Age Problem
A person has three daughters. The multiplication of their age is 36. But if we say the summation of their age you'll find it difficult cause you can have more than one set of possible answer. For your help we can give the characteristics of the girls. The eldest one likes dog very much while others hate it. Question is, what are the ages of three daughters? (Type the answers without any comma or gap and keep in mind that answer should have the biggest number at first then gradually smallers)
The answer is 922.
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1 solution
First condition is the multiplication of their age is 36. Now we see how we can make 36 by the multiplication of 3 positive integers.
3 6 ∗ 1 ∗ 1 = 3 6
1 8 ∗ 2 ∗ 1 = 3 6
1 2 ∗ 3 ∗ 1 = 3 6
9 ∗ 4 ∗ 1 = 3 6
9 ∗ 2 ∗ 2 = 3 6
6 ∗ 6 ∗ 1 = 3 6
6 ∗ 3 ∗ 2 = 3 6
Now the second condition, if we say the summation of their age you'll find it difficult cause you can have more than one set of possible answer. So we now we find the summation of those sets above.
3 6 + 1 + 1 = 3 8
1 8 + 2 + 1 = 2 1
1 2 + 3 + 1 = 1 6
9 + 4 + 1 = 1 4
9 + 2 + 2 = 1 3
6 + 6 + 1 = 1 3
6 + 3 + 2 = 1 1
So here it comes. We see there are two possible sets, which's summation are 13. Those are {9,2,2} and {6,6,1}. Any of these can be the answer. But the characteristics says the the "eldest" one likes dog and others hate it. Which means there's an eldest daughter which we can't find in {6,6,1}. But we can find an eldest one in {9,2,2}. So the set is {9,2,2} and answer is "922".
*PS: This was my first problem and I couldn't find anyway or codes to give alternative answers that's why I used Z -> A which means largest to smallest. If anyone used 292 or 229 they were equally correct. The answer should've been 922/229/292 but I said I couldn't find any code...