shivaraj iyer wrote:7 bowlers in Indian cricket team from a list of 16 playes. Statisticians discovered that if you looked at the number of wickets taken by any one of the 7 bowlers of the current team, they had a strange property. The numbers were such that for any team selection of 11 players ( having 1 to 7 bowlers) by using the number of wickets taken by each bowler and attaching coefficients of 1, 0, -1 to each value available and adding the resultant values, any number from 1 to 1093 both included would be formed. If we denote W1, W2, ....W7 as the 7 values in the ascending order what could be the answer to the following questions.



find the value of W1 + 2W2 + 3W3 + 4W4 + 5W5 + 6W6

find the index of the largest power of 3 contained in the product of W1W2W3W4W5W6W7

if the sum of seven coefficients is 0, find the smallest number that can be obtained.