Thanksgiving Day
My three nieces are coming to visit for Thanksgiving. My neighbor came over
and wanted to know how old they are. I told her that the product of their
ages is 72.
"That's not enough information for me to figure out how old they are," she
complained.
I offered that the sum of their ages is my street address.
"But that's still not enough information."
After a moment's thought, I added that my eldest niece loves pumpkin pie.
She then knew how old the girls are,...but was afraid to ask their names.
How old are my nieces?
Answer
Since the product of the ages is 72, the ages must be
among the factors of 72. This gives the following possibilitites.
| First Age |
Second Age |
Third Age |
Sum of Ages |
| 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 |
6 |
4 |
13 |
Since knowing the sum of the ages did not uniquely identify
the ages of the nieces, you must conclude that the sum of the ages is 14,
as no other sum appears more than once. The final information about
the likes of the eldest niece tells the neighbor that there is an
eldest niece, which would not be the case if the nieces ages were 2, 6
and 6. The only remaining possibility is that the nieces are 3, 3
and 8, and that incidentally, the house number is 14.
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