Question 1093117
<br>There is no solution to the problem.<br>
Since we are talking about the average of 5 consecutive odd numbers, let's choose x to be the middle number, since it is the average.  Then the numbers are x-4, x-2, x, x+2, and x+4.  The problem says the average is 6 less than the sum of the largest two.  That gives us
{{{x = (x+2)+(x+4)-6}}}
{{{x = 2x+6-6}}}
{{{x = 2x}}}
which gives us the answer x=0, making the 5 numbers -4, -2, 0, 2, and 4.<br>
But the problem requires the five numbers to be consecutive odd integers -- so there is no solution.