ColorCode

What you see

Every item in ColorCode is described by five yes-or-no features, shown in a legend at the top of the screen:

• V: has a vowel
• E: has an even digit
• L: has more letters than digits
• C: has a corner digit
• A: has an accent mark

On each item, a feature's glyph is solid when the item has it and an outline when it does not. The legend at the top pairs each glyph with its letter and name. You never see the underlying words or numbers. Only the five flags matter.

A trial has two phases.

Study. A panel of worked examples shows items with the colour the hidden code gave each one. Each example is numbered. Take as long as you need. When you are ready, press Start (or Space). The examples then disappear for the rest of the trial.

Apply. Items come up one at a time. For each, choose the colour you think the code gives it, by clicking a colour or pressing its number key. The item is stamped and the next one appears. Stamped items cannot be changed. A row under the colours shows the colours you have given so far, and the line beneath says which item you are on. When every item is stamped, the items are listed with your colours; press Check answer, and each one is marked right or wrong, with the right colour beside any you missed.

What the hidden code looks like

The code is an ordered list of rules, each of the form if the item has feature X, colour it Y, followed by a default colour for items where no rule applies. To colour an item, you check the rules from the top. The first rule whose feature the item has decides the colour, and later rules are ignored. Computer scientists call this structure a decision list, a term from Ronald Rivest's 1987 work on learning rules from examples.

Four facts about our generator make the code learnable from the examples alone.

1. Rules only ever use V, E, L or C. The accent mark A is never part of the code.
2. Each rule gets its own colour, and no rule shares a colour with the default.
3. The examples always include at least two items that isolate each rule (only that rule's feature among the rule features) and at least one item with none of the rule features, which shows you the default.
4. Extra examples are added until exactly one code with that number of rules or fewer fits them all. If you find a code with no more than the level's number of rules that explains every example, it is the answer.

An overlap item has two rule features at once, so only the rule order can tell you its colour. From level 5 at least one is always among the items you stamp. The accent decoy (levels 8 to 10) is described under Tips and traps. There is no countdown in practice mode; a clock counts up in the side rail and a session starts at level 3.

What it measures

ColorCode measures rule induction: inferring a hidden classification rule from labelled examples and applying it to new cases. On our profile it feeds the Rule learning facet of Reasoning, next to Rule Learning, Rule Sorter, SwapCode and Object Sorting, and carries 8 percent of the Reasoning dimension score. Internally the game is weighted 70 percent inductive reasoning and 30 percent rule application.

This is one of the oldest questions in cognitive psychology: how do people learn a category from examples? In a landmark 1961 study, Roger Shepard, Carl Hovland and Herbert Jenkins taught people six classifications of simple objects that varied in shape, size and brightness. Classifications that turned on a single dimension were learned fastest, and the one that required all three dimensions with no simplifying rule was hardest. The lesson carried into ColorCode: each extra rule adds a dimension you must track, and our session report measures exactly that cost.

ColorCode punishes the same habit. A code that explains the first two examples you looked at feels right. The test is whether it explains all of them, including the ones that could break it.

How it is scored here

Each stamped item is right or wrong. Your trial score is the share of items right: 7 of 8 is about 88 percent. Only a perfect trial is marked Correct.

• All items right: Correct, and you move up a level.
• Some right: Partly correct, with partial credit, and you stay at the same level.
• None right: Incorrect, and you move down a level.

Your 0–100 ColorCode score is centred so that 50 means what the difficulty you work at predicts, and each trial's credit is weighted by its level. Time is not part of the score. Studying the examples carefully is the intended strategy, not a cost. A score appears after at least four trials, and recent sessions count for more.

The session report shows Items coloured correctly (your overall accuracy) and Score drop on 3-rule policies: your average trial score on one-rule codes (or on two-rule codes, if you had no one-rule trials) minus your average on three-rule codes, in percentage points. It appears once you have at least two trials of each kind. A large gap means your method holds up for simple codes but breaks down when there are more rules to hold.

Where you will meet it

Assigning new items to categories whose rules you must infer is a standard inductive reasoning format.

Aon's scales cls is the closest cousin: learn rules from grouped examples, then assign new items. The vendor versions use pictures rather than feature flags, so the first job is to decide what the features even are. ColorCode strips that step away and trains the part that follows: turning a set of labelled examples into an exact, ordered rule and applying it without the examples in view.

The method

1. Find the default first

   Look for an example with none of V, E, L or C. Its colour is the default. Every other colour belongs to a rule.

2. Group the examples by colour

   Take each non-default colour in turn and look at every example with that colour. One of V, E, L or C will be present on all of them. That feature is the rule for that colour.

3. Settle the order

   Find an example that has two rule features. The colour it was given belongs to the rule that comes first. With three rules, you need the order of each pair; the examples always contain enough overlaps to fix it.

4. Check every example against your list

   Walk each example through your ordered list from the top. If one comes out a different colour, your list is wrong. Look first at the order, then at which feature you picked for each colour.

5. Say the code, then press Start

   Compress it to one line, such as V Blue, then E Red, else Green. Say it twice. Once the examples go, that line is all you have.

6. Apply from the top, every time

   For each item, ask the first rule's question, then the second, then fall to the default. Do not jump to the feature that catches your eye first.

Worked example 1

Use the study figure near the top of this lesson: seven worked examples in three colours.

Show the solution

Default. The card with no features at all is Green, so Green is the default. (The card with L and C is also Green, which tells you L and C are not rules.)

Rules. Blue cards: V; V L; V E. V is on all of them. Red cards: E; E C. E is on both. So the rules are V gives Blue and E gives Red.

Order. The card with both V and E is Blue, so the V rule comes first.

Code: V Blue, then E Red, else Green. Check: every example fits.

Now apply it:

• E L: no V, has E. Red.
• C: no V, no E. Green.
• V E C: has V. Blue (the E rule is never reached).
• L: no V, no E. Green.

Worked example 2: a level 8 trial

Show the solution

Default. The blank card is Blue. The V-only card is also Blue, so V is not a rule.

Rules. Amber cards: C A; C V A; C E A. Both C and A are on every one. The accent mark is never part of the code, so the rule is C gives Amber. Red cards: E; E L. The rule is E gives Red.

Order. The card with C and E is Amber, so C comes first.

Code: C Amber, then E Red, else Blue.

Now apply it, including the decoy items:

• E A: no C, has E. Red, not Amber. The accent was only ever a coincidence in the examples.
• L A: no C, no E. Blue.
• V E: no C, has E. Red.
• C L: has C. Amber.

Tips and traps

That last tip depends on the examples showing every colour, which our design guarantees, because each rule and the default has its own isolating examples.

Levelling up

Difficulty rises along four lines: more rules (up to three), a fourth colour, guaranteed overlap items, and from level 8 the accent decoy. Three-rule codes at levels 7, 9 and 10 are where most people's accuracy drops, because the order involves three pairs and the one-line summary gets longer.

• For three rules, order them like a ranking. Find the overlaps: if V beats E and E beats C, the order is V, E, C.
• Rehearse a fixed phrasing. V Blue, E Red, C Amber, else Green is easier to hold than a sentence.
• Keep the study phase unhurried. Time does not count here. A wrong code costs every item that depends on it.

1. Week 1
   • Three sessions of 10 to 12 trials, writing each code down before pressing Start
   • Check every example against your written code before you start stamping
   • After each session, look at which items you missed: overlap items point to order errors
2. Week 2
   • Three sessions aiming for level 5 and above
   • Say the code aloud in one line instead of writing it
   • Pair with one Rule Learning session to practise induction from a different kind of example
3. Week 3
   • Three sessions at level 7 and above, where three-rule codes appear
   • Before Start, name the default, each rule and the order in ten seconds or less
   • Track the Score drop on 3-rule policies figure and aim to shrink it

Check yourself

5 practice questions

1. The code is: V gives Blue, then E gives Red, otherwise Green. What colour is an item with V and E?
2. Which worked example tells you the default colour most directly?
3. A trial has 8 items to stamp and you get 7 right. What happens?

and 2 more

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Sources

1. Shepard, R. N., Hovland, C. I., & Jenkins, H. M. (1961). Learning and memorization of classifications. Psychological Monographs: General and Applied, 75(13), 1–42. doi.org
2. Navarro, V. M., Jani, R., & Wasserman, E. A. (2019). Pigeon category learning: Revisiting the Shepard, Hovland, and Jenkins (1961) tasks. Journal of Experimental Psychology: Animal Learning and Cognition, 45(2), 174–184. Includes a summary of the human difficulty ordering. PMC
3. Wason, P. C. (1960). On the failure to eliminate hypotheses in a conceptual task. Quarterly Journal of Experimental Psychology, 12(3), 129–140. doi.org
4. Rivest, R. L. (1987). Learning decision lists. Machine Learning, 2(3), 229–246. doi.org
5. Aon. Prepare for your online assessment: Inductive-logical Thinking (scales cls). aon.com
6. SHL. SHL Direct practice tests: inductive reasoning. shl.com
7. PrepInsta. Capgemini Exceller game-based aptitude test questions (candidate-reported). prepinsta.com

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