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Which cards to turn

A rule, some cards, and only one side of each showing. Pick exactly the cards that could break the rule — the test most people fail.

  • Logic
  • Untimed
  • 10 levels

How it plays

Each card has something on both sides; you see one. The rule says “if this is on one side, then that is on the other.” Choose the cards you must turn over to find out whether the rule is broken — no more, no fewer. You are told how many.

A card can only break the rule if it might have the first half true and the second half false. So turn the cards showing the first half, and the cards showing the second half false. The card showing the second half true tells you nothing: the rule never said only the first half leads there.

Levels negate one half or both, put the rule the other way round, phrase it as “only if”, and deal more cards. Some rules are abstract letters and numbers; some are everyday permissions, which people find easier — the logic is the same.

Keys

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

What it trains

This practises looking for the case that could prove a rule wrong rather than the cases that agree with it, on rules like these. It claims nothing wider.

Learn

How to get better at which cards to turn: 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. Find the “if” half of the rule and the “then” half. With “only if”, the half before “only if” is the “if” half.
  2. Say what would break the rule: the “if” half true and the “then” half false, on the same card. Nothing else breaks it.
  3. Go through the cards one at a time and ask: could this card, whatever is on its back, turn out to be that breaking case? If yes, turn it.
  4. Count your picks against the number you are told to turn. If they differ, go back over the cards you left.

Techniques and tricks

  • Turn the “if” true and the “then” false

    Turn every card that shows the “if” half true, and every card that shows the “then” half false. Leave the rest. This works for every rule in the game, negated or not.

    e.g. “If the letter is a vowel, then the number is even”: of A, K, 4, 7, turn A and 7.

  • Hunt for the rule-breaker

    You are not trying to find cards that agree with the rule. A card that agrees proves nothing; only a card that could break it is worth turning.

    e.g. The 4 could have a K on the back, and the rule would still stand — the rule never said only vowels go with even numbers.

  • Rewrite “only if” as “if … then”

    “A only if B” means the same as “if A, then B”. Rewrite it before you look at the cards, and keep the halves in that order.

    e.g. “The letter is a vowel only if the number is even” is “if the letter is a vowel, then the number is even”: turn A and 7.

  • Carry the “not” into the halves

    When a half is negated, work out what “true” means for that half first. In “if the letter is not a vowel, then the number is even”, the “if” half is true for a consonant, so turn K and 7.

    e.g. “If the letter is a vowel, then the number is not even”: the “then” half is false for an even number, so turn A and 4.

  • Read it as a permission

    Recast any rule as “to do this, you must have that”, and check the people who did it and the people who lack it. That is how you would check a bar: the beer drinker and the 16-year-old, never the cola drinker or the 25-year-old.

As the levels climb

  • You start with the plain rule, “if P, then Q”, on four cards. Each level then changes one thing, in turn: the rule’s form, the number of cards, the clock.
  • The forms arrive in order: the “then” half negated, then the “if” half negated, then both, then “only if”, where either half may also be negated. From the first negated form on, the rule may also start from the other side — “if the number is even, then …” — so find which face each half is about before you pick.
  • More cards are dealt, up to the “Most cards dealt” setting. You may get two vowels or two odd numbers; every card of a kind to be turned must be turned, and the count you are told includes them all.
  • With “Time pressure” on, the clock gives 15 seconds plus 4 per card, closing to 80% and then 65%.

Traps to avoid

  • Turning the “then” card: picking the 4 for “if vowel, then even”. It feels like a check, but whatever is on its back, the rule survives.
  • Missing the “then”-false card: leaving the 7. It is the card that can catch the rule out, if a vowel is on its back.
  • Reading “only if” backwards: taking “A only if B” as “if B, then A”. It flips which cards to turn.
  • Dropping a “not”: reading “if the letter is not a vowel” as “if the letter is a vowel”. Re-read each half and mark which faces make it true.
  • Stopping at one card of a kind: with more cards dealt, there may be two that show the “if” half true. Turn them all.

How to practise

  • Start with “Kinds of card” on “Permissions (age, licence)” only, where the right picks feel obvious, then switch to “Letters, shapes and numbers” and use the same reasoning.
  • Keep “Most cards dealt” at 4 until the negated and “only if” forms are reliable, then raise it to 8.
  • For every card you leave, say why aloud: “this shows the ‘if’ half false, so the rule says nothing about it.” The working gives the same reason for each card.

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.

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