three of these puzzles have more than one answer. try to find all the possible answers for each puzzle one of these puzzle 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 a factor of 45.
3. my number is between 40 and 50. it's a prime.
4. my number is a multiple of 4. it's a square number. it's less than 50.
1. Factors of 20 = 1, 2, 4, 5, 10, 20. Factors of 30 = 1, 2, 3, 5, 10, 15, 30
There -- the first one is done for you. If you post your answers to the others, we'll be glad to check them.
2.) 1,9,5, 45
3.) 41, 43 &47
4.) 16
To find the possible answers for each puzzle, let's analyze each puzzle individually:
1. Puzzle 1:
- We are looking for a number that is both a factor of 20 and 30.
- To find the possible answers, we need to list the factors of both 20 and 30.
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- The common factors of 20 and 30 are 1, 2, 5, and 10.
- Therefore, the possible answers for this puzzle are 1, 2, 5, and 10.
2. Puzzle 2:
- We are looking for a number that is both a multiple of 10 and a factor of 45.
- To find the possible answers, we need to find the multiples of 10 and the factors of 45.
- Multiples of 10: 10, 20, 30, 40, 50, ...
- Factors of 45: 1, 3, 5, 9, 15, 45
- The common numbers between the multiples of 10 and the factors of 45 are 10 and 45.
- Therefore, the possible answer for this puzzle is 10.
3. Puzzle 3:
- We are looking for a prime number between 40 and 50.
- We need to list the numbers between 40 and 50 and check if they are prime.
- The numbers between 40 and 50: 41, 42, 43, 44, 45, 46, 47, 48, 49, 50
- From this list, the only prime number is 41.
- Therefore, the possible answer for this puzzle is 41.
4. Puzzle 4:
- We are looking for a number that is both a multiple of 4, a perfect square, and less than 50.
- To find the possible answers, we need to list the multiples of 4 that are perfect squares and less than 50.
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
- Perfect squares: 4, 9, 16, 25, 36, 49
- The common numbers between the multiples of 4 and the perfect squares that are less than 50 are 4 and 16.
- Therefore, the possible answers for this puzzle are 4 and 16.
From the analysis:
- Puzzle 1 has the possible answers 1, 2, 5, and 10.
- Puzzle 2 has the possible answer 10.
- Puzzle 3 has the possible answer 41.
- Puzzle 4 has the possible answers 4 and 16.
It is not specified which puzzle is impossible, so we cannot determine an impossible puzzle from the given information.