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?
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 :-
so, only possible value of c must be 8 .
then,
→ a * b * 8 = 72
→ a * b = 9
Possible values :-
therefore, we can conclude that,
hence,
→ Sum of their ages = 3 + 3 + 8 = 14 (Ans.) (b)
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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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