Brain Teaser?

Question

I asked this earlier, but no one seemed to be able to solve it so I will ask it again. I got it from the website http://www.mindchallenger.com

Answers are on the site.

This can be a little tricky and there is a simple way to solve it. All the information needed is here for those of you who think it is "unsolveable." The beauty of this puzzle is it appears unsolveable.

Tom and Sally are neighbors and Sally say to Tom, "I want you to guess the ages of my three children. The product of their ages is 36 and the sum of their ages equal your house number." Tom thinks for a minute and says, "I can't solve it. I need another clue." Sally says, "OK. My eldest daughter is doing the laundry." Tom says, "I know their ages." Do you?

Answer 1

hmmm...
Let's try this...
Tom obviously knows his house number, and with simple algebra, he can do this:

xyz = 36
x + y + z = house number

the possible values are:
1, 1, 36 (highly implausible, I sure hope that a 36-year old isn't still at home...) adding up to 38
1, 2, 18 - adding up to 20
1, 3, 12 - adding up to 15
1, 4, 9 - adding up to 14
1, 6, 6 - adding up to 13
2, 2, 9 - adding up to 13
2, 3, 6 - adding up to 11
3, 3, 4 - adding up to 10
0.08, 72, 6.25 - adding up to 78.33 (ok... not so much... as awesome as it would be to have a house number with a decimal point in it)

The only way he'd need another clue would be if there two or more values x, y, and z that would lead to the same house number. This is the case for 6, 6, and 1 as well as 2, 2, and 9, as they both add up to 13, which is his house number. He gets the number after the "eldest daughter" clue, letting him know that there is in fact an "eldest" daughter and it is 2, 2, and 9 rather than 1, 6, and 6, as the latter would have twin eldest daughters, which wouldn't have worked in her phrasing.

So yes, the answer is 2, 2, and 9.

Great brain teaser, I just took a victory lap around the house after getting it.

Answer 2

That's a cool brain teaser. It really does seem unsolvable. I had to read it a few times to give it a shot. Well since the product of their ages is equal to 36, then we know that two random variables (x)(y)(a)=36. let x= first daughter, let y= second daughter, let a= third daughter.

hmmm....so her daughter is doing the laundry? well, what age does a girl do that laundry all on her own? 18,17,16,15,14,13,12,11,10.

let's rule out 17,16,15,14,13,11 and 10. according to conventional mathematics, this is just not possible.

that leaves 18 or 12 for the eldest daughter. let's plug this into the system of equations.

1) (x)(y)(18) = 36
2) (x)(y)(12) = 36

then (x)(y)= 2 or (x)(y)=3

for the first equation the only possible values are 1 and 2, and for the second equation 1 and 3.

since you mention it, house number? either, 16 or 21
wow, confusing from here. i got it! no, sorry.

umm, i believe it's 18, 1 and 2. OK i may be wrong but i tried, at least i get credit for that.

lol

Nice Problem.

Answer 3

They are 9, 2, and 2.

The product of 9, 2, and 2 is 36.
His house number must be something where you can add up factors of 36 in several different ways to get it.

18 + 2 + 1 = 21 would be obvious. Likewise 6, 3, 2 (11), 12, 3, 1(16), and 4, 3, 3 (10). However, there are three different ways to get a sum of 13 - (9, 4, 1), (9, 2, 2), and (6, 6, 1).

The statement "my eldest daughter is doing laundry" means that there's one older one and also makes it clear. It's not 6, 6, 1. I think her children are 9, 2, and 2.

Answer 4

Sally's kids are 2, 2, and 9.

Tom needs another clue because there are two possible solutions to x*y*z = 36 that have equal sums. The possible sets are {2,2,9} and {1,6,6}.

When Sally confirms that she has an eldest daughter, this indicates that the twins are the younger kids.

Answer 5

A * B * C = 36

A + B + C = Integer (house number)

possible combinations:

(12, 3, 1)
(9,4,1)
(6, 6, 1)
(6, 3, 2)
(4,3,3)

Only the first one allows for the child to be old enough to do the laundry:
A = 12
B = 3
C = 1

Update:
Answer depends on the judgement of how old should be a child to be able to do the laundry.
Conservative answer is 12. However, some people obviously think that 9 is old enough for this chore.

Answer 6

the correct answer is 9, 2, 2, as stated above.

this puzzle is called metapuzzle.

Answer 7

oops
1,3,12

A house has four digit number
so it's 1312
otherwise it would be a three digit number (which is wrong)
and..
12 is old enough to do laundry.
One age must be older than 9
12 is the lowest pluasible integer.
36/12=3
the products of the other two must be 3
1*3=3
so
1,3,12 :)

I had to solve a similar one before.

Answer 8

18, 2, 1
an 18 year old would do laundry, but there are probably other answers. House number is irrelevant

Answer 9

difficult stuff. lookup from search engines like google. this can assist!

Answer 10

Wow, not only did it tease my brain, but it insulted it and spat on it's mother. u ppl r too smart.