# THE GAME OF CATS AND MICE

A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice.

How many cats do you think there were?

Ob, by the way let me clarify just two points—it is not one cat killed the lot, because I have said ‘Cats’ and it is not-999919 cats each killed one mouse, because I have used the word ‘mice’.

I can give you just one clue—each cat killed more mice than there were cats.

**There were 991 cats, and each of them killed 1009 mice.**

To check, 991*1009 = 999919

Solution:

**Get the prime factorization of 999919
The prime factors are 991 and 1009 only**

Using fermat’s method find the Prime factor.

Now Let n = 999919 and square root is appx 1000

so i = 1000 , we find that sqrt(999^-999919)

= sqrt(81) = 9

Then 1000 – 9= 991 and 1000+ 9 = 1009

By multificaton we verify that 991*1009 = 999919

As Each cat killed more mice than the numebr of cats

Hence there were 991 cats and each cat killed 1009 mice.

### Your Answer

## More puzzles to try-

### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »### What is the age of grand father puzzle

A boy asks his father, “what is the age of grand father?“. Father replied “He is x years old in ...Read More »### Maths Genious Riddle

If u r genius solve it:- 40 * 14 = 11 30 * 13 = 12 20 * 12 = ...Read More »