The Famous Pudding Problem?

Question

I am really stumped at this problem. I tried Googling it and Wikipeding it but no luck. Any help? Please include a reference.
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The host of a party turned to a guest and said, "I have three daughters and I will tell you ow old they are. The product of their ages is 72. The sum of their ages are 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 chocolate pudding." The guest then announced the ages of the three girls.

What are the ages of the three daughters? (Hint: All the ages are whole numbers)
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HELP PLEASE??

Answer 1

For the guest to need more information, and for sufficient information to be that there WAS an oldest daughter, the guest must have had two answers both with the same total, but with the two oldest daughters being the same age in one answer. Then the chocolate pudding makes that answer wrong, and the other answer correct.

By searching, we find that it is impossible for the youngest daughter to have an integer age if the two oldest daughters are more than 6, or less than 6, therefore the wrong answer is (6, 6, 2) totalling 14, and the right answer is (8, 3, 3) also totalling 14, because by searching there no other set of three integers totalling 14 with a product of 72.

Answer 2

I won't do all the details but I can tell you how to do it yourself. Figure out all the possible age combinations that when multiplied gives 72.
Then figure out the sum of these ages.
One of the sums will repeat for two different age combinations. Since the guest was unable to figure out their ages when he knew the sum, their sum must be one of the repeating ones. Otherwise he'd know their ages. When the host says "the oldest..." we know that there IS an oldest. In other words, we know that the two oldest children don't have the same age. This should eliminate one of the repeated sums as a possibility. The other repeated sum is then the correct combination of ages.

Answer 3

the 1st time I observed this question posed here, I even though it became no longer a severe question. I actual have discovered. i'm hoping that's a great recipe: a million/3 cup (84g) butter a million/3 cup (84g) white sugar 2 eggs a million½ cups (168g) self elevating flour a million tsp (5ml) baking powder Pinch of salt a million/3 cup (80 5 ml) milk a million tbsp (15 ml) water a million/2 cup (112g) sultana raisins Cream jointly the butter and the sugar, formerly progressively including the eggs, jointly as beating. heavily upload the flour in small quantities alongside with the baking powder and salt. Beat interior the water accompanied by way of milk to get a soft creamy consistency - regulate parts of liquid for this reason. Stir interior the sultana raisins. circulate the aggregate to a greased pudding bowl, approximately 2 pint means. hide with double layer of waxed paper tied with string around the exterior of the bowl and place in a great Dutch oven or comparable pot with adequate water to realize 0.5 way up the outdoors of the bowl. Simmer for 2 - 2½ hours, coated.