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At a particular time in the twenty first century there were seven bowlers in the Indian cricket team's list of 16 players short listed to play the next world cup. Statisticians discovered that that if you looked at the number of wickets taken by any of the 7 bowlers of the current Indian cricket team, the number of wickets taken by them 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, or -1 to each value available and adding the resultant values, any number from 1 to 1093 , both included could be formed. If we denote W1, W2, W3, W4, W5, W6 and W7 as the 7 values in the ascending order what could be the answer to the following questions :. Q1 Find the value of W1 + 2W2 + 3W3 + 4W4 + 5W5 + 6W6. Q2 : Find the index of the largest power of 3 contained in the product W1W2W3W4W5W6W7 . Q3 : If the sum of the seven coefficients is 0, find the smallest number that can be obtained.

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Hi,

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4
700

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