What are the ages of the 3 puppies ? – Funny Logical Questions

Question:

The following is a conversation between Dog and Fox while walking back home.

Dog: I have 3 puppies. Assuming that their ages are whole numbers,
         the product of their ages is 288, and the sum of their ages is your house number.

Fox: Of course I know my house number, but I still don’t know their ages.

Dog: Oh, I forgot to tell you that two of my youngest puppies have the same age.

Fox: Oh, now I know their ages.

What are the ages of the 3 puppies ?

[ Try your Best before Scroll down for the answer  ]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Funny Logical Questions and Answer :

The age of the 3 puppies are 4, 4, and 18.

Let’s work out how the answer is derived.

From the Dog’s 1st statement, we know that

• The product of the 3 puppies ages is 288
• The ages are whole numbers
• The sum of their ages is the Fox’s house number

With the above information,we list out all distinct possibilities such
that the product of the 3 ages (whole numbers) will give us 288:

1, 1, 288   [sum: 290]
1, 2, 144   [sum: 147]
1, 3, 96     [sum: 100]
1, 4, 72     [sum: 77]
1, 6, 48     [sum: 55]
1, 8, 36     [sum: 45]
1, 9, 32     [sum: 42]
1, 12, 24   [sum: 37]
1, 16, 18   [sum: 35]

2, 2, 72     [sum: 76]
2, 3, 48     [sum: 53]
2, 4, 36     [sum: 42]
2, 6, 24     [sum: 32]
2, 8, 18     [sum: 28]
2, 9, 16     [sum: 27]
2, 12, 12   [sum: 26]

3, 3, 32     [sum: 38]
3, 4, 24      [sum: 31]
3, 6, 16      [sum: 25]
3, 8, 12      [sum: 23]

4, 4, 18     [sum: 26]
4, 6, 12      [sum: 22]
4, 8, 9        [sum: 21]

6, 6, 8        [sum: 20]

From the above, there are quite a handful of possibilities where the
product of the 3 ages equals 288.

Hence, we need more clue from the Dog,

“Dog: Oh, I forgot to tell you that two of my youngest puppies have the same age.”

Great, now we can narrow down the possibilities to just 5 possible answers (in bold),
so how do we know which is correct ?

Remember the Fox’s remark
“Fox: Of course I know my house number, but I still don’t know their ages.”

This means that with his house number, there are more than than 1 possibility and hence
the Fox is unable to determine exactly the 3 ages.

Of the 5 possible answers (in bold),

1, 1, 288   [sum: 290]
2, 2, 72     [sum: 76]
3, 3, 32     [sum: 38]
4, 4, 18     [sum: 26]
6, 6, 8       [sum: 20]

Only the sum of 4, 4, 18 is the same as 2, 12, 12. The sum of the other 4 possibilities
are unique thus the age of the 3 puppies are 4, 4 and 18.

 

Scroll down if you want to solve more Funny Logical Questions…