SOLUTION: A list of consecutive integers starting with 1 is written on the blackboard. One of the numbers is erased. If the average of the remaining numbers in 35 6/17, then the number erase

The average of a list of any number of consecutive integers
is the average of the first and last numbers

The first number is 1.  Let the last number be n

Then the average would be 

The average must be somewhere not too far from 35 6/17.

If the average were 36 then we would have:

 = 36

1+n = 72
  n = 71

Since the average is 36 6/17 then that denominator
of 17 tells us that 1 less than the number of terms must 
have been a multiple of 17.  The nearest multiple of 17 to 
71 is 68.  So that means the number of terms is one more 
than that or 69.

The formula for the first n counting integers is 

So the sum of the first 69 counting numbers is   = 2415

Let k be the number erased, then the average of the remaining
68 terms is

 = 

 =   

Multiplying both sides by 68

2415 - k = 2404
      -k = -11
       k = 11

So the term that was erased was 11.

Edwin