"Looking for a non or minimal "calculation-based" solution, I came up with the following.
1. Consider all the moons as one large pie.
2. Due to the four planets, the average number of moons will be ¼ of the pie.
3. The number of moons of Nymeria will be twice this or ½ of the pie.
4. The remaining number of moons (29 = 7+10+12) represent the other ½ of the pie.
5. With the two halves equal, Nymeria must have 29 moons.
"
Rick, United States
Tuesday, November 19, 2024
"Algebraic solution:
Let n be the number of moons for the planet Nymeria. Then we know the average (mean) is n/2, since Nymeria has twice as many moons as the mean number for the system. The mean is also the sum of the moons divided by four.
N / 2 = (n + 7 + 10 + 12) / 4 = (n + 29) / 4
Solving for n, we get 29 moons for Nymeria.
Intuition
We know the moon mean is half the number of moons for Nymeria. We know the mean is also the number of moons for Nymeria plus the sum of the moons from the other three planets and that this is divided by four. Hence the numerator needs to be double the number of moons for Nymeria, hence the number of moons for Nymeria must be equal to the number of moons for the other three planets, which is 29.
"
Leonard,
Saturday, November 2, 2024
"Looking for a non or minimal "calculation-based" solution, I came up with the following.
1. Consider all the moons as one large pie.
2. Due to the four planets, the average number of moons will be ¼ of the pie.
3. The number of moons of Nymeria will be twice this or ½ of the pie.
4. The remaining number of moons (29 = 7+10+12) represent the other ½ of the pie.
5. With the two halves equal, Nymeria must have 29 moons. "
Rick, United States
Tuesday, November 19, 2024
"Algebraic solution:
Let n be the number of moons for the planet Nymeria. Then we know the average (mean) is n/2, since Nymeria has twice as many moons as the mean number for the system. The mean is also the sum of the moons divided by four.
N / 2 = (n + 7 + 10 + 12) / 4 = (n + 29) / 4
Solving for n, we get 29 moons for Nymeria.
Intuition
We know the moon mean is half the number of moons for Nymeria. We know the mean is also the number of moons for Nymeria plus the sum of the moons from the other three planets and that this is divided by four. Hence the numerator needs to be double the number of moons for Nymeria, hence the number of moons for Nymeria must be equal to the number of moons for the other three planets, which is 29. "