7 numbers in ascending order W1, W2, W3, W4, W5, W6, W7. They can be multiplied with coefficients 1 , 0 or -1 and added to generate any number between 1 to 1093. determine the value of W1+2W2+3W3+4W4+5W5+6W6?

Hi Shivendra,

Consider another example: What numbers are required to obtain any number from 1 to 16 using the operators 0 and 1. The required numbers in this case are $$2^0, 2^1, 2^2 and 2^3$$. Since the operators are two in number - binary - we have to consider the powers of 2.

Now consider your question. Since there are three operators in the case, we have to consider the powers of 3.
If the numbers are 1, 3, 9, 27, 81, 243 and 729, then all the numbers in the range 1 - 1093 can be obtained by using the operations 1, 0 and -1 on these numbers.
So, the value of the expression is 1 + 2*3 + 3*9 + 4*27 + 5*81 + 6*243 = 2005