Results of Zeno's Problem Challenge #22
Many conflicting results were submitted to this challenge. One in paticular, relates to the heart of the matter, I suspect. Troy Wiiliamson writes:
comments: Maggie's nephews are 2, 2, and 9 years old, and her
number is 13.
Unfortunately, this cannot be known for certain. There is an
assumption involved in arriving at this solution (which is the
only solution possible, based upon the information given).
The first bit of information allows us to list the possible
ages of Maggie's nephews. Assuming that the three ages are
all given in whole numbers (as we must), there are only eight
combinations which would yeild a product of 36:
1 1 36 1 6 6
1 2 18 2 2 9
1 3 12 2 3 6
1 4 9 3 3 4
The second piece of information, that the sum of their ages
is the same as Maggie's house number, adds a fourth column
of information to our data:
1 + 1 + 36 = 38 1 + 6 + 6 = 13
1 + 2 + 18 = 21 2 + 2 + 9 = 13
1 + 3 + 12 = 16 2 + 3 + 6 = 11
1 + 4 + 9 = 14 3 + 3 + 4 = 10
At this point, we still have eight possibilities for the ages
of Maggie's three nephews.
Then a third piece of information is given: that Maggie has
an oldest nephew. The only way that this could provide an
answer to the dilemma is if this were enough information to
distinguish between two (or more) possibilities. This does
occur in the case where Maggie's house number is 13. In that
instance, the nephews could be 2, 2, and 9 years old, or they
could be 1, 6, and 6 years old. But if they are 1, 6, and 6,
then there is not a single oldest nephew. Thus, the ages
must be 2, 2, and 9, with a house number of 13.
As stated, however, this is an assumption. The only way that
the information Maggie offered can provide an answer is if
we approach the problem with the assumption that the information
offered does, in fact, provide a solution. Only then will
the third piece of information single out a solution from
among the eight possibilities.
But this is clearly an assumption, and a pretty big one.
Maggie's nephews could be 1, 1, and 36; they could be 1, 2,
and 18; they could be 1, 3, and 12; they could be 1, 4, and
9; they could be 2, 3, and 6; or they could be 3, 3, and 4.
Any of these possibilities satisfy the information which
Maggie provided. This problem suffers the problem of not
having a precise solution.
A Zeno's customer is talking
with Maggie one evening about her family, when Maggie decides to have a little fun. They
have the following conversation: