If eight animals, cats and mice, are sitting around a bowl of milk, how many mice could there be? - briefly
To determine the number of mice, consider the total number of animals and the possible combinations of cats and mice. There could be anywhere from 0 to 8 mice, depending on the number of cats present. The maximum number of mice would be 8 if there are no cats, and the minimum would be 0 if all eight animals are cats. There are multiple possibilities in between these extremes. Answer: The number of mice could range from 0 to 8, depending on the number of cats.
If eight animals, cats and mice, are sitting around a bowl of milk, how many mice could there be? - in detail
To determine the possible number of mice when eight animals, consisting of cats and mice, are sitting around a bowl of milk, one must consider the constraints and logical possibilities of the scenario.
Firstly, it is essential to recognize that the total number of animals is eight. This means that the sum of the number of cats and the number of mice must equal eight. Mathematically, if we denote the number of cats as ( C ) and the number of mice as ( M ), the equation is:
[ C + M = 8 ]
Given this equation, we can explore the various combinations of cats and mice that satisfy the condition. The possible values for ( M ) (the number of mice) range from 0 to 8, as there can be anywhere from zero mice to all eight animals being mice. However, since the problem specifies that there are both cats and mice, ( M ) cannot be 0 or 8. Therefore, the possible values for ( M ) are:
- 1 mouse (and 7 cats)
- 2 mice (and 6 cats)
- 3 mice (and 5 cats)
- 4 mice (and 4 cats)
- 5 mice (and 3 cats)
- 6 mice (and 2 cats)
- 7 mice (and 1 cat)
Each of these combinations is a valid solution to the problem, as they all satisfy the condition that the total number of animals is eight and that there are both cats and mice present. It is important to note that the problem does not provide additional constraints, such as the behavior of the animals or any specific characteristics of the cats and mice, which would further limit the possibilities. Therefore, any of the above combinations is a correct answer to the question of how many mice could there be.