Faites vos jeux messieurs, dames

[Jantje]

I'm not sure what to do with "The sum of their ages is the number of cars in my street."
Without this info I get to 1 4 9 or 1 3 12
Best regards
Jantje

[nickgammon]

I presume the fact that the youngest was ill rules out that the younger two are twins (then there wouldn't be a youngest).

I'm not sure about the cars in the street, except that maybe it makes the sum to be an integer.

[robtillaart]

I'm not sure what to do with "The sum of their ages is the number of cars in my street."
Without this info I get to 1 4 9 or 1 3 12
Best regards
Jantje

The trick is to get the information that can be derived from the sentences....

[Jantje]

Ok I missed one.
my bet : 1 2 18.
Jantje

[robtillaart]

The product of the ages = 36, that means the list of possible combinations is:

1 1 36
1 2 18
1 3 12
1 4 9
1 6 6
2 2 9
2 3 6
3 3 4

[nickgammon]

We need to know the name of his street and check how many cars are in it.

[radman]

Here is the answer to the original post.
'G' stands for Girl.
'B' stands for Boy.
'T' stands for Thinnest.
'N' stands for Not-thinnest.

If I just told you I have two children and asked what the odds were that they were both boys the answer would be 1:4 or 20%.
All the possible permutations of children being;

Code: [Select]


G G
G B
B G
B B


By telling you that one of my children is a boy I obviously increase the odds since the pair of girls is eliminated. At this point a lot of people go wrong because knowing I have one boy they just consider that the other child has to be either a boy or a girl so the odds must be 1:2 or 50% in fact they are 1:3 or 33% e.g.

Code: [Select]


G B
B G
B B


Now I confuse things by throwing in the information that the boy I mentioned is also my thinnest child. At first this appears to be totally redundant information but in fact something strange happens and it makes a big difference to the odds. Here is the complete table of permutations;

Code: [Select]


GN GN
GT GN
GN GT
GT GT
BN BN
BT BN
BN BT
BT BT
GN BT
BT GN
GT BT
BT GT
GN BN
BN GN
GT BN
BN GT


Now we can delete all invalid permutations that involve two girls or don't have one male child who is thinnest, this shows that the odds of me having two boy is in fact 1:2 or 50%

Code: [Select]


BT BN
BN BT
GN BT
BT GN


The strange bit though is that the odds have changed because there are now two rows containing two boys.

Truth tables are very powerful and help avoid mistakes in logic. Unfortunately they rapidly get very large and, as Nick wrote, you run out of margin.

[Simpson_Jr]

We need to know the name of his street and check how many cars are in it.

If you keep in mind it's a dad, there could be 73.5 cars in his street. 

[nickgammon]

Here is the complete table of permutations;

Code: [Select]


GN GN
GT GN
GN GT
GT GT
BN BN
BT BN
BN BT
BT BT
GN BT
BT GN
GT BT
BT GT
GN BN
BN GN
GT BN
BN GT


Hardly. You cannot have GN GN for example. They both can't be not thinnest. And you can't have GT GT. They both can't be thinnest. My solution (reply #22) was correct.

[radman]

Hardly. You cannot have GN GN for example.

I listed all the possible permutations (valid and invalid) then I said "Now we can delete all invalid permutations".

You got the right answer 50%, but this table from reply #22 is incorrect

Code: [Select]

TB G
TG B
TB B
TG G

You included TG G which is invalid as there are two girls, and you only included one permutation with two boys.

[robtillaart]

A hint ...

The product of the ages = 36, that means the list of possible combinations is:

1 1 36
1 2 18
1 3 12
1 4 9
1 6 6
2 2 9
2 3 6
3 3 4

(2) The sum of their ages is the number of cars in my street.
(3) And to determine their ages you must know that the youngest was ill recently.

3) states that even when you know the number of cars in my street, you still need extra information

...

[radman]

There has to be 'a' youngest so that seems to pin it down to;

Code: [Select]


1 2 18 sum 21
1 3 12 sum 16
1 4 9  sum 14
1 6 6  sum 13
2 3 6  sum 11


But I don see how "The sum of their ages is the number of cars in my street" comes into play.

[robtillaart]

OK,

(1) The product of the ages = 36
(2) The sum of their ages is the number of cars in my street.
(3)  And to determine their ages

Given the fact that I know the # cars in my street and I still say the first half of sentence 3, implicates that from the product and sum alone one cannot determine the ages.

1 1 36 sum 38
1 2 18 sum 21
1 3 12 sum 16
1 4 9 sum 14
1 6 6 sum 13
2 2 9 sum 13
2 3 6 sum 11
3 3 4 sum 10

given that sum and product is not enough to determine leaves only 2 options.

1 6 6 sum 13
2 2 9 sum 13

and the youngest was recently ill,  so ....

[radman]

Ah the light comes on - very clever.

[robtillaart]

I recall it took me quite some time too.
The trick is that you must not think from what you know , but from what the other person knows.