What Ages Solve the Postmen's Riddle?

[NateTG]

Be happy it wasn't "My youngest son has red hair"

Then the choices would be:
36:
2,2,9
1,6,6

40:
2,2,10
1,5,8

or

90:
3,3,10
2,5,9

 

[Brennen]

why couldn't you have 2 children of the same age who weren't twins? they could b 3, 3, 10 with one of the 3 year olds being older than the other. even if they are twins, one of them would still be older, and therefore the middle child.

 

[Gokul43201]

Unless the postman worked in Utah, this would be highly unlikely. I'll let the biology folks tell us the least time between successive births (I know there are several factors involved, including how long you breast-feed)...but I'm sure that 2 births from one woman, less than a year apart is virtually unheard of.

Or he could always divorce a pregnant wife; re-marry and make his new wife pregnant in short order...

Or there could be illegitimate children...

Clearly, we're nitpicking and getting beyond the intended realm of the puzzle.

 

[TENYEARS]

You really tripped them up with this one.

 

[PureEnergy]

I don't know how rare it is, but I'm 10 months older than my younger brother.

 

[NateTG]

why couldn't you have 2 children of the same age who weren't twins? they could b 3, 3, 10 with one of the 3 year olds being older than the other. even if they are twins, one of them would still be older, and therefore the middle child.

Well, while you're at it, why don't we allow non-integer ages. That way there's an infinite number of possible combinations.

In practice, there is almost always an older twin and a younger twin, since they don't come out at the same time, but a few minutes apart.

 

[Averagesupernova]

I grew up with 2 kids that are 11 1/2 months apart.

 

[ExtravagantDreams]

not to mention that a 90 year old man probably wouldn't have kids that younge.
Great problem though

 

[Adelaine]

Be happy it wasn't "My youngest son has red hair"

Then the choices would be:
36:
2,2,9
1,6,6

40:
2,2,10
1,5,8

or

90:
3,3,10
2,5,9

Speaking of a postman who's 36, is it not also possible that the children are 1, 3, and 9? This still satisfies all the requirements of the original problem, it seems to me.

 

[Gokul43201]

Speaking of a postman who's 36, is it not also possible that the children are 1, 3, and 9?

1*3*9=27

 

[davee123]

For anyone interested, I ran a script on all the possible solutions for this problem assuming that:

1) the product is <= 1000
2) the numbers ("ages" in this case) are positive, whole numbers

Solutions assuming there's a "middle child":
1,5,8
2,5,9
3,6,8
1,13,18
1,12,21
1,11,27
2,10,16
5,8,9
2,9,24
3,10,15
1,10,45
3,8,27
3,9,25
6,8,15
4,10,18
1,25,32
1,24,34
2,17,25
1,22,40
5,9,20
2,9,50

If the problem specified "youngest child", you would get:
1,6,6
1,5,8
2,6,6
2,5,9
3,6,8
1,15,15
1,13,18
1,12,21
2,12,12
1,11,27
2,10,16
5,8,9
2,9,24
3,10,15
1,10,45
4,12,12
3,9,25
4,10,18
1,28,28
2,20,20
1,25,32
1,24,34
2,17,25
1,22,40
3,18,18

"Oldest child":
2,2,9
3,3,8
3,3,25
4,4,18
6,6,16
3,8,27
6,8,15
4,4,49
5,5,32
5,9,20
2,9,50
6,6,27

DaveE

 

[Office_Shredder]

If you really wanted to be fussy, since a house cannot have a fraction of a window, it also means that the ages of the sons must all be in integers (whole numbers) and not involve fractional ages.

What if more than one of them has a fractional age?

This part is just stupid