard.

There are three ways to enter a number:

Click a number to highlight it, then click (or drag to) an adjacent cell to place the next number in the sequence. If the number just before it is placed and the one after is not, that is the one after; the other way round, the one before; and if neither is placed yet, the one after. Then click the highlighted number again to offer the one before instead, and once more to deselect it; or, once a number is placed beside it, click that square again for the one before, and once more to empty it. The arrow keys and Enter can be used to emulate mouse clicks, and Space or Backspace at the cursor does what a right-click does. Once the numbers after the one you place are already on the board, the highlight moves on to the end of that run; the Skip past already-placed numbers when advancing preference turns that off.
Click an empty cell, then type a multi-digit number, on the keyboard or the on-screen keypad. To confirm a number, either press Enter, an arrow key, or click any cell; Clear or Backspace rubs out the last digit. Set the Numpad inputs preference to Move cursor to have the numeric keypad move the cursor instead of typing, its 7, 9, 1 and 3 diagonally.
On an Edges board, click and drag from an edge number, then release in an empty grid cell in the same row, column or diagonal.

To remove numbers, right-click or right-drag a number (on a touch screen, a long press, or hold and then drag).

It’s also possible to draw a path while the numbers inside the path are still unknown. Left-click and drag across cells to draw a line, starting from an empty cell (a drag starting from a number places numbers instead). Right-click or right-drag to clear the line going through a cell.

If a path has only a single number, the endpoints will display one or two smaller numbers, which represent the numbers which are valid for this cell.

Where a cell has exactly two candidate numbers like that, right-clicking (on a touch screen, a long press) cycles through them instead of clearing — empty, then the lower number, then the higher, then empty again — so an either-or square can be tried both ways without typing.

Where the puzzles come from

Classic mode is the puzzle invented by Gyora Benedek, known as Hidato (or the non-trademarked name Hidoku). Orthogonal mode is the puzzle known as Numbrix, created by Marilyn vos Savant. A Classic board with Edges is an implementation of 1to25 invented by Jeff Widderich.

More information: http://www.janko.at/Raetsel/Hidoku/index.htm

Hints

Hint explains the next step rather than simply making it. A step places one number, or one whole run where that run has only one route, and it reasons only from the numbers on the board and, on an Edges board, the arrows, so it carries on from wherever you are, as long as none of your numbers is wrong; if one is, it asks you to fix the highlighted mistakes first. Lines you have drawn are yours: the hint neither reads them nor draws any.

A ring marks the square the step fills. When the step fills a whole run at once, each square it fills is ringed, with the line of its only route, from one end to the other, inside the rings: the drawn route, in its words.
An outline marks what the step reasons from: the numbers the new one sits between, a dead end’s one way in, the squares a missing run has to step through, and in Edges mode an arrow the step reads.
Stripes mark the row, column or diagonal an arrow points along, or every square a run of missing numbers can reach.

When a step places the first number of a run and the rest of that run follows just as simply, the hint carries on through the run as one hint, a number at a time, each with its reason. And when the run has only one route between its two ends, the hint shows the whole run at once: every square it fills is ringed, with the run’s line drawn inside the rings. Often a run is forced onto its route because some squares can be reached by no other run: those have to be on this run’s route, or they would be left empty, so the hint stripes them. And sometimes a run could take several routes, but every one except one would cut a neighboring run off from its own ends: then the run must take the one that leaves room. On an Edges board, the arrows often leave a run only one route: when they are the reason, the hint says so and outlines them.

A step is one move to a neighboring square, so two numbers can be no more steps apart than they are apart in the sequence. That one idea gives most of the hint’s reasons:

Next to its neighbors. A number must sit next to the numbers just before and after it, so when only one empty square touches both, or the one that is placed, it goes there.
Within reach. A number must be within as many steps of the nearest placed numbers below and above it as they are apart in the sequence: 10 is within 2 steps of 8 and within 3 of 13. When only one empty square is in reach of both, the number goes there. On an Edges board it must also be on its arrow’s line.
Only one run can reach it. A run is the missing numbers between two placed ones, like 14 and 15 between 13 and 16; the hint calls it “the run between 13 and 16”. A run can only use squares close enough to both its ends: here, the steps to 13 and the steps to 16 add up to at most 3. So each run has an area it can reach, and an empty square inside only one run’s area belongs to that run. Often only one other run comes close, and the hint names it and why it falls short (“the run between 41 and 43 can’t, as this square doesn’t touch 41”); when several do, it says that none of them reaches the square, and a look at the runs nearby shows why. Which number of the run it is follows the same way: only one is close enough to both ends (“3 steps from 67 and 2 from 72 rule out the rest”). When there are no counts to give, as for a run of a single number, the hint stripes the squares the run can reach and outlines its ends instead. The hint only names numbers you can see on the board, and the one it is placing.
A dead end. A square the path can enter from only one neighbor must be an end of the path, so it holds 1 or the highest number. A neighbor is closed to the path when it is a wall, an arrow, or a number already joined to both of its neighbors in the sequence.
On an Edges board: where the lines cross. Every missing number already has a line, its arrow’s, and it must be within a step of the line of the numbers just before and after it, within 2 steps of the lines of those two away, and so on. So 12, on its column, must be within a step of 11’s row and 13’s row: where those cross its column, often only one square remains. The hint outlines the arrows it reads and stripes the lines of the other numbers.
On an Edges board at Tricky or Hard: only one arrow still fits. Only the missing numbers whose arrows point at a square can go there. When all but one of them are too far from a line or a number they must be near, the square is the last one’s. The hint outlines every arrow pointing there and stripes the lines that rule the others out.
On harder boards, and on an Edges board: stepping through empty squares. A missing run of numbers has to step from one placed number to the next through empty squares, one square per number, so walls and filled squares in the way stretch the distance. Sometimes only one square works for a number on any such route.

Ascent parameters

These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.

Game mode: Which puzzle to play: Orthogonal, Hex or Classic. The rules of each are at the top of this page.
Edge clues: When on, a number in an arrow round the grid points along the row, column or diagonal it lies on. Orthogonal always has it off. Hex always has it off.
Width, Height: Size of the grid in squares. The smallest boards lack some difficulties: a 2x2 has only Easy puzzles, a 3x3 Classic or Hexagon board has none at Normal, and a Classic board two squares wide has none at Hard. Each must be between 2 and 50.
Always show start and end points: When enabled, the first and last number are always given. Disable this option for an added challenge.
Symmetrical clues: When enabled, all given numbers form a symmetric pattern. This usually leads to easier puzzles. While Edge clues is on, it is always off.
Board shape: The outline of the board: 'Rectangle', 'Honeycomb', 'Hexagon'. A Honeycomb is a rectangle of hexagons, and a Hexagon is one large hexagon, whose size is the length of its middle row. Orthogonal offers only Rectangle. Hex offers only Honeycomb and Hexagon. Classic offers only Rectangle.
Difficulty: Determine the difficulty of the generated puzzle; see what the names mean. While Edge clues is on, only Normal, Tricky and Hard are offered.

More help

Features every puzzle shares: hints, checking your work, checkpoints, playing by touch
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