Logic puzzles

Logic puzzles have interested me since childhood. I’d like to know how to make them, hence this post.

To begin with, what are logic puzzles? With logic puzzles, you basically have two lists of data.

For example, one list may be people:

  • Kyle
  • Danielle
  • Rebecca

A second list may be their favourite foods:

  • lobster
  • Chinese
  • spaghetti

Your task is to correctly match items from the first list with items on the second list. Here’s a picture to illustrate what I mean:

To help you match match the items up, a logic puzzle will give you a grid like this one:

The information you need to match the items correctly are in the form of clues. What clues could we do for this puzzle?

The = clue

The = clue tells you a ‘postive’ fact. An example of an = clue is Kyle’s favourite food is lobster.

So we can put a tick in the grid for Kyle – lobster.

Also, we can cross out the rest of the Kyle row (since we now know his favourite food isn’t chinese or spaghetti).

What’s more, we can cross out the rest of the lobster column (since we now know Danielle and Rebecca’s favourite food isn’t lobster).

So our grid would look like this:

The ≠ clue

The ≠ clue tells you a ‘negative’ fact. For example, Danielle does NOT like chinese food. Here, we can only put a single lonely cross into the grid.

From these two clues alone, we can now solve the puzzle. In the image below, the left grid contains the tick and crosses from the two clues. The right grid shows my deductions and the final answer.

How did I get to the second grid from the first grid? Well the chinese food can only belong to Rebecca, since it isn’t Kyle or Danielle’s favourite food. And the spaghetti, the only food left, can only be the favourite food of Danielle, the only person left.

Other types of clue

Other clues are just variations on the = clue and the ≠ clue. Think of the = clue as being able to put a tick in a box, and the ≠ clue as being able to put a cross in. Since all you can put in the boxes are ticks and crosses, it follows that the only types of clue are = and ≠ clues.

The nor clue

This clue says that an item on the list doesn’t match with two other items. It’s basically two ≠ clues in one.

Examples are the fish isn’t owned by Henry, nor Julie and the bank heist didn’t happen on Tuesday nor Wednesday. You can put two crosses in to the grid with this clue.

The either clue

This clues gives you a pairing but hides it amongst a false pairing.

Examples are either Dan or Adam is going to lift these boxes and either the red door or the blue door leads to safety.

In the first example, you now know nobody other than Dan or Adam will lift the boxes (and can put crosses in at their names). In the second example, you now know that none of the other doors leads to safety – e.g. the green, yellow and orange doors will lead to danger – so you can cross these possibilities out.

Another variation involves four items. For example, of the red door and blue door, one leads to safety and the other leads to a bottomless pit. This is the same as the last clue, except you can rule out ‘bottomless pit’ for the other colour doors as well (green, yellow, orange, etc).

The more than (or less than) clue

When a list of items is numerical (amounts of money, times, dates) , or can be naturally ordered (days of the week), you may come across this clue.

For example, Jill earns more than Chris. Here, you know initially that Jill can’t be the lowest earner, and Chris can’t be the highest earner. Once you know exactly how much either of the 2 earns, then you can rule out more possibilities for the other person.

The list clue

This type of clue gives you a list of items, and the relationships between them all are ≠. This type of clue conveys a lot of information in a short sentence.

For example, The 4 people are: Sally, Adam, the person wearing jeans, and the fire-eater.
From this you can gather that:
Sally nor Adam ≠ jeans,
Sally nor Adam ≠ fire-eater,
and fire-eater ≠ jeans.

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