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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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Chatham, NJ
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This page revised   August 3, 2004
 
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