2.1 The Core Distinction
The Puzzle Solver
- Skill: Deductive reasoning & process of elimination.
- Input: Rules, conditions, and constraints.
- Trap: Missing a key deduction that simplifies the board.
The Relationship Finder
- Skill: Finding the mathematical link (ratio, difference).
- Input: Numbers, rates, and formulas.
- Trap: Doing heavy calculation instead of finding the shortcut.
2.2 Variant 1: The Logic Puzzle
Scenario: A writers' conference needs to schedule 5 writers. Rules involve gender, language, and nationality.
- Achebe (male, English, Nigeria)
- Weil (female, French, France)
- Gavalda (female, French, France)
- Barrett Browning (female, English, UK)
- Rowling (female, English, UK)
- Austen (female, English, UK)
- Ocantos (male, Spanish, Argentina)
- Lu Xun (male, Chinese, China)
- Rule 1: One day needs "at least 4 women".
- Rule 2: Other day needs "majority non-English" (max 2 English).
- Rule 3: Neither day should have more than 2 writers from the same country
- Observation: Day 2 already has 2 men. So "4 women" rule MUST apply to Day 1.
Select a writer who could be added to the schedule for either day. Then select a writer who could be added to the schedule for neither day. Make only two selections, one in each column
| Either Day | Neither Day | Writer |
|---|---|---|
| LeGuin (female, English, USA) | ||
| Longfellow (male, English, USA) | ||
| Murasaki (female, Japanese, Japan) | ||
| Colette (female, French, France) | ||
| Vargas Llosa (male, Spanish, Peru) |
2.3 Variant 2: The Math Relationship
"Organization A currently has 1,050 members. Organization B currently has 1,550 members. The number of members of Organization A and the number of members of Organization B are increasing annually, each at its own constant rate. Analysts project that if each of these organizations maintains its constant annual rate of membership increase, five years from now they will for the first time have the same number of members, and in subsequent years Organization A will have more members than Organization B.
In the table below, identify a rate of increase, in members per year, for Organization A, and a rate of increase, in members per year, for Organization B that together are consistent with the analysys' projection. Make only one selection in each column."
The Trap: Calculating year-by-year growth for different pairs.
The Insight: A is behind by 500. To catch up in 5 years, A must gain 100 per year over B.
Target: Rate A - Rate B = 100
| Org A | Org B | Rate (members/year) |
|---|---|---|
| 10 | ||
| 30 | ||
| 40 | ||
| 120 | ||
| 130 | ||
| 150 |
