Table 1.
The 30 rules used during fMRI
| Rule ID | Rule | Example | Arithmetic description | Geometric description | ADL | GML | Per | MDL | ADT | DL |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Same | 4-4-4-4-4-4 | Same | Same | 1 | 1 | 1 | 1 | 2.72 | E |
| 2 | Add 2 | 8-10-12-2-46 | +2 | →→ | 3 | 2 | 1 | 2 | 2.89 | E |
| 3 | Subtract 2 | 8-6-4-2-12-10 | −2 | ←← | 3 | 2 | 1 | 2 | 2.72 | E |
| 4 | +1, 0 | 6-7-7-8-8 | +1 | → | 3 | 2 | 2 | 2 | 3.82 | E |
| 0 | . | |||||||||
| 5 | −1, 0 | 6-5-5-4-4-3-3 | −1 | ← | 3 | 2 | 2 | 2 | 4.21 | E |
| 0 | . | |||||||||
| 6 | Top down | 1-8-2-9-3-10 | +7 | ↘ | 8 | 2 | 2 | 2 | 2.71 | E |
| −6 | ↑ | |||||||||
| 7 | Bottom up | 11-4-10-3-9-2 | −7 | ↖ | 8 | 2 | 2 | 2 | 3.33 | E |
| +6 | ↓ | |||||||||
| 8 | Diagonal | 2-9-4-11-6-7 | +7 | ↘ | 8 | 2 | 2 | 2 | 3.57 | E |
| −5 | ↗ | |||||||||
| 9 | Add 3 | 3-6-9-12-3 | +3 | →→→ | 3 | 3 | 1 | 3 | 2.94 | E |
| 10 | Subtract 3 | 2-11-8-5-2 | −3 | ←←← | 3 | 3 | 1 | 3 | 3 | E |
| 11 | +2, 0 | 6-8-8-10-10-12-12 | +2 | →→ | 4 | 3 | 2 | 3 | 3.89 | E |
| 0 | . | |||||||||
| 12 | −2, 0 | 8-6-6-4-4-2-2 | −2 | ←← | 4 | 3 | 2 | 3 | 4.76 | E |
| 0 | . | |||||||||
| 13 | 1; same | 1-6-2-6-3-6-4-6 | x = current pos, pos | x = current pos, pos | 3 | 3 | 2 | 3 | 5.37 | E |
| x + 1 | x→ | |||||||||
| 14 | +2, +1 | 9-11-12-2-3-5-6 | +2 | →→ | 5 | 3 | 2 | 3 | 3.82 | E |
| +1 | → | |||||||||
| 15 | −2, −1 | 9-7-6-4-3-2-1 | −2 | ←← | 5 | 3 | 2 | 3 | 4.14 | E |
| −1 | ← | |||||||||
| 16 | +2, −1 | 5-7-6-8-7-9-8 | +2 | → → | 5 | 3 | 2 | 3 | 4.66 | D |
| −1 | ← | |||||||||
| 17 | −2, +1 | 4-2-3-1-2-12 | −2 | ←← | 5 | 3 | 2 | 3 | 3.91 | D |
| +1 | → | |||||||||
| 18 | Vertical | 12-6-10-4-8-2-12 | −6 | ↑ | 8 | 3 | 2 | 3 | 4.91 | D |
| +4 | ↙← | |||||||||
| 19 | Parallel diagonal | 5-12-4-11-3-10 | +7 | ↘ | 9 | 3 | 2 | 3 | 3.94 | D |
| −8 | ←↖ | |||||||||
| 20 | Left loop diagonal | 6-5-12-5-4-11-4 | −1 | ← | 10 | 3 | 3 | 3 | 6.5 | D |
| +7 | ↘ | |||||||||
| −7 | ↖ | |||||||||
| 21 | Right loop diagonal | 1-2-9-2-3-10-3-4 | +1 | → | 10 | 3 | 3 | 3 | 5.90 | D |
| +7 | ↘ | |||||||||
| −7 | ↖ | |||||||||
| 22 | 1 (2), 2 | 6-7-8-10-11-12-2 | +1 (2) | → | 6 | 4 | 3 | 4 | 6.16 | D |
| +2 | → | |||||||||
| →→ | ||||||||||
| 23 | Greek fret | 11-5-4-10-9-3 | +6 | ↑ | 6 | 4 | 4 | 4 | 3.93 | D |
| +1 | → | |||||||||
| ↓ | ||||||||||
| → | ||||||||||
| 24 | Extremes | 12-6-1-7-12-6-1-7 | −6 | ↑ | 8 | 4 | 4 | 4 | 3.89 | D |
| −5 | → | |||||||||
| ↓ | ||||||||||
| ← | ||||||||||
| 25 | Central square | 9-3-4-10-9-3-4-10 | −6 | ↑ | 12 | 4 | 4 | 4 | 4.37 | D |
| +1 | → | |||||||||
| −6 | ↓ | |||||||||
| −1 | ← | |||||||||
| 26 | Series on two rows | 1-6-2-7-3-8-4-9-5-10-6 | +5 | ← (only once) | 8 | 4 | 3 | 4 | 4.78 | D |
| −4 | →→ (only once) | |||||||||
| ↓ | ||||||||||
| ↗ | ||||||||||
| 27 | 1; diagonal | 8-9-4-5-12-7 | +1 | → | 12 | 4 | 4 | 4 | 6.69 | D |
| −5 | ↗ | |||||||||
| +1 | → | |||||||||
| +7 | ↘ | |||||||||
| 28 | +1, +2 (2) | 3-4-6-8-9-11-13 | +1 | → | 6 | 4 | 3 | 4 | 5.92 | D |
| +2 repeat | →→ repeat | |||||||||
| 29 | 3, 1 (2) | 7-10-11-12-3-4-5-8 | +3 | →→→ | 6 | 5 | 3 | 5 | 6.91 | D |
| +1 repeat | → | |||||||||
| → | ||||||||||
| 30 | Progression | 7-8-10-1-5-10-4 | Load x, + x | — | 6 | 45 | — | 6 | 4.00 | D |
| x = x + 1 |
The numbers in the example column refer to the position of the blue circle in the 2 row × 6 column array. ADL, Arithmetic description length; GML, geometric description length; Per, period (number of cards, excluded the first, before rule starts repeating); MDL, minimum description length; ADT, average discovery trial (trial at which the rule is acquired); DL, difficulty level (easy/difficult). Despite equal ADL, GML, Per, and MDL, rules 16 and 17 were considered to be more difficult than rules 14 and 15 because they involve two different arithmetic operations.