Logic grid puzzles, every step explained

A logic grid puzzle hands you a few people, or boats, or market stalls, and a few lists about them: who sat where, who brought what, who came first. Each one matches exactly one thing on every list, and no two share. Your job is to work out every match from a handful of clues.

The best-known one is the Einstein puzzle, also called the zebra puzzle: five houses in a row, five owners, five pets, and the question of who keeps the zebra. It is often credited to Albert Einstein, though nobody has shown that he wrote it. Big or small, every puzzle of this kind works the same way.

The grid is where you keep track. Every pair of lists gets its own block of squares. You cross out a square when a pairing cannot be true and tick it when it must be. When a row is down to one square, that square is the answer.

1. Mark the plain facts first. A clue that says one thing is not another is a cross you can draw straight away.
2. Look for a row with one square left. If three of four options are crossed out, the fourth one is true: tick it, then cross out the rest of its row and column.
3. Carry what you know from one block to the next. If Ana owns the red bike and the red bike is not in the garage, Ana's bike is not in the garage either. Most of a puzzle is solved this way.
4. Read order clues slowly. “Before” and “right before” are different clues: the first leaves room in between, the second allows exactly one spot.
5. Don't guess. Every GRIDIGMA puzzle has exactly one answer, and you can always reach it by reasoning. When you are stuck, read each clue again against what the grid shows now; one of them will have become useful.

Still stuck? A hint in the game points to the clue that moves you forward and says why.

Colors on the Wall

Here is a whole puzzle solved from the first clue to the last. It is Colors on the Wall, the smallest free puzzle in the game, so if you would rather crack it yourself, play it first and come back.

The story

The long gray community wall finally got its mural this weekend. The wall was split into panels, each named after a plant, and from left to right they ran willow, fern, reed and moss. Someone had chalked a number in the corner of each one, counting from 1 on the left up to 4 on the right. Iris, Caleb, Zoe and Marcus turned up with brushes and buckets. Each of them took a panel and painted it in a single color, and no two of them picked the same color. By sunset the wall was bright from one end to the other. The only trouble was the sign-up sheet. It listed the names and nothing else, so nobody could say who painted where, or in which color.

The clues

1. Of Iris and Caleb, one painted the willow panel and the other painted the fern panel.
2. Iris worked somewhere to the left of Caleb.
3. The navy paint went on the panel just to the right of the one painted coral.
4. The chalked number on Zoe's panel and the one on the panel painted mint added up to seven.
5. The moss panel was not painted mint.

The solve, step by step

The game's solver has checked that each step below follows from the clues it names.

1. Clue 1 gives the willow and fern panels to Iris and Caleb, one each. So neither of them painted reed or moss, and those two panels belong to Zoe and Marcus.
2. Clue 2 says Iris worked to the left of Caleb. Willow is panel 1 and fern is panel 2, so Iris painted willow and Caleb painted fern.
3. Clue 4 is the clever one. Zoe's panel is reed (3) or moss (4), and her number plus the mint panel's number makes seven. Only 3 and 4 add up to seven, so mint went on whichever of reed and moss Zoe did not paint. That means neither willow nor fern was painted mint, and Zoe did not use mint.
4. Clue 5 says the moss panel was not mint, so mint went on reed. Going back to clue 4, Zoe's panel must then be moss, and reed, the mint one, was Marcus's.
5. Clue 3 puts navy on the panel right after the coral one. Reed already has mint, so the only neighboring pair left is willow and fern: willow is coral and fern is navy. That makes Iris's paint coral and Caleb's navy.
6. That leaves ocher, so Zoe painted the moss panel ocher.

The answer

Every panel found its painter. Iris started the row with coral paint on the willow panel, and Caleb came next, painting the fern panel navy. The reed panel went to Marcus, in mint. Zoe finished the row with ocher paint on the moss panel.

A new puzzle comes out every day at 00:00 UTC, and it is free to play on its day.

Play today's puzzle

Every earlier day is in the daily puzzle archive.

The catalogue is free to play, with no account needed. Each level is a step up from the one before.

Very Easy

• Closing Time at the Beach Huts
• Colors on the Wall
• Icing on the Seating Card

Easy

• Kids on the Scale
• Rough Air
• The Smudged Sign-In Sheet

Medium

• Cider Day at Ashford
• Down Into the Cave
• The Clipboard in the Waves

Hard

• The Last Throw at the Crown
• The Lost Exam Page
• The Torn Docket

Very Hard

• Smoke on the Quarter Mile
• The Clerk's Slip
• The Greenhouse on the Roof

Themed packs

Each themed pack follows one event of its week. They come with a subscription, like past days.

Championship Night

• Painting the Court (Very Easy)
• The Lost Lineup Card (Easy)
• First Baskets of Game Two (Easy)
• Ink in the Margin (Easy)
• The Missing Score Sheet (Medium)
• The Soaked Box Score (Medium)
• Lemonade on the Stat Sheet (Hard)
• The Missing Ballot (Very Hard)

Match Day

• Off the Bench (Very Easy)
• Gone Down the Tunnel (Easy)
• The Soaked Notebook (Medium)
• Notes in the Heat (Hard)
• What the Rain Left (Very Hard)

The Grass-Court Fortnight

• Mabel's Lucky Notebook (Very Easy)
• A Sleepless Night in the Line (Easy)
• Cool Box at the Courts (Medium)
• Rain on the Clipboard (Medium)
• Washed Out (Hard)
• Tallies in the Players' Box (Very Hard)

The Heritage List

• Knots by the Water (Very Easy)
• The Running Order (Easy)
• First Tours of a Heritage Town (Easy)
• Pressed into Paper (Medium)
• First Light on the Walls (Hard)
• Fresh Paint on the Temple Beams (Very Hard)
• Splashed by the Ferry (Very Hard)

The Robot Games

• Next-Door Numbers (Very Easy)
• Robots on the Big Board (Easy)
• Don't Drop the Blocks (Medium)
• A Badge for Every Robot (Medium)
• Waiting for Applause (Hard)
• Until the Battery Blinks Red (Very Hard)
• A Slip in the Logbook (Very Hard)

Are the puzzles free?

The catalogue and each day's new puzzle are free to play in your browser, with no account needed. A subscription opens past days and the themed packs.

Will I ever have to guess?

No. Every puzzle has exactly one answer, and the solver checks that you can reach it by reasoning alone.

What makes a puzzle hard?

Mostly how long you go without a clue giving you a new square. In an easy puzzle nearly every clue gives you a mark at once. In a hard one you hold two or three facts together, or follow a “what if” until it breaks.

Can I play on my phone?

Yes. GRIDIGMA runs in the browser on a phone, a tablet or a computer, with nothing to install.