Strawberry cake and house number

Number Theory Level pending

You want to know how old my three daughters are. The product of my three daughter's ages is 72. Since you can't find out how old they are, I will give you another clue. The sum of their ages is equal to our two-digit house number. You step outside and see the house number, but still you can't figure out their ages. Then I gave you another clue, the oldest one likes strawberry cakes. After hearing that, you already know their ages.

Now that you know their ages, give me the average of their ages.

round off to the nearest two decimal places

The answer is 4.67.

2 solutions

Jesse Nieminen
Aug 27, 2016

Let the ages be $a,b,c$ . Clearly they are all positive integers.
Since $abc = 72$ , we can list all possible unordered triples $\left(a,b,c\right)$ .
Now, $a + b + c = 14$ because $14$ is the only number which is the sum of the ages in at least $2$ distinct triples.
(There must be more than one possibility for the ages because knowing the sum and product of the ages is not enough information.)

Hence, the answer is $\boxed{4.67}$ .

Emmanuel John Baliwag
Oct 12, 2014

1st clue: Think of factors. Some of which are

{9, 4, 2}

{18, 2, 2}

{8, 3, 3}

{6, 6, 2}

{6, 3, 4}

{12, 3, 2}

There are many solutions, so you proceed to the next clue. It states that the 2-digit house number is the sum of the ages. You "saw" the house number in the problem, that means you know which is right.

9 + 4 + 2 = 15

18 + 2 + 2 = 22

8 + 3 + 3 = 14

6 + 6 + 2 = 14

6 + 3 + 4 = 13

12 + 3 + 2 = 17

Since you asked for another clue, that means you are unsure whether the answer is {6, 6, 2} or {8, 3, 3}.

Since the third clue states that his OLDEST daughter likes strawberry cakes, you know that there is an oldest child. Only one. Meaning {8, 3, 3} is the answer.

Proceeding to the problem's question 8 + 3 + 3 = 14. Getting the average, 14 / 3 = 4.67

You may think that the answer can also be {18. 2. 2} but take note, you will not ask for the third clue if you already know that the house number was 22. :)

Emmanuel John Baliwag - 6 years, 8 months ago

Strawberry cake and house number

The answer is 4.67.

2 solutions

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