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← The Logic Grid

The Logic Grid

Three short lessons on solving logic-grid puzzles: one of each per row and column, mark what cannot be true, and follow one clue into the next.

Spark & Whetstone · sparkwhetstone.org/learn/the-logic-grid · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. One of each

A logic-grid puzzle matches people to things, like three friends and three pets. Draw a grid: names down the side, pets across the top.

Each person has exactly one pet, and each pet belongs to exactly one person. So every row and every column ends with exactly one tick.

Question. In a three-by-three grid, a row already has two crosses. What goes in its last box?

  1. A tick.
  2. Another cross.
  3. It cannot be known yet.

Say it back. In your own words: what is the rule for every row and column?

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Lesson 2. Mark what cannot be

Most clues tell you what is not true. "Ana does not have the cat" is a cross in Ana's cat box. Crosses are most of the work.

When you place a tick, cross out the rest of that row and column at once. That is often what unlocks the next step.

Question. You put a tick for Ben and the dog. What should you do straight away?

  1. Cross out the rest of Ben's row and the dog's column.
  2. Move on to the next clue.
  3. Put a tick for the dog for everyone.

Say it back. Say it back: why cross out the row and column as soon as you tick?

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Lesson 3. One clue into the next

Try this. Ana, Ben and Cai own a cat, a dog and a fish. Ben does not have the cat. Cai has the fish. Who has the dog?

Cai has the fish, so neither Ana nor Ben has it. Ben does not have the cat and does not have the fish, so Ben has the dog. Each fact made the next one possible.

Question. In the puzzle above, who has the cat?

  1. Ana
  2. Ben
  3. Cai

Say it back. In your own words: how does one clue lead into the next?

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At the table: Make a grid for each other

Players: two people, 8 or older. You'll need: squared paper and pencils.

  1. Each person secretly matches three family members to three foods.
  2. Write three clues that are just enough to work it out.
  3. Swap clues and solve each other's grid.
  4. If a puzzle could not be solved, find the missing clue together.

Answers

  1. A tick. — With two boxes ruled out and one tick needed, the last box must be the tick.
  2. Cross out the rest of Ben's row and the dog's column. — Ben has no other pet and nobody else has the dog, so the rest of the row and column become crosses.
  3. Ana — With the fish and dog taken by Cai and Ben, the cat is Ana's.