The Neighbour Problem
"Oh my goodness! Your 3 children are sooooo cute!" the new neighbour said as she looked at Mrs Margaret's family photo. "What are their ages?
" " Mrs Margaret said with a glint in her eyes, "The product of my children's ages is 40, and the sum of my children's ages is the same as your door house number!"
The new neighbour thought about it and said sadly: "I still do not know your children's ages!"
Mrs Margaret then said, "3 years ago, my son was 4 years old!"
The new neighbour promptly said, "That is impossible!"
Find the children's ages, by using logical thinking.
Note: This question is difficult, but please try not to guess!
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1 solution
After going through the factors of 40, only two remaining possibilities are left, (2, 2, 10) and (1, 5, 8), which sum to 14.
Mrs Margaret said that 3 years ago, her son was 4 years old. That would mean in the present, her son would have to be 7 years old.
But 7 is not a factor of 40.
It starts to seem that Mrs Margaret has lied in her statements, but wait!!
Why must the son's age now be 7?!
It could be possible that the son's birthday is on 29th Feb!
Thinking about this unique assumption, the solution to this problem has become much clearer!
Between 3 years ago and in the present, there are a total of 4 years.
So either the son's age now is:
still 4, as not all 4-year intervals have a leap year in it
8, as there was a leap year in between the 4-year interval
Looking back at the two possibilities, none of them has 4 in it, but one of them has an 8! , which is (1, 5, 8)
Hence, the answer is 1, 5, 8.