Four consecutive even positive integers are removed from a set containing precisely N consecutive positive integers starting with 1, such that the arithmetic mean of the remaining numbers is equal to 825/16.

Determine the four integers that were removed from the set.

Remove 22, 24, 26, 28 from sequence 1 .. 100 

Full set has sum (100 * 101 / 2 )  or 5050,  / 100 mean 50.50

Cut gives 4*25 or 100 sum 4950, / 96 mean 51.5625 = 825/16

Just two loops, with simplification that removing four consecutive even numbers, removes 4 * their midpoint, and subtracts 4 from the denominator -- goal to find the ratio requested.  

Posted by ed bottemiller on 2009-08-05 12:57:52