What is the Mystery of the Three Sons' Ages?

  • Context: High School 
  • Thread starter Thread starter Gypsy
  • Start date Start date
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Discussion Overview

The discussion revolves around a puzzle involving the ages of three sons, where participants analyze the clues provided about the product and sum of their ages, as well as the implication of having an "oldest" child. The scope includes logical reasoning and mathematical exploration.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests the ages could be 2, 2, and 9, noting that there are six possible combinations with a product of 36, but only two combinations yield ambiguous sums.
  • Another participant proposes the ages as 2, 3, and 6, questioning what other integer triplet with a product of 36 has a sum of 11 and equal largest members.
  • Some participants highlight the significance of the clue about the oldest child, with one humorously referring to it as a "red herring."
  • There is mention of the alternative combination of 1, 6, and 6, which would not have a distinct oldest child, leading to ambiguity.

Areas of Agreement / Disagreement

Participants express differing views on the possible combinations of ages, with no consensus reached on a single solution. Multiple competing views remain regarding the correct ages of the sons.

Contextual Notes

The discussion does not resolve the ambiguity surrounding the sums and products of the ages, nor does it clarify the implications of the clues provided.

Gypsy
I thought this was a good one. All my friends who I've shown it to (except for one) haven't been able to solve it.

Many years from now, two men are sitting in the county park. The
following is part of their discussion:

Man 1: Yes, I'm married and have three fine sons.
Man 2: That's wonderful! How old are they?
MaN 1: Well, The product of their ages is equal to 36.
Man 2: Hmm. That doesn't tell me enough. Give me another clue.
Man 1: Ok, the sum of their ages is the number on that building
across the street.
Man 2: A ha! I've almost got the answer, but I still need another
clue.
Man 1: Very well. The oldest one has red hair.
Man 2: I've got it!
 
Mathematics news on Phys.org
in white:
2 2 9 [/color]
 
a nice puzzle

answer in white font 2, 2, and 9 ... there are 6 possible age combinations, only two give ambiguous sums of ages (2, 2, and 9; 1, 6, and 6) and it must be one of these or else the house number would have solved the problem in step 2; only 2, 2, and 9 gives a single 'oldest' child as the alternative (1, 6 and 6 has tiwn boys as oldest
 
Or simply 2, 3 and 6 years old.
 
I make it 9, 2 and 2
 
At first, that last clue seemed like something of a red hairing. :redface:
 
echoSwe said:
Or simply 2, 3 and 6 years old.
What other integer triplet with product 36 has sum 11 and also has the two largest members being equal to each other ?

Ha ha...a red hairing, indeed ! :smile:
 

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