What are the ages of the three sons?

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  • Thread starter Ackbach
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    2015
In summary, the ages of the three sons are influenced by a combination of genetic and environmental factors. There is no specific formula for determining their ages, as each individual's genetic makeup and environment is unique. While it is not possible to accurately predict their exact ages, scientists can use statistical analysis and population studies to estimate the average age range for individuals with similar factors. The ages of the three sons may have some correlation with each other, but other factors also play a role. Scientists study their ages by conducting research, analyzing data, and using statistical analysis and modeling.
  • #1
Ackbach
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Here is this week's POTW:

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Two men meet on the street. They haven't seen each other for many years. They talk about various things, and then after some time one of them says: "Since you're a professor in mathematics, I'd like to give you a problem to solve. You know, today's a very special day for me: all three of my sons celebrate their birthday this very day! So, can you tell me how old each of them is?"

"Sure," answers the mathematician, "but you'll have to tell me something about them."

"OK, I'll give you some hints," replies the father of the three sons, "The product of the ages of my sons is 36."

"That's fine," says the mathematician, "but I'll need more than just this."

"The sum of their ages is equal to the number of windows in that building," says the father pointing at a structure next to them.

The mathematician thinks for some time and replies, "Still, I need an additional hint to solve your puzzle."

"My oldest son has blue eyes," says the other man.

"Oh, this is sufficient!" exclaims the mathematician, and he gives the father the correct answer: the ages of his three sons.

What are the ages of the three sons?

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  • #2
This problem is on page 9 of How to Solve It: Modern Heuristics, by Michalewicz and Fogel.

Kiwi had the right idea in his partial solution, so I will simply post his solution with my completion thrown in:

The sons are 2, 2 and 9.

Since the product of their ages come to 36 their ages are one of the following:

1,1,36 (sum = 38)
1,2,18 (sum = 21)
1,3,12 (sum = 16)
1,4,9 (sum = 14)
1,6,6 (sum = 13)
2,2,9 (sum = 13)
2,3,6 (sum = 11)
3,3,4 (sum = 10)

The building has 13 windows because if it has any other number of windows, then the professor would have sufficient information to answer the problem without the last clue.

The last clue tells us that the age of the oldest son is distinct. So having twins aged 6 is not a possibility. Therefore, the man has twins aged 2 and a 9 year old with blue eyes.
 

Related to What are the ages of the three sons?

1. What factors determine the ages of the three sons?

The ages of the three sons are determined by a combination of genetic factors and environmental factors. Genetic factors include the parents' age, health, and genetic predispositions. Environmental factors include nutrition, exposure to toxins, and lifestyle choices.

2. Is there a specific formula for determining the ages of the three sons?

No, there is no specific formula for determining the ages of the three sons. Each individual's genetic makeup and environment are unique, making it difficult to predict the exact ages of the three sons.

3. Can the ages of the three sons be accurately predicted?

While it is not possible to accurately predict the exact ages of the three sons, scientists can use statistical analysis and population studies to estimate the average age range for individuals with similar genetic and environmental factors.

4. Do the ages of the three sons have any correlation with each other?

Yes, the ages of the three sons may have some correlation with each other. For example, if the parents are older, there is a higher likelihood that the sons will also be older. However, other factors such as genetics and lifestyle choices can also play a role in the individual ages of the three sons.

5. How do scientists study the ages of the three sons?

Scientists study the ages of the three sons by conducting research and analyzing data from various sources such as population studies, medical records, and genetic studies. They also use statistical analysis and modeling to better understand the factors that influence the ages of individuals.

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