The Proof in the Pudding
The host at a party turned to a guest and said, "I have three daughters and I will tell you how old they are. The product of their ages is 72. The sum of their ages is my house number. How old is each?" The guest rushed to the door, looked at the house number, and informed the host that he needed more information. The host then added, "The oldest likes strawberry pudding." The guest then announced the ages of the three girls. What are the ages of the three daughters?
Here are two possible answers from Phil
72 years old, 1 year old, 1 year old. The elderly daughter has lost all her teeth, so she likes strawberry pudding, which is easier for her to eat than say, nuts or steaks.
So the house number must have been 72 + 1 + 1 = 74. This is the number that the guest saw when he rushed out to look.
But waiddaminute... Why did he then say that he needed more information? Knowing that the product of the three ages is 72 and their sum is 74 is enough to find the three ages. There is something that I don't understand here.
9 years old, 4 years old, 2 years old. Strawberry pudding is an acquired taste, like good cheese or jazz music. You may love it by the time you're 9, but 4 year old kids are certainely too young to really appreciate it, and 2 year old babies just gulp wathever comes their way.
So the house number must have been 9 + 4 + 2 = 15. This is the number that the guest saw when he rushed out to look.
But now hold on... Why did he then say that he needed more information? Knowing that the sum of the three ages is 15 and their product is 72 is enough to find the three ages. There is something that I'm not quite getting here.