```Question 129610
During a recent cesus, a man was being interviewedby the census taker. When asked, he told the census taker that he had 3 children. When asked their ages the man replied, "The product of their ages is 72.
<pre>
So their ages are one of these

1,1,72
1,2,36
1,3,24
1,4,18
1,6,12
1,8,9
2,2,18
2,3,12
2,4,9
2,6,6
3,3,8
3,4,6

I know that the first three cases are ridiculous because children can't
be 24, 36 or 72.  But this just shows that the problem didn't have to say
they were children.  They could have just been any three people that live
in the house with them.
</pre>
The sum of their ages is the same as my house number."
The census taker ran to the front door, looked at the house
number and returned saying "I still cant tell!"
<pre>
So we find all the sums:

1+1+72 = 74
1+2+36 = 39
1+3+24 = 28
1+4+18 = 23
1+6+12 = 19
1+8+9 = 18
2+2+18 = 22
2+3+12 = 17
2+4+9 = 15
2+6+6 = 14
3+3+8 = 14
3+4+6 = 13

So we see from the list he could have told their ages if
the sum of their ages (and therefore the house number) had been
anything other than 14 because 14 is the only sum that occurs
more than once in the list.  So he has narrowed it down
to two possibilities:

2, 6, and 6
3, 3, and 8

an OLDER set of twins, and a YOUNGER set of twins.
</pre>
The man replied, Oh that's right! I forgot to tell you the oldest one likes chocolate pudding."
<pre>
Well, the chocolate pudding had nothing to do with it. :-)  But
the fact that there is an OLDEST one does. It rules out the case
of their ages being 2, 6, and 6 for then the oldest two would be
twins and neither would be the OLDEST, so there couldn't have been
an OLDEST.

So he now knows that they are 3, 3, and 8.

Edwin</pre>
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