Question 1148996
Suppose the average of 999 numbers is also 999. Suppose further that from these numbers you chose 729 of them and their computed average is coincidentally also 729.  What would be the average of the remaining numbers?
<pre>If average of 999 numbers is 999, then sum of those 999 numbers = 999(999), or <b>999<sup>2</sup></b>
If average of 729 numbers is 729, then sum of those 729 numbers = 729(729), or <b>729<sup>2</sup></b>
Therefore, sum of the other 270 (999  -  729) numbers is: <b>999<sup>2</sup> - 729<sup>2</sup></b>
Further, the average of these 270 remaining numbers would be: {{{highlight_green(matrix(1,10, (999^2  -  729^2)/270, or, ((999  -  729)(999 + 729))/270, "=", ((cross(270))(999 + 729))/cross(270), "=", highlight(matrix(1,3, 999, "+", "729")), ",", or, "1,728"))}}}
Although somewhat irrelevant, the answer can also be expressed as: {{{highlight(highlight_green(highlight(matrix(1,7, 2^6(3^3) , or, (2^2)^3(3^3), or, (2^2 * 3)^3, or, 12^3))))}}}
<b><u>What to learn from this:</b></u> The average of a LIST of 999 numbers is 999. Of these 999 numbers, 729 have an average of 729, and the remaining 270 
                         have an average of 999 + 729. Quite UNUSUAL, isn't it?