puzzle

crowl

Two people are talking to each other and one says to the other, 'I have 3 children, can you guess their ages'.
First he says 'The sum of their ages is 13'
Then he tells him 'The product of their ages is the same as your age'
Then he says 'The eldest child weighs 61lbs.'
At this point the second person correctly tells him the ages of the 3 children.

How old are the 3 children?

Note: This has a definate answer and is not a trick question.

Just interested to see if anyone can get this. The only other person I saw get it was 11 years old.

dave_eire

they are 2 2 and 9.

reasoning / spoiler:

there are 14 posibilites of their ages if they add up to 13:

1,1,11
1,2,10
1,3,9
1,4,8
1,5,7
1,6,6
2,2,9
2,3,8
2,4,7
2,5,6
3,3,7
3,4,6
3,5,5
4,4,5

'The product of their ages is the same as your age'


you say after the next "hint" "At this point the second person correctly" --> this means at this stage he still did not know, why?

well the product of more than one of the above must add up to his age.

1*1*11=11
1*2*10=20
1*3*9=27
1*4*8=32
1*5*7=35
1*6*6=36
2*2*9=36
2*3*8=48
2*4*7=56
2*5*6=60
3*3*7=63
3*4*6=72
3*5*5=75
4*4*5=80

so the guy must be 36 leaving 2 possible correct answers:

1,6,6
2,2,9

'The eldest child weighs 61lbs.' --> meaning there is an eldest child, therefor 1,6,6 con not be correct and 2,2,9 is the only possible answer.

is this right? yeah?

Sherifu

I think you're wrong Dave
Spoiler:
The key is the only other person to get it is 11, i.e. the second person is 11
This is the product of their ages.
This means the answer is 11,1,1

dave_eire

The only other person I saw get it was 11 years old.

really?!! if my answer is correct, must have been a bright 13 yr old, or am i just a bit... what was i saying?!

d

dave_eire

ahhh!

i was taking it that was just a btw. but i actually disagree

but if you take that after clue 1:

"First he says 'The sum of their ages is 13'"

he did NOT know the answer. and after clue 2:

"Then he tells him 'The product of their ages is the same as your age'"

he did not know the answer, if your answer is correct then he should have know now as the product of all the possible ages, 1*1*11 would be unique, therefore would have to be the answer.

i think the key is after he was told about the "eldest" child he got it:

Then he says 'The eldest child weighs 61lbs.'
At this point the second person correctly tells him the ages of the 3 children.

ONLY "at this point" --> meaning there must have been abiguity till now, and he now knows there is an eldest, hence it HAS to be 2, 2, 9.

or am i looking into this a bit too much!?!!?

:eek:

Sherifu

Maybe
Now im not sure Dave. Missed that subtle timing. Perhaps i'll google it and see what i get!

dave_eire

cool, let me know!!

crowl

yeh dave that looks right, well done

Sherifu

Well done Dave