Logic Puzzle challenges – part 2

The most common combined task among Logic Puzzles in official UCAT materials is sequencing and matching.

In these puzzles, you will have to:

• Put people or things in order while also matching them to another category, or
• Match three categories of entities while putting one category in order.

Notice that the main difference is whether it is single or double matching.

In any case, you will want to focus on the sequencing task as it will allow you to arrange the people or things with a clear, consistent approach.

In a combined sequencing and matching puzzle, use the sequencing task to guide your sketch.

Think about the real-world context of the sequencing task, as you can capture its logic in your sketch.

Examples of everyday logic implicit in sequencing tasks:

• people in a queue could be drawn left to right, with the front of the queue at the left; include additional rows underneath for single or double matching.
• people finishing a race or otherwise ranked could be drawn top to bottom, with the first place person at the top; include additional columns to the right as needed for matching.
• items or activities with different prices could have the prices in descending value from top to bottom; use further columns to match up the other categories.

In a combined sequencing and matching puzzle, you can apply the matching task using the simplest, quickest approach for the particular rules.

It will generally be more straightforward to assign people or things to their slots, then match secondary categories like colours or activities.

You may find that you need to deduce every slot in a single category, then use your work to make further deductions for the next category.

Sometimes, though, you can fill in all the slots to match up everything for a single person or thing. This is a huge advantage, as it limits the possibilities for the rest of the row or column.

Even in a more complex Logic Puzzle, some rules are simpler than others.

Look for the most concrete rule – or part of a rule – that you can add directly into your sketch.

Proceed with the next most concrete rule, or favour simpler rules over longer, more complex ones.

A sequencing and matching puzzle may include a diagram. You will likely need to recreate it in your notebook with a quick sketch.

However, keep it simple – do not make your sketch more complicated than absolutely necessary.

Think about the sequencing element and if it is horizontal or vertical, then draw blanks or a table with the same orientation.

Note that in many cases, you will simply want to draw a row of blanks rather than squares or rectangles to represent hotel rooms, parking bays or any side-by-side locations. You just need people or things in a row, not enclosed in quadrilaterals.

A rule might limit one person or thing to two possibilities to match in another category. Notate this quickly and simply using abbreviations with a slash.

Put any such rules – the ones you can notate easily but can’t make deductions from yet – to one side of your notebook.

This way, you can quickly compare notations and see what becomes clear as you add notes for any such rules.

Often, you will find you can combine the rules to see that a person or thing is the only possibility for one match in another category. This makes for an absolute deduction; it also lets you cross out possibilities from your other notations with slashes. It might just help you fill in most of your sketch, or even prove the correct answer.

Keep an eye on the answers as you work through a Logic Puzzle.

You may find that you have proven the correct answer before you finish filling in the sketch. This is more likely in a sequencing and matching puzzle, since there are so many interlocking elements you can use to make deductions.

Sometimes, it is not possible to match all entities in a sequencing and matching puzzle.

It may be impossible to deduce an exact placement for some people or things, or to match every item from every category.

Don’t worry, as this is by design. In many puzzles, you cannot fill in the entire sketch and match everything up exactly. But you don’t need to do so to get to the correct answer.

If you find you are stuck after making several deductions, check the answers as it is possible you can eliminate one or more wrong answers. Or you may have already proved the correct answer.

The key in Logic Puzzles is to know when to stop working. Do only as much as you need to click the correct answer and move on.

You are highly likely to see a double matching puzzle in your DM section on Test Day.

To double match, you must connect each entity with others from two more categories.

This means each person or thing will have two links – thus, it’s double matching.

You can work from any entity or category to start making matches, but there will be a huge amount of information to organise as you try to make deductions.

Some Logic Puzzles are a pure double matching task, without a sequencing or spatial element. You will simply have three categories of entities to pair up.

As a result, there is no orientation to allow you to set up a sketch in an obvious way. This can make it a bit more challenging to make notes in a double matching task.

Instead, you may prefer to:

• Notate the rules one at a time, from most concrete to least concrete – or from most positive to most negative.
• Add deductions as extra notations, as these will be essential for connecting the rules and matching the entities. Sometimes, this will be enough to prove the correct answer.
• In a harder question, make a column of the main entities to which you will match the other categories. Usually, this will be people; in the absence of people, use the biggest thing (such as cars or houses) or places/nationalities.

In a double matching puzzle, be ready to link up people or things across different rules.

Focus on positives and look for limitations – such as negatives that can turn into positives.

Keep an eye on the answers, as you can often eliminate wrong answers as you work through the rules.

Occasionally, a double matching puzzle may have a repeated colour or some other entity that occurs more than once.

Watch out for any initial limitations on the number of each colour or repeated element.

You may be able to deduce a limitation as you combine information from different rules. Use the limitations to help you fill in gaps and match up entities across the categories.

Leave any unknowns – such as a colour or entity not mentioned in the rules – until you make all other possible deductions. Unknowns could match with anything, so you will need to limit the possibilities quite significantly to see where they could or must fit in.

Turn negative rules to your advantage in a double matching puzzle. Use the number limitations to guide your deductions.

If there are five people in a puzzle and a detail does not match with two of them, there are only three people it could match.

If there are four people in a puzzle and a detail does not match with two of them, there are only two people it could match.

Remember, everyone must match with something in each category. Eliminating options for a match will leave fewer and fewer possibilities.

In checking answer choices, watch out for anything that could be true.

Remember, anything that could be true also could be false.

You may need to test and disprove answers by seeing if you can match a different entity instead of the one in the answer choice.

If the correct answer must be true, any answer choice you can disprove is incorrect. Even if it is possibly true – show it could be false. If it’s not true in 100% of cases, it’s wrong.

Sometimes, all the entities in each category will be clearly listed in the puzzle’s set-up.

Other times, one or more categories will have its entities only in the rules.

In a double matching puzzle, you may find it helps to make a quick list of the entities in each category, especially if they are not listed in the set-up.

You could easily have 12 or 15 entities across three categories in a double matching puzzle.

As you practise, experiment with different ways to abbreviate in each category. This will help to avoid confusion if some of the entities start with the same letter.

A common approach is to abbreviate:

• People with a capital first letter and possibly a second lowercase letter if two names start with the same letter.
• Colours with two lowercase letters, but be prepared to adjust for two colours with the same first two letters (black and blue, green and grey, etc.).
• Activities or items with three lowercase letters or two capital letters.
• Place names with one capital and two lowercase letters.