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Free printable Logic grid with answers

A logic grid puzzle, also called a logic problem, gives you a short scene and a list of clues. Five neighbours, five houses, five pets, five drinks: work out which goes with which. No clue tells you an answer outright, and together they allow exactly one arrangement. The grid down the page is where you keep track, ticking what a clue settles and crossing what it rules out.

By size

A grade is how many categories you are matching and how many people are in them. The bigger grades also drop the clues that place someone outright, so every square has to be reasoned to rather than read off.

By audience

It is the puzzle for people who like reading as much as counting: there is no arithmetic anywhere in it, and the whole thing is argued rather than calculated.

One answer, and no guessing

Two promises, and the second is the one printed books most often break. The first is ordinary: the clues allow exactly one arrangement. The second is that the arrangement can be REACHED by reasoning, with nothing left to try. Those come apart more often than you would think. Cut a clue list back as far as it will go while only checking the first, and you reliably end up with a puzzle whose last step is a coin toss. So every board here is checked for both, and a board that needs a guess is thrown away rather than printed. The clue list is then cut back one clue at a time: on the wider boards that takes about twenty clues down to thirteen, and nothing left on the page follows from the rest.

How to solve a logic grid puzzle

Read the scene, read the clues, and work out which of each category goes with which. The grid down the page is where you keep track: tick what a clue settles, cross what it rules out, and the arrangement falls out of what is left.

The method

  1. 1Mark the clues that say no. Most clues rule something out rather than pinning it down, and those are the ones to put on the grid first. Find the block that pairs the two categories the clue names, and cross the cell where they meet. Nothing has been decided yet and that is fine: four crosses in a row of five decide the fifth for you.
  2. 2A tick clears its row and its column. The moment a cell is settled, nothing else in that row or that column can be true, because each item belongs to exactly one person. Crossing all of them out is not bookkeeping, it is where the next deduction usually comes from.
  3. 3Carry a fact sideways. The step people miss. If Alice is in house three, then everything you learn about house three you have learnt about Alice, and everything you learn about Alice you have learnt about house three. Copy the whole row from one block into the other. On a four or five category board this is most of the solve.
  4. 4Read the ordering clues from both ends. Somewhere to the left of, two places before, somewhere between. Each of those trims both ends of a line at once: if the cat owner is left of Alice, the cat owner is not in the last house and Alice is not in the first. Taken one at a time they say very little; taken together they close a board.
The one rule people get wrong
A cross means those two items belong to different people. It does not mean either of them is settled anywhere else, and it is easy to tick a neighbouring cell out of impatience. Only tick when the row or the column has nothing else left in it.
What the answer page shows
A table of who had what: one row per person, one column per category, so you can check a line at a glance rather than reading a filled-in grid.
How the grades differ
More categories and more people, and from the hard grade up, no clue that places anybody outright. The clue count falls relative to the board as the grades rise, which is most of what you feel.
Will I ever have to guess?
No. Every board here is checked twice before it prints: that the clues allow one arrangement, and that reasoning alone reaches it. A board that needs a guess is thrown away rather than printed.
Is it the same as a sudoku?
No. A sudoku gives you the rules and some of the answer; a logic grid gives you all of the rules in words and none of the answer. There is no arithmetic in it anywhere, and the work is reading rather than scanning.
Good for
Anyone who likes to argue their way to an answer in prose.

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