gamesblog

Knights and knaves

Everyone on the island always tells the truth or always lies. From what they say, work out who is which — more islanders, harder sentences.

  • Logic
  • Untimed
  • 10 levels

How it plays

A knight only ever says true things; a knave only ever says false ones. Read what each islander says and decide who is which.

The trick is to suppose: if Asha were a knave, her statement would be false — what would that make Bilal? Follow each supposition until it contradicts itself.

Levels add islanders and harder sentences — not, the same kind, or, counting, if–then — and eventually a normal, who may say anything. Every puzzle has exactly one answer, checked by trying every casting.

It is untimed by default. Slow is the point.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This practises deduction by supposition — holding a case in mind and following it to a contradiction. It is practice at these puzzles, not a measured improvement in reasoning elsewhere.

Learn

How to get better at knights and knaves: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Look for a statement that settles someone on its own — a speaker who talks about themselves, like “we are both knaves” or “I am a knave or …”. Start there.
  2. Otherwise, suppose. Take the first speaker and say “if she is a knight, her words are true”. Follow what that makes everyone else, statement by statement.
  3. If the supposition leads to someone being both a knight and a knave, or a count that cannot be, it was wrong: the speaker is the other kind. If it runs clean through every statement, keep it.
  4. Before you pick, test your casting against every line, not only the ones you used. The wrong options are castings that fit most of the statements and break just one.

Techniques and tricks

  • Talking about the other one

    Between knights and knaves, when one islander calls another a knight, the two are the same kind; when one calls another a knave, they are different kinds. A knight tells the truth about the other; a knave reverses it.

    e.g. Asha: “Bilal is a knave.” Either Asha is a knight and Bilal a knave, or the other way round

  • We are both knaves

    Between knights and knaves, no knight can say it, since it would be a lie. So the speaker is a knave, the claim is false, and the other person must be a knight.

    e.g. Asha: “Bilal and I are both knaves.” Asha knave, Bilal knight

  • The same-kind shortcut

    With no normal on the island, “X and I are the same kind” always makes X a knight, whoever says it; “X and I are different kinds” always makes X a knave. The speaker stays open.

    e.g. Chen: “Dara and I are the same kind.” If Chen is a knight, Dara is too; if Chen is a knave, the two differ — so Dara is a knight either way

  • A false half proves the rest

    A speaker who says “I am a knave, or …” must be a knight — a knave saying it would make the first half true — and then the second half must hold. In the same way, “If I am a knight, then …” from anyone makes them a knight and the then-part true.

    e.g. Asha: “I am a knave, or Bilal is a knight.” Asha is a knight, so Bilal is a knight

  • Count the knights

    For “exactly k of us are knights”, try the speaker both ways and count. If the speaker is a knight, the total is k; if a knave, it is anything but k. The total must agree with everyone else you have placed.

    e.g. Three islanders; Gita says “exactly one of us is a knight”. If Gita is a knight, the other two are knaves

  • Spot the normal

    When one islander is a normal, a statement no knight or knave could make — such as “I am a knave” — gives the normal away at once. The rest are then plain knights and knaves.

As the levels climb

  • The ladder starts with two islanders who only say what people are, then three. Next, sentences can say “not” and whether two people are “the same kind”, which brings in the same-kind shortcut.
  • With “Normals” on “From the higher levels”, a normal joins at level 4 and stays: exactly one islander who may say anything. Their words tell you nothing, so find them first and set their statement aside.
  • Then the ladder alternates: a fourth islander, then “or”; a fifth, then counting (“at least two of us are knaves”); a sixth, then if–then. With the default “Most islanders” of 6, that is the top.
  • More islanders mean more castings to keep in mind. Keep the roles in a line as you settle them — knight, knave, not yet known — and test each new statement against that line.
  • The clock is off unless you turn on Time pressure; then you get 20 seconds plus 9 for each statement.

Traps to avoid

  • Checking only the statements you used. The other options are the castings that fit the most lines, so one usually agrees with everything you looked at and breaks a line you did not.
  • Using the shortcuts while a normal is on the island. A normal can say “we are both knaves” or “I am a knave, or …” and be neither knight nor knave, so settle who the normal is before you lean on any of them.
  • Forgetting that a knave’s whole sentence is false. “A and B are knaves” from a knave means at least one of them is not a knave, not that both are knights.
  • Reading a normal’s words as true or false. A normal may say either, so never build on what the normal said — use what the others say about the normal.

How to practise

  • Set “Normals” to “Never” while you learn supposition and the shortcuts, then to “Always one” to practise finding the normal first.
  • Lower “Most islanders” to 4 if the bigger islands feel like guesswork; raise it to 7 when six fall without a wrong pick.
  • Raise “Options shown” to 6 to face more near-miss castings, which forces the full check against every line.
  • When you miss one, read the working: it gives each statement with whether it is true and why that suits the speaker. Find the line your answer broke.

Levels

It is untimed unless you turn the clock on. There are 10 levels with the default settings, and the counter stops at the real top. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More logic

All games →