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Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 4, November 2017

2017-10-26

What are the ages of the children?

Andy's three children
Find out the ages of the three children!

Andy and Jan are childhood friends, and met again as adults to catch up on their lives. “Don't you have three children?” Jan asks. “How old are they now?” “The product of their years is 36,” Andy answers, “and the sum of their years is your birthday.”

“Hmm, that is not enough information for me,” Jan replies. Andy counters with “Oh, of course, you're right. I forgot to mention that my oldest son has blonde hair.”

How old are Andy's three children?

Tips:

  • Only eight combinations have the product 36
  • Each month has a maximum of 31 days

Solution

  1. All three children must be at least one year old—otherwise the product of their years is zero.
  2. List all conceivable age combinations, and the sum of the years.

Age child one: 1 Age child two: 1 Age son: 36  Sum of the years: 38 
Age child one: 1 Age child two: 2 Age son: 18  Sum of the years: 21 
Age child one: 1 Age child two: 3 Age son: 12  Sum of the years: 16 
Age child one: 1 Age child two: 4 Age son: 9  Sum of the years: 14 
Age child one: 1 Age child two: 6  Age son: 6 Sum of the years: 13 
Age child one: 2 Age child two: 2 Age son: 9 Sum of the years: 13
Age child one: 2 Age child two: 3 Age son: 6  Sum of the years: 11 
Age child one: 3 Age child two: 3 Age son: 4  Sum of the years: 10 

3. The first combination, 1/1/36, is not possible because there is no date 38.

4. Although he knows his birthday, Jan did not know how old the children are. As a result, there must be at least two age combinations for this date.

5. So only 13 comes into question as it occurs twice (1+6+6 and 2+2+9).

6. Now the reference to the hair of the eldest son is decisive. Especially, there is an oldest son.

7. Only in the combination of 2/2/9 there is an oldest son, in 1/6/6 the two oldest children are the same age. The solution must be 2/2/9.


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