​In Order to Rank the Five Members of Its Chess

question 169

Multiple Choice

​In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​​

Let matrix A represent the matrix with the following elements: .
Let matrix B represent the matrix with the following elements: .
The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?
​

• A) ​player 3
• B) ​player 2
• C) ​player 5
• D) ​player 1
• E) ​player 4

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Definitions:

Syntax

The set of rules and principles that govern the structure of sentences in a language, including word order.

Psycholinguistics

The study of the psychological and neurobiological factors that enable humans to acquire, use, and understand language.

Phonemes

The smallest units of sound in a language that distinguish one word from another, essential for speech and language.

Linguistic Relativity

A theory suggesting that the structure of a language affects its speakers' world view or cognition.