Problem with animals

Number Theory Level pending

Paul lined up his animals in a farm. In front of a \(pig\) is a \(dog\) and a \(sheep\). Behind a \(cat\) is a \(pig\), \(dog\), and \(sheep\). In front of a \(sheep\) is a \(cat\), a \(pig\), and a \(dog\).

  • Question 1: If there are as few animals as possible, what animal is directly in front of a cat?
  • Question 2: If Paul has as few animals as possible, how many of each animal does he have?

\(Pig\) = 1

\(Cat\) = 2

\(Sheep\) = 3

\(Dog\) = 4

\(None\) = 5

\(Indeterminate\) = 0

Your answer to question 1 should be the assigned value of the animal that is directly in front of a \(cat\). The answer is none if you think no animal is in front of a cat. If you think that there are multiple cats, and each one has a different animal in front of it, then just answer indeterminate.

Your answer to question 2 should be the sum of values of all the animals that Paul owns. That is, if your answer is \(300\) pigs, \(17\) dogs, \(30\) cats, and \(12\) sheep, then your answer should be \( (300 \times 1)+ (30 \times 2) + (12 \times 3) + (17 \times 4) = 464 \).

If your answer to question 1 is \(x\), and your answer to question 2 is \(y\), input your answer as \(x \times y\).

This problem is an adaptation.


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