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Tue 5 May, 2009 07:46 pm
A veterinarian approaches a house and asks the woman who opens the door: "How many cats do you have and what are their ages?
Woman: " I have 3 cats, the product of their ages is 36 and the sum of their ages is equal to the house next door."
The veterinarian walks next door, comes back and says, " I need more information."
The woman replies, " I have to go, my oldest cat is hungry and scratching the door upstairs."
Veterinarian: "Thank you, I now have everything I need."
What are the ages of the 3 cats?
@ajettin,
Product means to multiply, so divide 36 by 3 which equals 12. 12 x 3 = 36 (which would be the product) and the sum of all their ages 12 +12+12 = 36 is still 36.
Since she said "oldest", I assume she has a young cat , then a cat "older" than this cat, and then the "oldest" cat.
That is, cats of three different ages.
the possible combinations to arrive at 36:
2 x 2 x 9
3 x 3 x 4
2 x 3 x 6
The last combination is correct (three different numbers).
The ages of her cats are 2, 3, and 6.
Her house next door is no. 11.
Now please tell me if this is correct.
@sakhi,
You could also have
1 x 2 x 18
1 x 3 x 12
1 x 4 x 9
or even
1 x 1 x 36
just to add to the confusion. I've no idea which one is correct or why.
@lmur,
Or 1, 6 months and 72. Dang, that's one old cat.
@lmur,
ooopppss. You are right. I forgot about 1...
we can leave out 1 x 2 x 18....and may be even 1 x 3 x 12 because a cat usually lives upto 13 or maximum of 15 yrs...And if the cat is so old he may not have the strength to go upstairs and scratch the door...
that still leaves us with 1 x 4 x 9.....
@sakhi,
oh he comes back after seeing the door number and asks for more info.
Which means that two or more of the combinations have the same sum? but no..they all have different sums...
?
OK, here's the answer. The sums of their ages are each different and unique, except for 2, 2, and 9 or 1,6, and 6, both of which total 13. If it were any of the other possibel sums, each of which is only possible with one set of ages, he would know immediately which set of ages it was. Since he couldn't tell which of the possible sets it was, the house next door had to be number 13. When she said she had an oldest cat, it ruled out the possibility of 1,6, and 6. lleaving only 2,2, and 9.
@sakhi,
the riddle has been known to be more elegantly expressed
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