Who is Good?

Logic Level 2

For people living in the Philippines, this question is similar to a question in UP Little Math Wizard.

This (similar) question was given in 2018.

A person who is good is not bad.

If $\color{#20A900}{\text{Pam}}$ is $\color{#20A900}{\text{good}}$ , then $\color{#20A900}{\text{Ann}}$ is $\color{#20A900}{\text{good}}$ or $\color{#20A900}{\text{Ian and Sam}}$ are both $\color{#20A900}{\text{good}}$ .

If $\color{#20A900}{\text{Ann}}$ is $\color{#20A900}{\text{good}}$ , then all of $\color{#20A900}{\text{Candy, Dan, and Cindy}}$ are $\color{#20A900}{\text{good}}$ .

If we know that $\color{#D61F06}{\text{Dan}}$ is $\color{#D61F06}{\text{bad}}$ and $\color{#20A900}{\text{Pam}}$ is $\color{#20A900}{\text{good}}$ , at least how many people are $\color{#20A900}{\text{good}}$ ?

The answer is 3.

2 solutions

Jerome Te
Nov 19, 2018

If Dan is bad, then Ann is bad.

Why?

If Ann was good, then Dan is good. So, the above statement is correct.

If Ann is bad, Candy and Cindy may be good or bad. But we want the least number of good people, so we have Candy and Cindy to be bad.

Pam is good and Ann is bad, so Ian and Sam are both good. So 3 people.

Chew-Seong Cheong
Nov 18, 2018

Since we know that $\color{#20A900} \text{Pam}$ is $\color{#20A900}\text{good}$ , this means that either $\color{#3D99F6} \text{Ann}$ or both $\color{#3D99F6}\text{Ian and Sam}$ are $\color{#20A900}\text{good}$ .
But $\color{#D61F06}\text{Dan}$ is $\color{#D61F06}\text{bad}$ , this means that $\color{#D61F06}\text{Ann}$ isn't good or is $\color{#D61F06}\text{bad}$ too.
This means that $\color{#20A900} \text{Ian and Sam}$ are both $\color{#20A900}\text{good}$ .
Therefore, there are at least $\color{#20A900} \boxed 3$ people $\color{#20A900} \text{Pam, Ian, and Sam}$ are $\color{#20A900}\text{good}$ .

Who is Good?

The answer is 3.

2 solutions

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