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Binary grid

Fill the grid with 0s and 1s: no three alike in a line, equal counts in every row and column, no two lines the same. 4×4 up to 10×10.

  • Logic
  • Untimed
  • 11 levels

How it plays

Every cell is a 0 or a 1. No row or column may hold three of the same digit in a row; each holds as many 0s as 1s; and no two rows, or two columns, are identical.

Two alike side by side force the other digit on both sides; a gap between two alike is the other digit; a line with its half of 0s is finished with 1s. Most of the board falls to those three moves.

Levels take givens away, then grow the board. Every puzzle has exactly one solution, checked by a solver.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This practises spotting forced moves under several simple rules at once. It is practice at these puzzles, not a measured gain in reasoning elsewhere.

Learn

How to get better at binary grid: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Sweep the whole board for pairs and gaps first: every 00 or 11 side by side, and every 0_0 or 1_1. Each one fills a cell for free, and each new cell can make another pair.
  2. Then count. Go line by line and ask whether any row or column already holds its half of one digit — 2 on a 4×4, 3 on a 6×6, up to 5 on a 10×10. If so, the rest of that line is the other digit.
  3. When pairs and counts run dry, take the line with the fewest blanks and list the ways to finish it. Strike out every way that makes three alike; the cells that agree in every way that is left are forced.
  4. After each cell you place, look along both its row and its column before moving on. A new cell often makes a pair or completes a count in the line you were not looking at.

Techniques and tricks

  • The pair pushes out

    Two alike side by side can never have a third beside them, so both ends of the pair take the other digit.

    e.g. _ 1 1 _ becomes 0 1 1 0

  • The sandwich

    A blank between two alike must be the other digit, or the three would match.

    e.g. 0 _ 0 becomes 0 1 0

  • Finish the count

    Once a line has its half of one digit, every blank left in it is the other digit. Count the digit you see more of first.

    e.g. On a 6×6, 1 0 _ 1 1 _ already has three 1s, so it is 1 0 0 1 1 0

  • Block the triple

    When a line needs several of one digit and just one of the other, that lone digit has to sit where it breaks up any run of three. The cells it cannot reach are fixed.

    e.g. 1 _ _ _ _ 1 needs three 0s and one 1. A 1 at either end of the gap leaves 000, so the 1 is in the middle two, and the gap’s ends are 0: 1 0 _ _ 0 1

  • No copies

    With “No two lines the same” on, a line two blanks from done that matches a finished line everywhere else must take its two blanks the other way round.

    e.g. Row 1 is 0 1 1 0 and row 3 is 0 1 _ _: 1 0 would copy row 1, so row 3 is 0 1 0 1

  • Count the remainder

    For a long line, say what it still needs, not what it has: “two 0s and one 1 to go”. Small remainders are where Block the triple bites.

As the levels climb

  • The ladder starts on a 4×4 with half the cells given, then takes the 4×4 down to as few givens as the puzzle allows. Here pairs and the count of two finish almost everything.
  • Next the board becomes 6×6, first half given, then 38%, then the fewest. Fewer givens means fewer free pairs at the start, so the count of three and Block the triple start doing the work.
  • Then 8×8 — 45%, 35%, fewest — and finally 10×10 — 40%, 32%, fewest. The counts are four and five now, too many to eyeball: count each line and say what it still needs before you guess anything.
  • On the fewest-givens boards the start can have nothing forced by a pair or a count. Go to the line with the fewest blanks and list its ways out; with the distinct rule on, also compare it with every finished line.
  • The clock is off unless you turn on Time pressure; then each board gets 60 seconds plus 6 seconds for every open cell, so a 10×10 at the fewest givens still has minutes. Spend them on counting, not on guessing.

Traps to avoid

  • Checking only the row you are filling. A cell that is fine across can make 1 1 1 down its column. Look both ways every time.
  • Miscounting the half on a big board. On a 10×10 a line holds exactly five of each; four 1s is not finished, and filling the rest with 0s there breaks the count.
  • Forgetting the distinct rule. If you are stuck on a nearly full board with “No two lines the same” on, the last move is almost always a line that would copy another.
  • Guessing a cell and carrying on as if it were known. If you must try a value, follow it only until a rule breaks, then undo every cell it led to — a lost guess left on the board spoils the lines around it.

How to practise

  • Set “Largest board” to 6 to drill the 4×4 and 6×6 rungs until pairs, sandwiches and counts are instant, then raise it to 8 and 10.
  • Turn “No two lines the same” off for a few sittings to learn the counting moves alone, then back on to add the copy check to your sweep.
  • Leave Time pressure off while you learn; turn it to Relaxed once you finish 8×8 boards without guessing, to make the sweep a habit rather than a hunt.
  • When the working shows “A first step”, find that move on the board before you read on. It shows which rule you overlooked at the start.

Levels

It is untimed unless you turn the clock on. There are 11 levels with the default settings, and the counter stops at the real top. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More logic

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