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### The 3 Children Problem: Answer

Last week I gave you all a teaser question to demonstrate the way that some problems can seem impossible (see “Physics on Tour: Coloma Convent Girls’ School, Croydon”). In physics, we learn to deal with these problems by ignoring that instinctive negativity, and giving it a go with the information we have. We also learn that the useful information is not always obviously so.

In the puzzle, a man visits his friend and wants to know the ages of their 3 children. He is told that if you multiply their ages, you get 36. This is our first piece of useful information. We can write down the multiples of 36, just as the man can.

The next clue is that the ages add to make the number on the front door. This is where people usually get stumped first. Of course, we don’t have this information. However, the man does, so that doesn’t matter. What matters is the next piece of information: he can’t do the problem.

If you stick with it this far you will have in front of you several ways to make 36 from multiplying 3 numbers. By adding all of these numbers (despite the fact that you don’t know which number is correct) you will find that there are two solutions which give the same result: 13. This must be the number on the front door, because that is the only way that the man is left unable to solve the problem. So now we know a little more: the ages are either:

9, 2 and 2

Or:

6, 6 and 1

Now we need to have patience and stick with the problem a little longer. The man goes back for one more clue, and we are confused once again as we find out that the clue “My eldest is a boy” is enough for the man to get the correct answer.

Of course, the sex of the eldest child is of course irrelevant. However, the fact that there is an eldest led the man to conclude that the ages were 9, 2 and 2.

It has been pointed out to me in a comment that it is just possible for two children to be born within a year of each other, and in this case, at the right time of year, there could still be an “eldest” whereas the ages would still be the same. A very clever point! 😀 Luckily though, it was not us who made the assumption that this was not the case – it was the man, and we know the man guessed the ages correctly, so it doesn’t matter that he might have got it wrong.

Thanks to everyone for your comments. I am sorry that some of them took a little longer to approve (technical difficulties on my part!)

Well done to those of you who got it right!