3 girls' age solution

Yesterday I posted a tricky question of mathematics and IQ.

One could answer only; but couldn't explain properly. So now I am providing the solution.

For simplicity I'm writing the question here:

Clue 1: The product of three girls' age is 36

Clue 2: Though I tell you sum of the ages, you can't find out their ages

Clue 3: The eldest girl has a dog

Now find out the ages of the three girls😊

If you want to find out the solution by yourself, stop the article here and try. Otherwise go through it.

Let's find out the solution:

step 1:

First clue was the product of ages is 36. So you have to find out in how many ways you can make 36 using 3 numbers.

I've written all the cases here. And so the solution is in this list.

step 2:

Now let's move to the second clue. It says though I tell you the sum of their ages, you can't find out them.

Whatever has been told, forget for a moment and get the sum for all the cases above:

Now think why you can't find out the ages though you know the sum.

Look at the photo again. Here the sums are 38, 21, 16, 14, 13, 13, 11, 10 right?

If I told you sum is 38, 21, 16, 14, 11, 10, you surely could tell what are the ages. But you can't because the solution contains a sum that is present here twice.

Yes so the sum is 13.

It means that the solution will be either (1, 6, 6) or (2, 2, 9).

step 3:

The third clue says that the eldest girl has a dog.

Now look at the triplets.

For (1, 6, 6) there is no eldest one. But for (2, 2, 9) here the eldest age is 9.

So, finally we get the solution and the ages of the girl's are 2, 2 and 9 years.

Special thanks to @Ashma for this great support and cordial help to everyone.

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