Question

Puzzle Patel was out looking for a new apartment to rent. The landlord asks him if he has any pets.
Patel: "Three cats"
Landlord: "How old are they?"
Patel: "The product of their ages is 72."
Landlord: "What kind of answer is that!? I need more information."
Patel: "Sorry, that must have been unclear. The sum of the ages of my pets is the same as your house number."
Landlord: "Still not enough information, As we have only 20 houses in this society."
Patel: "My oldest cat is called Gypsy and sum of letters and her age is related as perfect square"
Landlord: "Okay, cool. Now that I know their ages, you can have the house."
What is the sum of the ages of Puzzle Patel's pets?​

Answer 1

Given : Puzzle Patel was out looking for a new apartment to rent. The landlord asks him if he has any pets.

Patel: "Three cats"

Landlord: "How old are they?"

Patel: "The product of their ages is 72."

Landlord: "What kind of answer is that!? I need more information."

Patel: "Sorry, that must have been unclear. The sum of the ages of my pets is the same as your house number."

Landlord: "Still not enough information, As we have only 20 houses in this society."

Patel: "My oldest cat is called Gypsy and sum of letters and her age is related as perfect square"

Landlord: "Okay, cool. Now that I know their ages, you can have the house."

To Find : What is the sum of the ages of Puzzle Patel's pets?​

Solution:

a * b * c =  72

1 * 1 * 72 = 72               Sum = 74

1 * 2 * 36  = 72             Sum = 39

1 * 3 * 24  = 72            Sum = 28

1 * 4 * 18 = 72              Sum = 23

1 * 6 * 12  = 72              Sum = 19

1 * 8 * 9  = 72               Sum = 18

2 * 2 * 18  = 72            Sum = 22

2 * 3 * 12   = 72          Sum = 17

2 * 4 *  9   = 72           Sum  = 15

2 * 6 *  6  = 72             Sum = 14

3 * 3 *  8    = 72            Sum = 14

3 * 4 *  6  = 72            Sum = 13        

only sum 14 is not unique

Hence possible solution can be

2 , 6 , 6   or  3 , 3 , 8

other wise he would have known ages.

Now he says oldest cat is called Gypsy hence 6 , 6 not possible as then it would have been oldest  cats.

Hence   3 , 3 , 8  is only possible solution

also GYPSY  = 7 + 25 + 16 + 19 + 25 = 92

92 + 8 = 100  = 10²

Hence  Ages of cat are  3 , 3 , 8

and sum of ages = 14

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Answer 2

Solution :-

Let ages of three cats be a , b and c .(where c is oldest.)

given that, The product of their ages is 72 .

so,

→ a * b * c = 72

also,

→ (a + b + c) < 20 . { As there are 20 houses in this society.}

now, oldest cat is called Gypsy and sum of letters and her age is related as perfect square .

so,

→ (G + Y + P + S + Y) + c = perfect square

→ (7 + 25 + 16 + 19 + 25) + c = perfect square

→ 92 + c = perfect square.

possible value of c :-

• 92 + 8 = 100 = 10² .
• 92 + 29 = 121 = 11² => But c cant be more than 20.
• so, only possible value of c must be 8 .

then,

→ a * b * 8 = 72

→ a * b = 9

Possible values :-

• a = 1 , b = 9 => if b = 9 , c cant be oldest cat.
• a = 3 , b = 3

therefore, we can conclude that,

• a = 3
• b = 3
• c = 8

hence,

→ Sum of their ages = 3 + 3 + 8 = 14 (Ans.) (b)

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