The main screen

From top to bottom:

• The toolbar: Settings on the left, the level of the puzzle in the middle, and the "…" menu on the right, with Share / Save, Enter puzzle, Scores, Favorites and Help.
• New and Clear: New starts a new puzzle with the current settings. Clear removes all your own entries and restarts the clock; the puzzle stays.
• The board.
• The transform bar: turning, mirroring and the binary switch.
• The status bar, or a message when there is something to tell you.

The board

Tap an empty cell to cycle it through 0, 1 and empty again. A long press puts a 1 in an empty cell directly. The clues, the digits the puzzle starts with, are on a slightly shaded background and can't be changed.

Digits that break a rule are marked in orange, a moment after you place them: three equal digits in a row, more 0s or 1s in a line than half its length, or a line that copies another complete line. The orange disappears as soon as the rule holds again.

The puzzle is solved as soon as every cell holds the right digit. In Speed solving the time is then stopped and recorded (see below).

Settings

Settings, at the left of the toolbar, has five choices:

• Grid: 6×6, 8×8 or 10×10.
• Difficulty: the level, one to five stars. See Rules, solutions and levels for what each level asks.
• Type: Random or Rare (see below).
• Appearance: light or dark, or as set on your iPhone.
• Mode: Speed solving or Zen (see below).

The checkmark at the top right applies the changes; the chevron at the top left closes Settings without changing anything. A new grid size, level or type starts a new puzzle at once. A new mode or appearance leaves the game in progress as it is.

Random and Rare

Turning, mirroring and switching a solved grid gives up to 16 grids that look different but are the same puzzle: its symmetry family. For almost every solution all 16 are different. A Random puzzle can have any solution.

A Rare puzzle has a solution with symmetry of its own, so its family has only 4 or 2 members: most transformations give back a grid already in the family. Of the about 3 billion 10×10 families, 2,096 are like this.

To see it, solve a rare puzzle and use the transform bar. With a family of 2, every turn or mirror shows either the same grid or its binary switch. With a family of 4, two more grids appear, and that's all. (During the game the clues don't show this: they are only part of the solution.) The figures for every size are on Rules, solutions and levels.

Speed solving and Zen

Choose the mode in Settings:

• Speed solving: with the clock. Your results are kept in the scores and with your favorites.
• Zen: no clock, and nothing is recorded. For playing without time pressure.

A puzzle keeps the mode it started with: a new mode applies from the next puzzle, New or Clear. Changing the size, level or puzzle type starts a new puzzle, so then it applies at once.

The clock stops when you can't see the board: when you switch to another app, take a call or lock the iPhone, and while Settings, Help, Enter puzzle or Share / Save is open. It continues where it stopped when you come back. It keeps running in Scores and Favorites.

The status bar

Under the board, in both modes. It shows, from left to right:

• The fill count: how many cells are filled, out of the total, for example 24/64.
• The time since the puzzle started, including any time added for hints (Speed solving only).
• The local-rule count: how many steps the local rules allow on the board as it is now.
• The hint button.

The local-rule count is worked out again after every step you make. While it is above zero, there is still at least one place where a local rule fills a cell: two equal digits side by side, two equal digits with one cell between them, or a line that already has all its 0s or all its 1s.

When the count disappears, the local rules have run out. The next step needs a technique beyond them. Which one depends on the level:

• ★★: look for a line with two empty cells left that need one 0 and one 1, where one way round would copy a complete line (duplicate avoidance).
• ★★★ and ★★★★: also look for a line where every possible completion puts the same digit in some cell (line enumeration).
• ★★★★★: also leave out the completions that would copy a complete line (line enumeration with duplicate avoidance).

Once that step is made, the local rules usually help again and the count comes back. The techniques are explained with examples on Rules, solutions and levels.

Turning the board

The transform bar turns the board a quarter left or right, mirrors it top to bottom, left to right or along either diagonal, and swaps all 0s and 1s (the binary switch). Your own entries go along. It is still the same puzzle, so it makes no difference to your score.

Hints

If you are stuck, or just don't see it, tap the hint button in the status bar. The hint shows the next step that can be made with the simplest technique, and explains why:

• The cell to fill is marked in strong blue.
• The cells that make it so are marked in light blue.
• Tap the marked cell, or the message, to place the digit.

Each hint adds time to the clock: a second for a local rule or duplicate avoidance, a few seconds for line enumeration, more for harder steps.

In Speed solving the hints are also counted, and the count is kept with your result: [2] 4 min 12 sec means solved in 4 minutes 12 seconds with 2 hints. Fewer hints always rank first, so a solve without hints beats every solve with hints, whatever the times. A solve with more hints than the limit is not recorded: the limit is 2 for 6×6, 4 for 8×8 and 8 for 10×10.

A hint starts from the correct digits only. If some of your digits are wrong, the hint first asks you to fix them: either correct the cells marked in orange, or let Nuleen clear the wrong cells, with a time penalty.

Messages under the board

Instead of the status bar, a message appears when:

• Duplicates found: two rows or two columns are the same. Go back to the last correct state, or clear only the wrong cells, with a time penalty.
• Filled, not solved: every cell is filled, but some are wrong. Clear only the wrong cells, with a time penalty.
• Solved: in Speed solving, your time and the hints you used, and what it means for the scores or the favorite. For a place in the scores, enter your name to keep it with the score. In Zen, just "Solved!".

When a solve in Speed solving is not recorded, the message says why:

• More than the hint limit was used (see Hints above).
• The solution was shown during this game: you looked at the solution of this puzzle while playing it, in the details of a score or favorite, or on the Enter puzzle screen. Looking at it before you start, or after you have solved it, doesn't matter.

On a small screen the board scrolls up when a message appears, so the whole message is visible.