Logic & mind · 5 min read
How to Solve a Sixteen-Word Grouping Puzzle
Why the first group you spot is usually a trap, which group to leave for last, and the three kinds of link that every one of these puzzles is built from.
In this article
Every board is built from three kinds of link
A grouping puzzle hides four sets of four among sixteen words, and once you have solved a few you notice the links only ever come in three flavours. The first is a plain category: four rivers, four kinds of pasta. The second is a shared partner: four words that can all follow "fire", or all precede "board". The third is about the word as a string of letters rather than a meaning: a hidden word inside each one, a shared sound, a letter pattern.
Naming the flavour out loud helps more than it sounds. When you are stuck, the problem is almost never that you do not know the words. It is that you are still reading them for their meaning while the last group is about their spelling.
The obvious group is usually bait
Puzzle setters put a fifth candidate into the most obvious category on purpose. If you can see five fruits, one of them belongs somewhere else, and submitting the first four you notice is how most mistakes happen.
The fix is to count before you commit. When a category has exactly four members on the board, it is probably real. When it has five or six, stop and ask which of those words has a second life: "date" is a fruit and a day, "jam" is a spread and a traffic problem. The word with a second life is the one the setter needs somewhere else.
Solve from the constraints, not from the easy end
The most reliable way through is to find the group that cannot be anything else. Look for a word that fits only one possible link, then find the three others that fit that link. That group is safe to submit even if it is not the easiest one, and removing it takes four decoys off the board at once.
Every solved group shrinks the problem. With twelve words left, the traps start to resolve themselves; with eight, the last two groups are often forced. This is why the hardest group so often gets solved last without ever being understood until it is sitting there on its own.
When you are one away
"One away" means three of your four belong together. The instinct is to swap a word at random, which burns mistakes. Instead, keep the three and ask what the link between them actually is, in as few words as possible. A precise description of the link usually excludes the wrong fourth word and points straight at the right one.
If you still cannot see it, leave that group and solve another. A word you were sure belonged in your three is often the one another group needs, and it becomes obvious once the rest of the board is gone.
A worked example
Say the board holds DATE, FIG, PRUNE, RAISIN and CURRANT, along with MONDAY, DEADLINE and APPOINTMENT. That is five dried fruits, which is one too many. DATE also sits naturally with MONDAY, DEADLINE and APPOINTMENT as things that go in a calendar, and none of those three could be a fruit. So the calendar group has to take DATE, and the fruit group is FIG, PRUNE, RAISIN and CURRANT.
Notice what did the work. It was not knowing more fruit. It was noticing that the calendar words had no other home, and letting them claim the word they needed. Most boards can be unpicked this way: find the group with no alternatives, give it what it needs, and see what that leaves behind.
Play something related
Keep reading
- Logic & mind · 5 min readA Better Strategy for Five-Letter Word GamesWhat your first guess is really for, why repeating a green letter is a waste, and how to handle the endgame where four letters are right and six words still fit.
- Logic & mind · 5 min readMental Math Shortcuts That Actually Save TimeSix moves that turn awkward sums into easy ones, why speed comes from recognising problems rather than calculating faster, and how to practise without a worksheet.
- Logic & mind · 7 min readHow to Estimate Almost Anything Without a CalculatorThe Fermi method for guessing numbers you have never looked up: break the question into parts, think in powers of ten, average your bounds the right way, and check the answer against something you already know.
