## number of ways in making 100

Please help in finding In how many ways one-hundred can be written as sum of natural numbers? Is there any general method which we can use to answer such questions? Like the question can be asked with many different numbers In how many ways two-hundred can be written as sum of natural numbers? In how many ways three-hundred can be written as sum of natural numbers? I want to know if there is any general method to solve such kind of questions ?

## One IDEA

Is there any general method which we can use to answer such questions?
The only method that is coming to my mind rgt now, first i am simplifying the question a bit In how many ways ten can be written as sum of natural numbers? Its not specified sum of how many natural numbers it can be two numbers, three numbers, etc (and one more assumption - repetition is not allowed) 1. Two numbers : 1 + 9 ; 2 + 8 . . . . .5 + 5 , Number of ways = 5 2. Three numbers : 1 + 2 + 7 ; 1 + 3 + 6 ; 1 + 4 + 5 2 + 3 + 5 Number of ways = 4 3. Four numbers : 1 + 2 + 3 + 4 Number of ways = 1 Total number of ways= 10 With this counting method we can find small numbers but for 100 there must be some other way out

## question : sum of different

question : sum of different natural numbers?

## one idea

first write 100 as 50 + 50 , then write possibilities for 50,likewise go down the tree ,i think -follow merge sort technique.ultimately u come to number 1.then stop splitting and go up the tree.if u people find any best method or any other interesting puzzle or cat material please post that to hello_siddu@yahoo.co.in