If eight animals, cats and mice, are sitting around a bowl of milk, how many cats could there be? - briefly
The number of cats sitting around the bowl of milk can range from zero to eight. The total number of cats depends on how many mice are present, as the total count of animals is fixed at eight.
There are several scenarios to consider:
- If all eight animals are mice, then there are zero cats.
- If there is one cat, then there must be seven mice.
- If there are two cats, then there must be six mice.
- This pattern continues up to the scenario where there are eight cats and zero mice.
If eight animals, cats and mice, are sitting around a bowl of milk, how many cats could there be? - in detail
To determine the possible number of cats among eight animals sitting around a bowl of milk, we must consider all the possible combinations of cats and mice. Both cats and mice are common household pets, and they are often depicted together in various scenarios, including sharing food sources like milk. The key to solving this problem lies in understanding the basic principles of combinatorics and set theory.
Firstly, it is essential to recognize that the total number of animals is eight. This total is composed of two types of animals: cats and mice. Let's denote the number of cats as ( C ) and the number of mice as ( M ). Since the total number of animals is eight, we can write the equation ( C + M = 8 ).
To find the possible values of ( C ), we need to consider all the integer values from 0 to 8, because the number of cats can range from zero (no cats) to eight (all animals are cats). For each value of ( C ), there is a corresponding value of ( M ) that satisfies the equation ( C + M = 8 ).
Let's list the possible combinations:
- If ( C = 0 ), then ( M = 8 ) (all animals are mice).
- If ( C = 1 ), then ( M = 7 ) (one cat and seven mice).
- If ( C = 2 ), then ( M = 6 ) (two cats and six mice).
- If ( C = 3 ), then ( M = 5 ) (three cats and five mice).
- If ( C = 4 ), then ( M = 4 ) (four cats and four mice).
- If ( C = 5 ), then ( M = 3 ) (five cats and three mice).
- If ( C = 6 ), then ( M = 2 ) (six cats and two mice).
- If ( C = 7 ), then ( M = 1 ) (seven cats and one mouse).
- If ( C = 8 ), then ( M = 0 ) (all animals are cats).
From this list, it is clear that the number of cats can range from 0 to 8. Therefore, the possible number of cats among the eight animals sitting around the bowl of milk is any integer from 0 to 8, inclusive. This detailed analysis shows that all values within this range are equally valid, depending on the specific composition of the group of animals.