Guest Posted March 31, 2008 Report Share Posted March 31, 2008 In one room there are certain cats and rats. Count of rats is 999919. Cats started eating the rats. Each cat had the same number of rats as the other cats. Also the count of cats is more than the number of rats they had Now the question is how many cats are there in the room and how many rats each cat had? PS: Mind you there is more than 1 cat and each cat had more than 1 rat. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 31, 2008 Report Share Posted March 31, 2008 In one room there are certain cats and rats. Count of rats is 999919. Cats started eating the rats. Each cat had the same number of rats as the other cats. Also the count of cats is more than the number of rats they had Now the question is how many cats are there in the room and how many rats each cat had? PS: Mind you there is more than 1 cat and each cat had more than 1 rat. the factors of 999919 are {1, 991, 1009, 999919}. As each cat has more than 1 rat and the number of cats is more than the number of rats: 991 rats and 1009 cats. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 31, 2008 Report Share Posted March 31, 2008 the factors of 999919 are {1, 991, 1009, 999919}. As each cat has more than 1 rat and the number of cats is more than the number of rats: 991 rats and 1009 cats. bingo brahn I would like to know your approach on this. how you factored this number Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 31, 2008 Report Share Posted March 31, 2008 bingo brahn I would like to know your approach on this. how you factored this number Some time ago I had a post with a title Lyran III inhabitants ... and with those prime numbers on hand, it is not difficult to do the factorization stuff in excel. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 31, 2008 Report Share Posted March 31, 2008 Some time ago I had a post with a title Lyran III inhabitants ... and with those prime numbers on hand, it is not difficult to do the factorization stuff in excel. See this solution instead of finding the factors Let there be x cats Let there be y rats each cat had so by question we have x*y=999919 Instead of finding factors for 999919 which are primes, x*y=(1000000 - 81) you must have read the formula a^2-b^2=(a+b)(a-b) x*y=(1000^2)-(9^2) x*y=(1000+9)(1000-9) x*y=1009*991 Hope this is clear. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 31, 2008 Report Share Posted March 31, 2008 See this solution instead of finding the factors Let there be x cats Let there be y rats each cat had so by question we have x*y=999919 Instead of finding factors for 999919 which are primes, x*y=(1000000 - 81) you must have read the formula a^2-b^2=(a+b)(a-b) x*y=(1000^2)-(9^2) x*y=(1000+9)(1000-9) x*y=1009*991 Hope this is clear. Waw, that is a very elegant way. Good one, and thanx for sharing. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 1, 2008 Report Share Posted April 1, 2008 1009 cats and with 991 rats each cat has. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 1, 2008 Report Share Posted April 1, 2008 See this solution instead of finding the factors Let there be x cats Let there be y rats each cat had so by question we have x*y=999919 Instead of finding factors for 999919 which are primes, x*y=(1000000 - 81) you must have read the formula a^2-b^2=(a+b)(a-b) x*y=(1000^2)-(9^2) x*y=(1000+9)(1000-9) x*y=1009*991 Hope this is clear. Wow! What a simple and smart way. Thanks for sharing. Quote Link to comment Share on other sites More sharing options...
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In one room there are certain cats and rats.
Count of rats is 999919.
Cats started eating the rats.
Each cat had the same number of rats as the other cats.
Also the count of cats is more than the number of rats they had
Now the question is how many cats are there in the room and how many rats each cat had?
PS: Mind you there is more than 1 cat and each cat had more than 1 rat.
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