Tuesday, September 20, 2011

A riddle- Mada

A census taker interviews a woman in a house.
"Who lives here?" he asks.
"My husband and I and my three daughters," she replies.
"What are the ages of your daughters?"
"The product of their ages is 36 and the sum of their ages is the house number."
The census taker looks at the house number, thinks, and says,
"You haven't given me enough information to determine their ages."
"Oh, you're right," she replies, "Let me also say that my eldest daughter is asleep upstairs."
"Ah! Thank you very much!"

What are the ages of the daughters?

This problem is out of my Fundamental Mathematics book. It is not one I had to do for homework but it is almost exactly like one I had to do for homework. It is not impossible and I think these kind of logic problems are extremely fun so I thought I'd share it with Classic Brian. I would really really love if anyone tried it. Also I would like to take a moment to say that you have no idea what you're getting into when you pick a major at 17. I just spent 4 hours on one math assignment. LoVe It!!! <3!

P.S For anyone who cares, I will post the answer to this in a comment next Tuesday.

16 comments:

  1. I wasted 5 minutes thinking about this and I will not waste any more. I will, however, probably call you later and demand to know the answer.

    - Conor

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  2. Brian, I'm impressed. I didn't realize you were good at logic now that you are a cinema studies major. That's the answer by the way, for any doubters out there.

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  3. I HATE THIS SO MUCH I NEED TO KNOW WHY THAT ANSWER IS THE CORRECT ONE.

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  4. First look at all the ways to get 36 by multiplying 3 integers. The man could not figure out the answer just from the product and the sum, meaning that there are at least two options that produce the same sum.

    (2, 2, 9) and (1, 6, 6)

    Because she said her eldest daughter is asleep, we know that there is an oldest daughter, and in the second option, there would be two "oldest daughters". Therefore, it has to be (2, 2, 9).

    Duhhhhhh

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  5. Oh yeah. I guess the census taker would know the house number...

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  6. Doesn't 2,3,6 also work?

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  7. No, because the sum, 11, is unique among the sets of numbers that produce 30, so the census taker would have been able to figure it out from just the house number and the product.

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  8. I obviously meant 36 in that last comment, not 30.

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  9. Is there a algebraic way of solving this problem, instead of guessing because any three integers that multiply to get 36 are possible and since we don't know the house number they could work.

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