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## Age of Three Kids 5

One day, a guy from census come into a house. When he rings the bell, a lady comes out. He then asks how many people lives in her house, and their age. And then she says:

I am 45 years old. I have three children. If you multiply their ages, the result is 36. If you sum their ages, the result is just like the neighbour's house number.

He then walks to the neighbour's house, and then he comes back. He says:

Ma'am, I STILL can't determine your children's ages. I need more clue.

She sighed, and then she says:

The oldest child is sleeping upstairs.

He then replies:

Now I know. Thanks, Ma'am!

What are her children's ages? What is the neighbour's house number?

See Explanation

List all the possibilities, sum them:

1+1+36=38

1+2+18=21

1+3+12=16

1+4+9=14

1+6+6=13

2+2+9=13

2+3+6=11

3+3+4=10

From all the possibilities, there are two possibilities which sum is the same. If the neighbour's house number is not 13, the census should have known their age. But he can't determine which age, so it must be 13.

And then the lady said that the oldest child was sleeping upstairs. This statement means that there is an oldest child. So the only possibility remaining is 2,2 and 9.

Therefore, her children's ages is 2 y/o, 2 y/o (probably twins), and 9 y/o.

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