gamesblog

Hidden rule

Shapes sorted into two piles by a rule you are not told — filled, triangles, three or more. Where does the new one go? Rules grow to “and” and “or”.

  • Pattern
  • Untimed
  • 9 levels

How it plays

Each thing is a shape, filled or hollow, drawn one to four times: ▲▲▲ is three filled triangles, ○ is one hollow circle. A hidden rule has put some in pile 1 and the rest in pile 2. Decide where the new one goes.

The rules start as one feature — filled, hollow, a shape — then counts join in (even, three or more, exactly two), then two features joined by “and”, then “or” and “not”. Fewer things are shown as you climb. There is a top: the last tier with the fewest things shown.

The piles are built so the answer is forced. Every rule of the level that fits both piles is checked, and things are added to the piles until all of them agree about the new one. The working names the rule.

Keys

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

What it trains

This practises inducing a rule from sorted examples and testing it on a new case. It makes you better at puzzles of this kind; it claims nothing wider.

Learn

How to get better at hidden rule: 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. Describe every thing by its three features: its shape, filled or hollow, and how many (one to four). ▲▲▲ is three, filled, triangles.
  2. Find a feature that everything in pile 1 shares, then check that nothing in pile 2 has it. Pile 2 is “the rest”, so the rule must leave every pile-2 thing out.
  3. If no single feature works, try two joined by “and”: everything in pile 1 has both, and everything in pile 2 lacks at least one.
  4. If “and” fails too, try “or”: everything in pile 1 has at least one of two features, and nothing in pile 2 has either. Then “not”: pile 2 is all one shape.
  5. Test the new thing against the rule, one feature at a time, and place it.

Techniques and tricks

  • Find the tight pile

    For an “and” rule, pile 1 is the tight one: everything there shares two features. For an “or” rule, pile 2 is tight: everything there lacks both. Look for the pile with the most in common first.

    e.g. Pile 2 is all hollow and all one or two, while pile 1 has filled things and hollow threes and fours: the rule is “filled, or three or more”.

  • Sort the counts

    List the counts in pile 1 as a set. {1, 3} is odd, {2, 4} is even, {3, 4} is three or more, {1, 2} is one or two, a single count is “exactly” that.

    e.g. Pile 1 holds ◆◆◆, ●, ★★★: counts {1, 3}, so “odd in number” is worth testing.

  • Test only the new thing’s features

    Only the features of the new thing can decide where it goes. For ○○○, ask just three questions: do hollow things go to pile 1? circles? threes?

    e.g. Pile 1: ◆◆◆ ★ ■■■ ▲. Pile 2: ◇◇ ☆☆ ◇◇◇ ☆☆☆. New: □□□. Threes are in both piles and hollow things only in pile 2, so it goes in pile 2.

  • One counterexample kills a rule

    Hunt for the one thing in the wrong pile rather than collecting things that agree. A rule that fits seven things and fails one is not the rule.

    e.g. “Filled” fits all of pile 1, but ■■ sits in pile 2 — so “filled” alone is out.

  • Spot a “not” rule

    When pile 2 is all one shape, of mixed fill and count, the rule is “not that shape”: pile 1 takes everything else.

    e.g. Pile 2: △, ▲▲, △△△△ — the rule is “not triangles”, so ★★ goes in pile 1.

As the levels climb

  • One feature at first — filled, hollow or a shape — with eight things to start.
  • Counts join next (even, odd, three or more, one or two, exactly one to four); then seven things to start; then 80% of the time.
  • Then two features joined by “and”, six things to start, 65% time; then “or” and “not”, then 55% time. That is the top.
  • Fewer things to start means more rules fit, so the game adds things to the piles until only one place is left for the new one. The piles you see can be bigger than the start count, and every extra thing is there to rule something out.

Traps to avoid

  • Stopping at the first fit for pile 1. If pile 1 is all filled but pile 2 holds a filled thing too, “filled” is not the rule. Always check pile 2.
  • The tempting new thing. It is often chosen so that a rule fitting all but one of the piled things puts it in the wrong pile. Check your rule against every thing, not most.
  • Reading “or” as “and”. Under “filled, or three or more”, ○○○ goes in pile 1: it needs only one of the two.
  • Miscounting at a glance. ★★★ and ★★★★ look alike when you are quick, and counts decide many rules. Count each group of symbols.

How to practise

  • Say the rule in words before you answer — “filled and exactly three” — and check it against every thing in both piles.
  • After a wrong answer, find the thing in the piles that rules out the rule you used. The working names the true rule; the killing thing is always there.
  • Expect a dip when “and”, then “or” and “not”, first appear. Each is a new way to combine features, and the piles take longer to read for a while.

Levels

It is untimed unless you turn the clock on. There are 9 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 pattern

All games →