"The number of precious stones of each colour are as follows: 35 fiery red, 8 cool blue and 7 verdant green. I used a mix of probability and algebraic skills to solve the problem. Here it goes: The number of stones in each colour multiply to 1960 (using probability methods) and the only factors of 1960 that add to 50 are 35, 8 and 7."
Leonard, US
Tuesday, July 2, 2024
"I was listening to the July puzzle this morning, and decided to give it a try.
After a couple of false starts, I came up with the following thinking.
- Probability of a single draw = \(R/50 * B/49 * G/48\).
- With 6 ways to arrange the drawn R/B/G gems, we want \(6(R/50 * B/49 * G/48) = 0.1\), where 0.1 is our 10% goal.
- Simplifying yields \(R * B * G = 50 * 49 * 48 / 60 = 117,600 / 60 = 1,960\).
- Prime factoring 1,960 yields \(2*2*2*5*7*7\), leading to possibly values of G of 2, 4, 5, 7, 8, 10, and 14.
- Working my way up from 2 (utilizing the constraint R+B+G = 50) led me to my answer of 35, 8 and 7.
I hope that is correct.
Love the website."
Farquad,
Friday, July 5, 2024
"Let’s say there are x red, y blue and z green, such that x+y+z = 50
The info we are given lets us deduce that the number of total outcomes is 50C3, or 19600.
The number of favourable outcomes would be the number of ways you can get a red, * the number of ways to get a blue * the number of ways to get a green, or xyz
so our total probability is xyz/19600 = 1/10, giving us xyz = 1960
combining this with x+y+z = 50 lets us find that the only solution that satisfies both equations, and x > y > z is:
x = 35
y = 8
z = 7"
Rick, Regular Podcast Listener
Monday, July 8, 2024
"There are six ways to pull three unique stones from the collection, where R=red, G=green, and B=blue:
RGB, RBG, GRB, GBR, BRG, and BGR.
The probability of pulling the first combination is R/50 x G/49 x B/48. This is the same for all the other combinations as well, only the order of the numerator changes.
Adding the six together and equating to the stated probability results in 6 x RGB / (50 x 49 x 48) = 1/10.
Solving for RGB and distributing the 10 and 6 appropriately = 50 / 10 x 49 x 48 / 6 = 5 x 7 x 7 x 2 x 2 x 2.
Since R + G + B = 50, an even number, and there are three odd and even factors, either all the odd factors need to be multiplied by an even factor (which would result in two values being the same, contradicting the statement that red was greater than blue which was greater than green). Therefor, assume one of the values is 35, leaving 7 and 8. Eureka. Red = 35, blue = 8, and green = 7, which, when added together, total 50.
"
Kirby,
Tuesday, July 9, 2024
"35 Red, 8 Blue, 7 Green.If you pick one at a time there are 6 ways to get one of each - RBG, RGB, BRG, BGR, GRB, GBR. The odds of any one of these scenarios is RxBxG/(50x49x48). So the odds you hit one of these scenarios is 6xRxBxG/(50x49x48) = 1/10. Simplifying you get RxBxG = 1960. You also know that R + B + G = 50. From there I looked up the prime factors of 1960 and tinkered with combining them until I found 3 that added up to 50. Assigned the order based on the questions saying more reds than blues and more blues than greens."
Alfonso Rodríguez, Mexico
Monday, August 5, 2024
"Amazing explanation about the earth´s curvature. I had never really understood this calculation until I followed this explanation."
Mala, New Zealand
Monday, July 1, 2024
"The number of precious stones of each colour are as follows: 35 fiery red, 8 cool blue and 7 verdant green.
I used a mix of probability and algebraic skills to solve the problem.
Here it goes:
The number of stones in each colour multiply to 1960 (using probability methods) and the only factors of 1960 that add to 50 are 35, 8 and 7."
Leonard, US
Tuesday, July 2, 2024
"I was listening to the July puzzle this morning, and decided to give it a try.
After a couple of false starts, I came up with the following thinking.
- Probability of a single draw = \(R/50 * B/49 * G/48\).
- With 6 ways to arrange the drawn R/B/G gems, we want \(6(R/50 * B/49 * G/48) = 0.1\), where 0.1 is our 10% goal.
- Simplifying yields \(R * B * G = 50 * 49 * 48 / 60 = 117,600 / 60 = 1,960\).
- Prime factoring 1,960 yields \(2*2*2*5*7*7\), leading to possibly values of G of 2, 4, 5, 7, 8, 10, and 14.
- Working my way up from 2 (utilizing the constraint R+B+G = 50) led me to my answer of 35, 8 and 7.
I hope that is correct.
Love the website."
Farquad,
Friday, July 5, 2024
"Let’s say there are x red, y blue and z green, such that x+y+z = 50
The info we are given lets us deduce that the number of total outcomes is 50C3, or 19600.
The number of favourable outcomes would be the number of ways you can get a red, * the number of ways to get a blue * the number of ways to get a green, or xyz
so our total probability is xyz/19600 = 1/10, giving us xyz = 1960
combining this with x+y+z = 50 lets us find that the only solution that satisfies both equations, and x > y > z is:
x = 35
y = 8
z = 7"
Rick, Regular Podcast Listener
Monday, July 8, 2024
"There are six ways to pull three unique stones from the collection, where R=red, G=green, and B=blue: RGB, RBG, GRB, GBR, BRG, and BGR.
The probability of pulling the first combination is R/50 x G/49 x B/48. This is the same for all the other combinations as well, only the order of the numerator changes.
Adding the six together and equating to the stated probability results in 6 x RGB / (50 x 49 x 48) = 1/10.
Solving for RGB and distributing the 10 and 6 appropriately = 50 / 10 x 49 x 48 / 6 = 5 x 7 x 7 x 2 x 2 x 2.
Since R + G + B = 50, an even number, and there are three odd and even factors, either all the odd factors need to be multiplied by an even factor (which would result in two values being the same, contradicting the statement that red was greater than blue which was greater than green). Therefor, assume one of the values is 35, leaving 7 and 8. Eureka. Red = 35, blue = 8, and green = 7, which, when added together, total 50. "
Kirby,
Tuesday, July 9, 2024
"35 Red, 8 Blue, 7 Green.If you pick one at a time there are 6 ways to get one of each - RBG, RGB, BRG, BGR, GRB, GBR. The odds of any one of these scenarios is RxBxG/(50x49x48). So the odds you hit one of these scenarios is 6xRxBxG/(50x49x48) = 1/10. Simplifying you get RxBxG = 1960. You also know that R + B + G = 50. From there I looked up the prime factors of 1960 and tinkered with combining them until I found 3 that added up to 50. Assigned the order based on the questions saying more reds than blues and more blues than greens."
Alfonso Rodríguez, Mexico
Monday, August 5, 2024
"Amazing explanation about the earth´s curvature. I had never really understood this calculation until I followed this explanation."