That's enough to catch someone

Logic Level 2

While Balbir had his back turned, a dog turned into his butcher shop, snatched a piece of meat off the counter and ran out. Balbir was mad when he realized what has happened. He asked three other shopkeepers, who had seen the dog, to describe it. The shopkeepers really didn't want to help Balbir. So each of them made a statement which contained one truth and one lie.

First Shopkeeper: The Dog had black hair and a long tail.

Second Shopkeeper: The Dog had a short tail and wore a collar.

Third Shopkeeper: The dog had white hair and no collar.

Based on the above statements, which of the following could be a correct description?

Can you catch some liars for me. Here are some of them who make statements worth deceiving

The Dog had black hair, long tail and no collar. The Dog had white hair, long tail and wore a collar. The Dog had black hair, long tail and wore a collar. The Dog had white hair, short tail and no collar. This is an impossible scenario. Cannot be determined.

1 solution

Chew-Seong Cheong
Jun 20, 2016

If we assume that the dog had black hair we get the following truth table, where $\color{#3D99F6}{\text{true}}$ is blue and $\color{#D61F06}{\text{false}}$ is red. It leads to the description that " The dog had black hair, short tail and no collar. ", which is $\color{#D61F06}{\text{not}}$ one of the answer options.

$\begin{array} {lccc} \text{First shopkeeper} & \color{#3D99F6}{\text{Black hair}} & \color{#D61F06}{\text{Long tail}} & \\ \text{Second shopkeeper} & & \color{#3D99F6}{\text{Short tail}} & \color{#D61F06}{\text{Collar}} \\ \text{Third shopkeeper} & \color{#D61F06}{\text{White hair}} & & \color{#3D99F6}{\text{No collar}} \end{array}$

Now, if we assume that the dog had long tail or white hair, we get " The dog had white hair, long tail and wore a collar. ", which $\color{#3D99F6}{\text{is}}$ one of the answer options.

$\begin{array} {lccc} \text{First shopkeeper} & \color{#D61F06}{\text{Black hair}} & \color{#3D99F6}{\text{Long tail}} & \\ \text{Second shopkeeper} & & \color{#D61F06}{\text{Short tail}} & \color{#3D99F6}{\text{Collar}} \\ \text{Third shopkeeper} & \color{#3D99F6}{\text{White hair}} & & \color{#D61F06}{\text{No collar}} \end{array}$

These are the only two possible descriptions of the dog. Therefore, the answer is $\boxed{\text{The dog had white hair, long tail and wore a collar.}}$

Emmm , I'm not pretty sure of it.

There are , independently of the answers list , two possible solutions as you observed those anyway being "dog black hair long tail no collar" and "dog white short collar".

You use the list as the reasoning for obtaining which of the 2 answers is right. Yet in the list of answers there is also the cannot be determined answer which would be still true.

As such , since there are 2 possible solutions and one possible answer is that it can't be determined that answer should be selected asit describes better the possible answer of the problem anyway. Supposing further that the author had in mind a question as "what can be necessary said based on the above information of the dogs ?" as usually happens in like problems it emphasizes that answer.

A A - 4 years, 12 months ago

That is why the question is "which of the following $\color{#D61F06}{\text{could}}$ be a correct description?"

Chew-Seong Cheong - 4 years, 12 months ago

Oh , right! Maybe anyway you should put that observation in the solution as it is part of the reasoning and thanks anyway.

A A - 4 years, 12 months ago

That's enough to catch someone

Can you catch some liars for me. Here are some of them who make statements worth deceiving

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