Let the 9 numbers from smallest to largest be
represented by the letters from "a" through "i", where
a < b < c < d < e < f < g < h < i
They have a mean of 9, so
a + b + c + d + e + f + g + h + i
————————————————————————————————— = 9
9
or, multiplying both sides by 9
a + b + c + d + e + f + g + h + i = 81
The object is to make "i" as large as possible.
"i" will be largest when "a" through "h" are smallest
Since the median is 9, e=9, and we have:
a < b < c < d < 9 < f < g < h < i
To choose "a" through "h" as small as possible, we have
a=1, b=2, c=3, d=4, e=9, f=10, g=11, h=12
Then
a + b + c + d + e + f + g + h + i = 81
becomes
1 + 2 + 3 + 4 + 9 + 10 + 11 + 12 + i = 81
Solving for i:
52 + i = 81
i = 29
That's the answer, 29.
This is the case when the 9 numbers are
a=1, b=2, c=3, d=4, e=9, f=10, g=11, h=12, i=29
Edwin
