Three of these puzzles have more than one answer. Try to find all the possible answers for each puzzle. One of these puzzles is impossible.

1.My number is a factor of 20.It's also a factor of 30.

2.My number is a multiple of 10.It's also a factor 45.

3.My number is between 40 and 50.It is prime.

4.My number is a multiple of 4.It's a square number.It's less than 50.

To find all possible answers for each puzzle, we need to analyze the given conditions one by one.

1. My number is a factor of 20. It's also a factor of 30.
To find the factors of 20, we can list out all the numbers that divide 20 evenly: 1, 2, 4, 5, 10, and 20.
Similarly, for 30, the factors are: 1, 2, 3, 5, 6, 10, 15, and 30.

By comparing the factors of 20 and 30, we find that the numbers that are common factors are: 1, 2, 5, and 10. Therefore, the possible answers are 1, 2, 5, and 10.

2. My number is a multiple of 10. It's also a factor of 45.
To find the multiples of 10, we can multiply 10 by different numbers: 10x1, 10x2, 10x3, and so on.
On the other hand, to find the factors of 45, we can list out all the numbers that divide 45 evenly: 1, 3, 5, 9, 15, and 45.

By comparing the multiples of 10 and factors of 45, we find that the numbers that are factors of 45 and multiples of 10 are: 5 and 15. Therefore, the possible answers are 5 and 15.

3. My number is between 40 and 50. It is prime.
To find numbers between 40 and 50, we can simply list them: 41, 42, 43, 44, 45, 46, 47, 48, 49, and 50.
Checking each of these numbers, we find that only 43 is a prime number. Therefore, the only possible answer is 43.

4. My number is a multiple of 4. It's a square number. It's less than 50.
To find the multiples of 4 less than 50, we can multiply 4 by different numbers: 4x1, 4x2, 4x3, and so on.
For each of these multiples, we can check if it is a square number (a number multiplied by itself) and if it is less than 50.

The squares of the multiples of 4 less than 50 are: 16, 36. Therefore, the possible answers are 16 and 36.

In summary, the possible answers for each puzzle are:
1. Possible answers: 1, 2, 5, 10
2. Possible answers: 5, 15
3. Possible answer: 43
4. Possible answers: 16, 36

Note: It is not specified which puzzle is impossible, so we cannot determine that from the given information.

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