There are 73 terms adding up to 546, so the average of the terms is 7+35/73.
That is, if each term were 7, the total would be 511. We need 35 more, so 35 of the terms should be pushed above 7: those with the highest 35 fractions, starting at 57/100.
For 7 + f + 57/100 to be 8 or above requires that f be at least 43/100.
For 7 + f + 56/100 to be less than 8 requires that f be less than 44/100.
7 + 43/100 <= M < 7 + 44/100.
floor(100*M) = 743.

Posted by Charlie
on 20141202 14:02:29 