Thursday, November 5, 2009

Math Problem solved using ScoT

I got a query from a in this problem. I solved using Science of Thinking(ScoT) approach.Observe the problem solving process.

The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n ?

These type of sums can be solved using my thinking skills – “pattern recognition” and “hypothesis testing”

Take sum of even numbers when n =5( N has to be an odd number)
Sum = 2+4 = 6 i.e 2 *3( Same pattern as 79*80 i.e n*(n-1))
Now take sum of even numbers when n = 7
Sum = 2+4+6 = 12 i.e 3*4

So you get a pattern 2*3, 3*4…………………….79*80
When n = 5,7……n
Do you observe that 2+3 =5 and 4+3 =7.

So our hypothesis is that n should be sum of the product of the numbers(in the form n*(n-1) which yields the sum of the even numbers.
Now lets check our hypothesis
When n =9
Sum = 2+4+6+8 = 20 = 4*5
4+5 is equal to n
Hence n can be concluded as 79+80=159

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