A teacher writes 6 consecutive integers on the blackboard. He erases one of the integers and the sum of the remaining five integers is 2016. What integer was erased?

Guest Dec 28, 2020

#1**+2 **

Let the first digit be x and the last x + 5

Let a be the sum of the constants of the five remaining integers

And we have that

5x + a = 2016

5x = 2106 - a

Notice that 2106 - a must be divisible by 5

So if a = 11 we have x + (x + 1) + ( x + 2) + (x +3)+ (x + 5) = 5x + 11 = 2016

Note that x + 4 was erased...so....

5x = 2016 -11

5x = 2005

x = 401

So

x + 4 = 401 + 4 = 405 was erased

CPhill Dec 28, 2020