Parity Bits

Eight bits in a row, and five parity checks printed underneath. Each check covers its own overlapping handful of positions and publishes what those positions should add up to — even or odd. Exactly one bit has been flipped since those parities were published, so some checks now disagree with what they promised and some still agree. Name the flipped bit.

The trick is that a check does not only say something is wrong. A check that fails must contain the flipped bit; a check that passes cannot. Cross one against the other and the suspects collapse to a single position — every time, because the board is generated and then verified so that no two bits could ever produce the same pattern of failures.

It runs entirely on your device: 0 network requests, works offline. No ads, no account, nothing to buy, and no betting, money or prizes of any kind.

1. Focus the board — click it, or press Tab until it is focused.
2. Read the failing checks first. Every check row ends in ✗ fails or ✓ passes. The squares along the row show which bits that check covers: ▪ covered, · not covered. The small numbers above the word are the bit positions, 1 to 8.
3. Step through the checks with the up and down arrows. The focused check marks the bits it covers on the word itself and spells out what it wants and what it currently reads.
4. Intersect. Keep only the bits covered by every failing check, then throw away any bit covered by any passing check. One position survives.
5. Move along the word with the left and right arrows, then press Enter or Space to name the bit under the cursor. Or just click the bit.
6. A wrong name costs one try and the bit is struck off with out so you do not name it twice. Looking around, stepping through the checks and changing your mind cost nothing at all.
7. Repair four words before the tries run out. Each round deals a fresh word and a fresh set of check groups, so there is no pattern to memorise between rounds.

How do overlapping parity checks find which bit is wrong?

Because each bit sits in a different combination of checks, and that combination is its signature. A single check over a group of bits can only ever tell you that an odd number of bits in that group changed — it detects, it does not locate. Add a second check that overlaps the first only partly, and the four possible outcomes (both fail, only the first fails, only the second fails, neither fails) already split the bits into four sets. With five checks there are 32 possible patterns of failure, which is more than enough room to give each of eight positions its own. So the failing set is not a warning; it is an address. That is the insight behind every error-correcting code — it is what Richard Hamming published in 1950 — and reading it off the board by hand is the entire game here. Work from the failing checks inward: their covered bits are the only candidates, and each passing check then deletes everything it covers.

Why do the check groups change every round?

Because a fixed arrangement stops being a puzzle after two rounds. The textbook version of this matrix is built so that the failing checks spell the position out in binary — check A covers every odd position, check B covers positions 2, 3, 6, 7, and so on — which is elegant but means a player quickly stops reasoning and starts reading a number off a lookup. Here the five groups are drawn fresh for every round, printed in full, and checked before the round is dealt, so the only way through is the actual move: intersect the failing groups, subtract the passing ones.

Can two bits ever produce the same failing pattern?

No, and it is verified rather than assumed. Before a round is dealt, the generator reads off each position's column — the set of checks covering it, which is exactly the pattern of failures a flip there would cause — and accepts the round only when all eight columns are distinct and none of them is empty. Distinct means no two bits could ever look alike. Non-empty means every bit is covered by at least one check, so at least one check always fails and a flip can never slip through unnoticed. If a draw fails either test it is thrown away and redrawn, with a hand-written matrix behind the loop so generation always finishes.

What happens when the tries run out?

The round ends and the flipped bit is named. The number of wrong names you get is not a fixed constant: the generator counts, for each round, how many other positions are one misread check away from the answer, and hands you more tries when the four matrices it drew are genuinely confusable and fewer when they are clean. It runs from three to eight. Nothing else costs anything — moving, reading and focusing checks are all free and unlimited.

Is there any money, betting or in-app purchase in this?

None, and there never will be. No currency, nothing to buy, no hints to unlock for a fee, no prizes.

Does it work offline?

Yes. Once the page has loaded once, the whole game — the board, the matrix generator and the solver that proves the failing pattern names exactly one bit — is on your device. No server is involved in play at any point.

Can I play it with a keyboard or a screen reader?

Both. Left and right move along the word, up and down step through the checks, Enter or Space names the bit under the cursor. Every bit announces its value and whether it has been struck off; every check announces the bits it covers, the parity it wants, the parity it currently reads, and whether it passes or fails. Coverage is a ▪, a verdict is a ✓ or a ✗, and a struck-off bit carries the word out — so nothing on the board depends on telling two colours apart.

Eight bits, five checks and four rounds per run. Check groups cover three to five positions each: fewer than three would hand the answer over, and a check covering everything says nothing useful. Exactly one bit is flipped per round — this is single-error location, so it deliberately does not cover the case where two bits flip at once, which no set of five parity checks over eight bits can distinguish from a single flip elsewhere. The word itself is always drawn with between three and five ones, so the flipped bit is never visible just by looking at a lopsided row. Difficulty comes from the matrix, not from a timer: there is no clock anywhere in the game.

Gap Logic is the other deduction puzzle built on constraints you can read off directly — it turns on order where this one turns on overlap. Light Grid and Signal Flip are the parity games: both are systems over the same two-element arithmetic, but there you change the state, and here you only read it.

Bookmark this page (Ctrl+D, or ⌘D on Mac) or install the app — it works offline the next time you need it.