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Analogies

2 : 8 :: 3 : 27 :: 5 : ? and AB : BC :: KL : ? — find the relation in the example and carry it over. The relations grow subtler as you climb.

  • Pattern
  • Timed
  • Endless levels

How it plays

An analogy says: as this is to that, so the new thing is to ?. Find the relation in the example — add 7, square it, reverse the digits; move every letter one on, write it backwards, swap each letter for its mirror — and apply it to the new term.

Numbers come with two examples, or three, because one example fits too many rules: 3 : 9 could be +6, ×3 or squaring. Letters come with one, or more when one is not enough. Every relation the game knows is tried on the examples; the question is only asked when all that fit agree.

The wrong options are what a rule that fits just one example would give. The working names the relation and shows each step.

Keys

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

What it trains

This practises finding a relation from examples and checking it against all of them. It is practice for analogy questions, not a test of intelligence.

Learn

How to get better at analogies: 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. Read the first pair and list every rule it allows. 3 : 9 could be + 6, × 3 or “square it” — do not choose yet.
  2. Test each candidate on the second pair, and the third if there is one. Keep only the rule that fits every pair; the game only asks when exactly one survives.
  3. Apply the survivor to the new term, then check the size: if the outputs dwarf their inputs in the examples, the answer must too.
  4. For letters, turn each letter into its place (A = 1 … Z = 26) and compare place by place: the same step everywhere is a shift, the order flipped is a reversal, one place changing is a last-letter move.

Techniques and tricks

  • Difference and ratio first

    For every pair, work out the output minus the input and the output divided by the input. A difference that never changes means add; a ratio that never changes means multiply.

    e.g. 12 : 60 :: 5 : 25 — differences 48 and 20, ratios 5 and 5. So multiply by 5: 9 → 45.

  • Two pairs fix “multiply, then add”

    When neither the difference nor the ratio holds, divide the change in output by the change in input. That is the multiplier; what is left over is the number added.

    e.g. 12 : 31 :: 5 : 17 — (31 − 17) ÷ (12 − 5) = 2, and 31 − 24 = 7. So × 2 + 7: 13 → 33.

  • Squares, cubes and the next number up

    Know the squares to 20², the cubes to 10³ and n × (n + 1): 6, 12, 20, 30, 42, 56, 72, 90, 110, 132. An output just above or below a square is “square it, then add”.

    e.g. 5 : 28 :: 7 : 52 — 25 + 3 and 49 + 3, so 9 → 84. 11 : 132 :: 4 : 20 — 11 × 12 and 4 × 5, so 9 → 90.

  • Look at the digits, not the size

    When an output has the input’s digits in another order, or is tiny beside a big input, try “reverse the digits” and “add up its digits”.

    e.g. 704 : 407 reverses, so 654 → 456. 1,274 : 14 adds digits: 1 + 2 + 7 + 4 = 14.

  • EJOTY landmarks

    E is 5, J 10, O 15, T 20, Y 25. Find any letter’s place from the nearest landmark instead of counting from A.

    e.g. HP : JR — H is 8, J is 10; P is 16, R is 18. Every letter moves 2 on, so DE → FG.

  • Mirror letters add to 27

    A↔Z, B↔Y, C↔X: a letter and its mirror always have places adding to 27. Subtract the place from 27 to find the mirror.

    e.g. D is 4, and 27 − 4 = 23, which is W. So the mirror of DOG is WLT.

  • Check for a reversal before a shift

    Compare the first letter of the output with the last letter of the input. If they are close, the rule writes the letters backwards first, and may then shift them.

    e.g. KLM : NML — M → N is 1 on, then L, then K → M. Backwards, then 1 on: DEF → GFE.

As the levels climb

  • You start with three relations: add, multiply, and moving every letter by the same step. Numbers come with two examples, letters with one, or more when one is not enough.
  • Relations open in three waves. First divide, square (perhaps then add), cube, letters backwards and moving only the last letter; then multiply-then-add, times the next number up, the mirror alphabet and backwards-then-shift.
  • The last wave brings reverse the digits, add up the digits, a letter step that grows by one at each letter (ABC : BDF) and swapping the first and last letters. Learn each new relation by name as it arrives.
  • After each wave the numbers grow and the clock tightens — to 80%, then 65%. Past the last wave only the size grows: numbers without end, letters up to four-letter strings and steps of up to eight.

Traps to avoid

  • The one-example rule. The wrong options include what a rule fitted to one pair alone would give: 12 : 60 alone could be + 48, which turns 9 into 57 — but 5 : 25 is not + 48. Test on every pair.
  • One off. The answer ± 1 is often among the number options (44 and 46 beside 45). They catch a slip in the last step, so redo the final sum rather than choosing on looks.
  • Right letters, wrong order. The answer written backwards (GF for FG) and the new term left unchanged (DE) are offered. Check the order as well as the letters.
  • One letter out. Options with one letter a place too far or too short (FH for FG) come from counting the letter you start on. Count jumps: two on from H is I, then J.
  • The step that goes down. Steps can be negative — 18 : 11 is subtract 7, LT from MU is one back. See which way the outputs move before you size the step.

How to practise

  • Use “Questions about” to practise Numbers or Letters alone when one lags. Letters alone have a last level; numbers never end.
  • Switch “Answer by” to “Typing the answer” once options feel easy. With nothing to test against, you have to find the rule rather than recognise its result.
  • Raise “Options shown” towards 8 to meet more one-example lures at once, or lower it to 2 while a new relation is still strange.
  • After a miss, read the working: it names the relation and the lure’s rule. On the next question, say the rule out loud before you look at the options.

Levels

Each question has a clock that comes from the work it asks for. There is no last level: at least one dial turns without end. 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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