25 Deducing Rules from Examples
Pattern Recognition
Logical Reasoning
Inductive Reasoning
Linguistic Analysis
Mathematical Thinking
Synthetic
25.1 Description:
This task involves analyzing a set of examples to infer the underlying rule or pattern that governs them. It evaluates the model’s ability to recognize patterns, generalize from specific instances, and formulate abstract rules.
25.2 Modality:
Text only
25.3 Examples:
25.3.1 Example 1:
Input:
Consider the following number sequence:
2, 6, 18, 54, 162, ...
What is the rule governing this sequence, and what would be the next number?Output:
Rule: Each number in the sequence is multiplied by 3 to get the next number.
Explanation:
2 x 3 = 6
6 x 3 = 18
18 x 3 = 54
54 x 3 = 162
The next number in the sequence would be: 162 x 3 = 486
This rule can be expressed mathematically as: a(n+1) = 3 * a(n), where a(n) is the nth term in the sequence.25.3.2 Example 2:
Input:
In a fictional alien language, consider these translations:
"zop bik" means "blue sky"
"bik mur" means "clear sky"
"zop taf" means "blue water"
What do the individual words likely mean?Output:
Based on these examples, we can deduce the following:
1. "zop" means "blue"
Reasoning: It appears in both "blue sky" and "blue water"
2. "bik" means "sky"
Reasoning: It appears in both "blue sky" and "clear sky"
3. "mur" means "clear"
Reasoning: It's used with "sky" but not with "blue", so it must mean "clear"
4. "taf" means "water"
Reasoning: It's used with "blue" in a phrase that doesn't mean "sky"
Rule: In this alien language, adjectives come before nouns, similar to English.
This deduction allows us to understand the meaning of each word and the basic structure of the language from just a few examples.